American Journal of Computational Linguistics Microfiche 74 
TWO PAPERS 
0 N 
SEllANTIC INTERPFETATION 
I N 
ROMTASUE GFbAMNAR 
Joyce Friedman 
Douglas B. Mpran 
David S. Warren 
nepartment of Computer and Communication Sciences 
The University of Michigan 
Ann Arbor, Michigan 48109 
Copyright @ 1978 
Association for Computational Linguistics 
CONTENTS 
EXPLICIT FINITE INTENSIONAL MODELS FOR PTQ 
...................... Abstract 3 
.................. I . Introduction 4 
.............. . I1 IntensionalModels 5 
.............. 111 . Specifying a Model 6 
............... IV . Reasonable ~odqs 10 
V . Using a .Model ........... 14 
. *....... VI . The Plolre Complex Case of Adverbs 18 
................ . VII SizeofaYodel 19 
. .................... VIII ~onclusions 21 References ................... 22 
AN INTERPRETATION SYSTEM FQR MONTAGUE GRAMMAR 
Abstract ...................... 23 
I . Introduction .... ............. 24 
11 . IntensionalLobic ............... 28 
III . Implementation of Named-Models ........ 37 
IV . Interpretation in a Model .. : ......... 48 
................ V . Using the System 54 References ................... 70 
Appendix A ..................... 71 
...................... Appendix B 53 
AppendixC ..................... 91 
N- 3 
Cpmputer Studie6 in 
Forn~al Linguistics 
Department of Computer and 
Comnunication Sciences 
THE UNIVERSITY OF MICHIGAN 
Ann Arbor, Michigan 48109 
Nbvember 1977 
Revised March 1978 
EXPLICIT FINITE INTENSTOl*JAL MODELS FOR PTQ 
Joyce Friedman, Douglas B. Moran afid D'avid S. Warren 
ABSTRACT 
The semantics of Moritague's The proper treatment of quan- 
tification in ordinary English (PTQ) uses an intensional model 
to evaluate formulas. In this primarily tutorial paper we show 
how a model can be explicitly constructed and used. Examples of 
the evaluation of formulas are worked through carefully. 
Partiqular attention is paid to the role of the meaning. 
postulates of PTQ in restricting the choice of models. 
An abbreviatory notation, giving names to complex elements, 
is used to sivplify khe process of constructing a model. At 
each level, complex elements are formed from simpler elements 
alfeady named. 
Tht; size of a finite model £01 PTQ based on two points of 
reference and two entities is calculated and its implications 
discussed. 
This research ik supported in part by National Science Foundation 
Grants BNS 76-23940 ahd MCS 76-0497 
I. INTRODUCTION 
In Thc plaopt;.r trt:ut~/i~:nl of ~llii~?~t i f icn t ir))t ii: or&i?~tz~vj 
dngrish (PTQ) , Richard Montague sets up a system which uses 
model-theoretic semantics to provide meanings for English 
sentences. Expressions of intensional logic hold a position 
intermediate between the English syntax and the model. 
For each 
syntactic structure of dn English phrase there is a corresponding 
formula of intknsional logic. The meaning of the English phra-se 
is taken to b.e the interpretation of the logical formula in the 
model. 
In this paper, which is primarily tutdrial, we show by 
example how a moikel can be explicitly constructed and how a 
logical formula is interpreted in a model. Our paper provides 
concrete examples of the semantic model and the definPtion of 
interpretation, given only formally by Monthgue. It is intended 
to be helpful to readers of PTQ. The reader of. this paper may 
need to have a copy of PTQ hn hand. 
We first review the definition. of intensional model, and 
begin ta specify a model. Then we examine the way in which 
meaning postulates constrain the model to be reasonable. In a 
reasonable model the interpretations of Enqlish words are 
consistent with their usual meanings. We select a pafticular 
reasonable model and use it to evaluate some formulas. Problems 
in building a larger explicit model are illustrated by 
considering the case of adverbs.. 
We conclude with calculations 
of the size of a model and a brief discussion of 
the possible 
use of computer+ for Montague grammar. 
11. INTENSIONAL MODELS 
An intensional mvdeL (or interprclation) a is a quintuple 
@ = (A, 1, J, 2, F) such that 
1) A, I, ,and J are non-empty sets, the set ofi entities, the set 
of possible worlds, and the set of moments in time, respectively. 
2) - < is a simple (linear) ordering on J. 
3) 
F is the meaning function, which assigns each logical 
constant an appropriate element from the model. If the 
constant is oE type a, the value of F ia of type <s,a). 
Each element of I x J, the qet of co-ordinates, is a single 
point of rcj'erencc or indax. 
To siwplify the notation, we use 
S for this cross-product. A model then becomes a quadruple 
a = ( A, S, - , F). E.6r a given A and S the- set of possible 
denotations of type a, D is given by: 
a,A, 5' 
- for simple types 
- for complex types 
(the set of entities) 
(0 - falsehood, 1 - truth) 
(the set of total functions 
from S to D 1 
(the set of total functions 
Wherk no confusion can arise, the subscripts il and S are omitted 
/n symbols for sets of possible denotations. 
The rules for evaluatkng an expression Of the logic are 
given in PTQ. An evaluation is performed with respect to a model 
4, a point of reference i in S, and a variable assignment 9. 
This function y 
assigns a denotation of the appropriate type to 
each variable in the expression, that is, for any variable u of 
type a '7 (u) E Da. 
The result ofi evaluating an expression a of 
type a is a possible denotation of type a, i.e,,a member of D 
cz 
This value is denoted by a 
d, i ,'t? 
and is called the denotation or 
extension of a with respect to , i, and g. 
111. SPECIFYING A MODEL 
The first step is to give the set A of entities and the set 
S of points of reference. These two sets uniquely determine for 
each type a each set Da of possible denotations of expressions 
of type a. To complete the model, the meaning function F must 
be specified. The values of F f~r constants of tgpe a are 
functi~ons from S to Dh. 
We mow begin to build the intensional model to be used in 
our examples. Because we wish to write out the sets D 
c7: 
explicitly, we construct a finite model. 
While it would be 
po-ible td write functions explicitly in ordered pair notation, 
the 
result would be long and cumbersome, because in general the 
elements of the pairs are themselves functions. We overcome 
this difficulty by ihtroducing names for functions and by taklng 
advantage of the type system of the model. 
We use the type 
system to provide an order in which to consider the denotation 
sets and their elements. The ordering is such that at each Stage 
the new functions can be specified as ordered pairs of names 
already intxduced. The meaning function F is also specifled 
using these function names. 
Let the set of points of reference S be 1, 121 and the 
set of entities, A or D , be {Jo, ~n}. 
C 
It is important to distinguish words in the English 
vocabulary from conlstants in the logic front elements of the 
1node1; for exfirnple, John and walk are English words, j and wtrZk' 
are logical constants, and Jo is gn entity, ana'element of De. 
English w~rds are given in italics. Logical constants that are 
direct translations of English words are ?rimed. 
The function F, which defines the relafionship between 
constants and elements of the mod&l, assigns to each congtant 
of type e a function from indices to entities. For example, for 
the ldgical constant j, F(j) E D = D 
$' 
where %s, &) e" In our 
0, e> 
finite model, there are only four m~mbers of D. and we use 
<s;e>,' 
do ,al ,a2 ,a3 as their names. They are defined by: 
If E't,i)+ =. ,u2, then ,i is* assigned { (7 1 L1r1) 
(12 JO) 1 , that is, the 
functipn whose value at index I1 is Llh and whose value at index 
72 is Yo. 
Words in both of the syntactic categories CIV.and IV 
translate inko logical constants of type C+..u",c>., t), so the 
values of for these constants are functions from inaces to 
elements of type (<b,e?,t). For example-, 
f (;cntcolvi!)* and F(r~:rZk') E 8 
<6, (4~,C),t>> 
IT 
L' IS, 62")' 
where 0 D~ = (D - 
&, <<s, ~>,~t?> (XS, E), t> t 1 
.. 
and 
PYu'nicoriz,') (i I and F (r~alk ') (i) E D &s, e):t> 
In the model, there are 16 meinbers of 9 and we use 
,e>, t> 
BOt - *,rB15 a$ their names; they are defined by: 
There are 16L = 256 members of D 
0, <cbe>, t>) 
and they wlll not 
be enumerated here. 
The set of- entities, A = D , is also known as the set of 
e 
individuals. The members of the set D. of possible 
.Cs, a) 
denotations of, type <a, a) are called individual concepts. 
The members of D are functions from 
(<t?, L?> , t > 
<s3 t\ > to 
{ 0 ,I], and thus a member df ? 
can be viewed as a st7?! J.( 
<<i> t3> J t> 
i l t for uhich the function is 1 (true) . A; 
clement of il is a !~PG~~,+ 13 t :i - , : / L?,. p;,. t, .?- f::. 
< t:> <&: L>> J t >> 
IV, REASONABLE MODELS 
Not a11 models that can be constructed are reasonable. 
Montague's meaning postulates are restricticns on models; they 
limit the choices for the values of the meaning function P, that 
is, they constrain the possible meaning of certain English words. 
Meanins Postulate 1 
We 'now examine how Meaning Postulate 1 affects the choice 
of values of ' for constants of type e. As an example, we 
consider F (,/). Meaning Postulate 1 fbr ,i is (314 U (I,) The 
denotation of this meaning postulate is [ (314) 0 (zc~J) ] n,i,g . 
This denotation must be 1 if the model is to be reasonable. 
Following the recursive defiflitio,~ in PTQ [pa 2581: 
[ (320 n (~ikj) 1 is 1 iff there exists v E D 
e 
(D = {Jo,Unl) such that [t3(u=j)] 
m,i,g 
e 
is , where ' 
is a @assignment like 9 except that () is .u. 
I O7,it,,7 I 
[ u (a=j)~ . is 1 if? (u=j) 
is, 1, for all i E S. 
Dz,itFg # 1 
is 1 iff 1.1 
.@,i ',a 
(~1= j) - I is 
@, i ',c 1 
~1 ' is gl(:c) , which fkoii~ above is v, and J 
is 
I.@., there exists v E 1) l: such that for all if E S, 
(i l) is 
%" 
V. In other words, Meaning Postulate 1 requires that the value 
of E' for the argument ,i be a constant funCtion, i .e., a function 
that has tk salne value at all points of. reference. 
Tl~us /+' (J) 
cannot be just any member of. 11 
< 3 y i' > 
; it must be cither 
MGaning Postulate 2 
For Meaning Postulate 2 similar analysis applies. This 
meaning postulate restricts the choice of values of ' for'the 
constants of type (Zs, e>, t > which are translations of 
extensional comqon nouns. For example, Meaning Postulate 2 for 
!cnicorn ' is I3 [iciiicor~i ' (x) -> (310 .c = 1 ] . A reasonable model 
must make it true. Again, following the recursive definition: 
( a [LO (x - (314) r 5 ^u] ) 07,L:7 is 1 iff 
. 
[of () + (310 .c =' O1 ,i l,:~ is 1 for 
L1 F, A?. (7 
[unic~~rn' (x) + (3u) .c = :uJ 
P,i1 
J' is 1 iff whenever 
[unico~vz ' (x) ] 
U'L5 i ' 9 
is ' 1, then [ (3u) r = "u] m3i',9 is I. 
r 
[unicor~z ' (3) ] J is [unicornr] 02 J i J:/ 
mJi ',:I 
[i~nicorn '1 U'zairJg is F (unico~~?~ I ) (i ) and 
x , IJ(7 is :7 (x). 
[unicorn ' (x) ] J is [~(unicoriz') (i I)] -(g (x)). 
[ (3u) x = ^u] 
ab,il 
'O,is 1 iff there exists a v E D 
such 
e 
[x = Au] 
is 1 where 9' is a d -assignmen< like 
g .except that 9 ' (10 is v . 
[X = "II] aJi'Jar is 1 iff ,-J ' is (\) 
t 
,C ' is ) and from above, I) is ;Ir) and 
01,i ',g 
I 
(^ ) is the function h such that for all it' c S, 
For all I ' E St whenever (r) (I)] ( () is 1, then 
there exists v L such that 3 (s) is X*iV(v) . 
t 
The consequent of the result says that %he individual 
concept that is the value of 
(2) must be a constant function, 
i.e.,it must evaluate to the same entity u at every point of 
referbnce. In our model, only do and a3 are constant individual 
concepts. 
Meaning Postulate 2 restricts the possible denotations for 
these logical coristants of type , , t to subsets of 'the 
individual concepts that are constant functions. In any 
reasonable model, ,we must choose F so tha* 
that is, ;tnicorrthobd can be true only ~~~ase  individual^ 
concepLs which yield the same entity at evdry point of 
reference, 
L 
We use A* as the h-operator of the metalanguage. 
Thus, hxi"(v) 
denotes the function from S to D 
with the conjtant value V. 
2 
Meaninq PostuLate 3 
Meaning Postulate 3 restricts the choice of values of P for 
the constants that are translations of extensional intransitive 
verbs. Meaning Postulate 3 for l~tr ik ' 'ip 
(3M) (Vr ) Cl [ua l ir ' (x ) ["iV] (*c) ] 
where M and .c are variables of type s c t and <s, n), 
respectively. , A reasonable model must make this meaning 
postulate true. 
[ (x [walk (2) ["All (%) ] ] m~i'g is 1 iff there exists an 
mc~ such that [ (VX) [walk1 (XI t, [V~l] 'ivr) I I Q4%,L41 
4% (e, t?> 
is 1 where g' is a @-assignment 1ike.g except thht '(b) is m. 
[ (Vx) u [waZkl.(x) t-, ["MI ("rc)I I 
d ,i,gr 
is 1 iff for all x E D 
ds, $7 
[wcr~k'(x) t, ["MI ("r)] ] 
m Ji3(]'' 
is 1 where gfl is a 
a-assignment like g ' except that 9." (x) is x. 
m ,i,g 11 , 
[a [wiz2k'(c) e ['MI (vr)]] 
1s 1 iff 
Y 
[I ' (x) ['MI ("x)] 0Z3i'3g" is 1 iff [walkr (s)] 
O1 ,i rJglt 
Q,i'Ji?"[,)az>il~, 11 
I~aZic' (x) 1 oLi',g" is [walk,j 
which is [E(waikl) (it)] (gl'(x)) 
which is [F(walkf) (if)] (x); 
which is [M , ir UL '~9.~~ (-,i 1 )$) 
which is [gU(M) (i I)] (g" fx) (i ') ) 
which is [p71([t)] (\(!'I). 
Thus the meaning pos4tulate is. true just in case there csists 
1 
vil E L such that for a11 \ i,? (c:,t3, , (: (i ')I (i) 
{SJ kt*, 0) I 
is [(I ((I' for all : Z :: Thus, dcpen~is only on 
the cntity and thc point of reference. If : *+ t is true at a 
" t 
point. of reference for an individual concept, then' *A:: i is true 
at that point sf reference for every individual concept that 
gives the same entity at that point of reference. 
Relating this to our model, we see that since 
aO(T1) = it1 (11) and LuZ(lI) = nj(ll), 
a (12) = a2 [I?) and 
0 
(I:) = i13 (12) 
Meanipg Postulate 3 requires: 
Thus, tre must choose F so that 
V, USING a MODEL 
We now explicitly construct a particular reasonable model in 
which tc evalqate some formulas. 
It must satisfy the constraints on F developed above. 
We 
assign to,the constant j the entity Jo at all points of reference: 
F (if = eo = 
(11 JO) (12 SO)}. 
We s.tipul'ate that there are no unicorns at point 0% reference 75 
and one unicorn, entity Un, at point of reference 12: 
P (u~~ie~rn') = { (1 l a,) (12 8,)) 
= { (11 { (aO 0) (al 0) (a2 0) (a3 0))) 
At pgint of reference 7 entities Jo and Un walk and at point of 
reference 12, only 30 walks: 
Our first etraLuation u'sing this model w141 be for the 
expression which is ,the translation of John: 
Finding the.. denotation of. this expression: 
'AP ["PI (rd I '~'~'9 is A function h 
j* 
such that h (p) is 
I 
j* 
[ ["PI (^j) la' 
where g ' is a -assignment like g 
exoept that is p+ 
whikh is [P 0Z3i9g' (i)] (h+iI[j 
which is [gl(P) (it)] (X*il[F(j) (i')]) 
which is [p (i)] (F(j)). 
Thus, the expression denotes the function ii .* = X*p [ [p (i) ] (F (j) ) ] 
J 
So hj, is the set of properties which, when evaluated at point of 
reference i, are true of the individual .concept that is the value 
of F for j. 
In this example of a reasonable model, P (,j) is no 
and the possible denotations, p (i) , for which ro gets true are B8 
through fils. 
At point of reference TI, the value of the function 
which is the denotation of the expression that translates John is 
1 for the arguments 
{(TI )(I2 f3 )} wherem > 8 
m n 
- 
and at point of reference 12, it is 1 for the arguments 
{ (11 f3 ) (12 f3 )I where n > 8. 
m n 
7 
Now, we evaluate the direct tralslation of the sentence 
At point of reference 11, the denotation of this expression is: 
up [ Vpl I 
&,lLg ("walk ' ) f1311,i7 
[XP[~PI (Aj)] ~~''~g,~(uc~k~) 
The model can be also used LG illastrate the general fact 
that the d'enotations of an expression and any of its reductions 
are the same. We have shown elsewhere [Friedman, 19781 that 
each expression of the logic has a unique reduced form in which 
no further contractioh is possible. We now evaluate the reduced 
form of the trahsldtion of John walks, [walk '.("j) ] . 
At point of r.eference t! : 
As another example, consider the logical expression 
[AP ["PI 
j) ] ("unicorn I). 
Evaluating in world I1 
['PI (^j 1 " 1 ' (F (unicorn ' ) ) 
The reduced form of the expression is unicornr(^j). 
Evaluating in world IT 
[unicorn ' (" j) ] mI7,g 
[I (a, 0) (al 0) (a2 0) (9 0131 (ao) 
Vim THE MORE COMPLEX CASE OF ADVERBS - 
We now consider extending our model to accommodate sentences 
with adverbs Such* as s 1~1dZy. "We have that 
F(szor~Lg ') E D + - 
0, (Ls, 3 t , t , as, C?, t>?> 
There are not only too many possible denot'aations to consider 
enumerating them, but in each possible denotation, there are.too 
many components to consider fully specifying it (see below) . 
Consequently, in this example, only that portion of F (s Zoz~Zy ' ) 
which is needed will be specified. 
The denotation for the sentence Joh?~ w~zzks slot~Zt~ is: 
[~F(sZOZ~ZZJ') (i)] (P(~~zlii'))] (F(j)) 
At point of reference 11, Jo and UII are both walking, and 
choosiqg that JO is walking slowly: 
and 
VIT. SIZE OF A MODEL 
The smallest interesting model for PTQ has two points of 
reference and two entities. For such a model, the size of the 
sets of possible denotrjtions and the size of their elements (in 
ordered pair representetion) are as given in the following table. 
Nw~ber of 
Ordered Pairs 
in Possible 
Denotation 
Number of 
Podsible 
.Set of possible Denotations Denotations 
These size computatiops have relevance to a possible 
computer implementation. For a typicai large-scale computer, 
the number of addressable memory locations is on the order of 
224 (about 16 million), yet 9 of the 16 sets of possible 
denotations have more inembers than this. This means that a full 
model cannot be explicitly represented in a computes. However) 
in evaluating expressions only some of the possible denotations 
are actually used. I~nplernentation on a cpmputes might allow a 
partial specification of a model, with only those possible 
denotations that are actually denoted by the expressiohs 
considered. In this context it is also interesting to note that 
the number of neurons in thelhuman brain is currently estipated 
to be about 2" (10 billion). 
- - - 
We have explicitly constructed an intensional model to 
illustrate the basic notions of the model-theoretic semantics of 
PTQ. We showed how the meaning postulates constrain the model to 
be reasonable and evaluated some simple formulas. 
The number of 
possible denotations in a small model was shown to present a 
problem to be solved if explicit representations of models are to 
be used. This problem is discussed further in Friedman, Moran, 
an& Warren 119781. 

nepart rnent of Gomp uter and 
7 Cammqnicat ion Sciences 
PWE IINIJJERSITY' OF MICHIGAN 
Ann Arhor, Michigan 48169 
.r\V IF'T~rT'3'~(r,4Tib1Li SY*CTEI*. FO:? VflNTh7rJl$ 2 RAMM Ail 
Joycg~ 7.ri) PRII, i):?~ 1113~ -tits Noran# irld Davi1 '7. Warren 
. ' r* 
V,!C ;t-+):~~or(7~.ic .~~.man+:ic iS OR~ important 
?~roich, + 3 r1ca.l ing in n?tb1ral-lanquage. In thzs 
~uprxi $2, l~;ric.~: 1 ~-)btainnd f ~grn En glis h 
senC,-.nr;~3~'~ r ~~v?iLr~n+:cd in an intensiona'l moiel to 
lot arninn t'~~\i:: truth value.-,. In this paper we 
j,y7y:r- 11 ,- 3 n i~t eracfiv~ f~ornpu tcr systen for 
specic yi:;; Eini tt? int siqn31 mudel an 3 
nvirbixt in J 177ic.11 f crrn 1~s. We first qive an 
.>v~rvii?w of ".P svsttxn an13 its intended uses. we 
?%en 7rwii.r- s Ietailcd description of the system 
k.3 o'lw what is w?ail~d in -1ctu3lly carrying ont 
t5Fq 3pprr3~h. ?xD{?nsive exam~l?s 3rt7 given in the 
43 P "R C! ic~s . 
. - 
qcran. is rnsponsihle FOC th~ de~ign and coding of the program. 
This rcsedrch is sunnorte I in part by N3tiona1 Science roundation 
P 
3rar!t3 ?YS 75-23,W3 and YCS 76-24297. 
Zodel- th~aar~t ic seniant ics is on~ irn~a~tant approach to 
analyzillq the rnoar:i~;q of zxpressio~~s uf 11dtura1- Ianguaqe. 
Irarski% .vdLuati~n ~t.th0.1 tor f crrnula~ af ma ttlematieal logic can 
be ~xt,eridr\i to ilatur'aJ-1nnjuaqt. i.ittl~.r direcrly or by an 
intcr!nrLiinta staur of 1~1ti1, into a mhthtmaticaL logic. 
This formnl trrlt h*cot;Ji tional tr~d tmant proqides a precise neans 
of assiq ninu a?anltitqs to n3tura1-Ianquage sentences. I model- 
thcoretic semantics, the rnctani~q of a Ecrnula is defined by a 
recursive process of evaluat ic~ ir. a model. 
;he formal system presente:I by Fichafd M.ontagile in --I The 
~rgy'z tr~ntgnwnt ,f quar.t.ificatiqc ..------I---- z&&arv fnqlish (PTQ) 
applies mo3~1- tb-eorat ic sewant ics to Fnqlish and forms the basis 
of the work described in tbis paper, In IT2 tht meaning of an 
Snglish phrase is obtained by intar ~rt;tj,o.'~ a correspondinq 
1agica1 forinuld in appropriate mcidel. FTQ uses a tensed 
intensional loqic: the fragment of Lnylish emphasizes quantifiers 
and intensioca--1 constructsa 
PTQ raisss a cumber of Interesting questions if one actuallv 
attenpts to use tht? i3~as in a computer systemr For example, 
there dr2 va~icus ways ir, which a model might be represented, 
There are also r,r-oblems in Eirdinq algorithms for the yrocesses 
suggested bv Pya. We have Fade sn.3cifi.c choicestin our solutiOns 
to these questians acd *re pursui'ng them to find their limits, 
E ' 
Q, 
+, 
ul 
h 
V) 
a, 
s 
P 
a 
Q, 
I-i 
qr4 
U) 
a, 
'd 
cu 
,ti 
U) 
F' 
0 
*d 
4J 
rd 
U 
*d 
rC1 
mrl 
U 
U) 
Lh 
U1 
a.' 
E 
C 
U1 
5. 
m 
d 
a.' 
T 
0 
4 ' 
k 
a 
V) 
3 
U, 
cc 
.C ' 
info~mation ;1rlcl then completes the interpretation, The systern 
also clsntains facilities t~) a110w 1: use;' ta ~~tld tb ar delete 
from the model, 
The syst~m i.s it tor ust in linquistic rzsearch and 
for exploci~~q pat6ntial apflic3tions af :;onta~.tie ar3mmar. 
Xontague qrds111ar j)rt?.s~v!ts FORI*~ difticulties bacause of the 
complaxity of the loqic and its sem~tntics. ;he loi~ic of PTQ is a 
typcd l=imbd;3 C~~CU~US with irrter,si~31.~dl typesu Inten~retation is 
based on possible- ori ids semantics. The aeaniny of a formula 
Hepends on th;3 actaal world in which it is avaluated, althauqh 
the actual world docs GOT; appsar explicitly in the Eormula, 
Informally, we miqht cocsider the hctual world as a hiddea free 
variabl? in the fcrmula, Scmct accus tomell la vs, in particular 
subs.titutivit y of equ-1.1s anfi univer-sal instarltiation, fail to 
,hold. Fesults dre thus often counter-i~ltuitive. 3ur computer 
a 
implementation of in€Grprvfa+ion has 6Gen valuable to us xn our 
own res2arch and as art 3 in verifyirg cr disproving conjectures 
that we havi; four:3 in thz literature. 
Nat ural-1a11guqe quest-ion answer ins systems trapslate an 
Epqlish sentence to intern'al repr~s~ntation and respond after 
processing h reprssentation against stored data, PTQ is a 
formal framework in ~hich an Eny lish sentence has a 
representation as a loqical formula, and forinulas have valuss 
defined hsing a lagical modsl, This formal framework provides an 
approach $0 the nat ura1-languaqe qrlestf 3n-answering pr~~larn, if 
computer representations and alyerIthms can be tound for its 
implements tion, Our implementation is of interest in this 
cant-axt; we plah to explore its applications further. (For 
another way of lookinq at ::ontaque8s fbram'e,work cosputationally, 
set3 HoPbs and Rascnsehei.11 (1 Q77) ,) 
This docup~r, dvscrihes the nodel;-builinq and interpretation 
system and how to use it. The underlying intensional loyic is 
presented in Secti~n 2;. The op~ration of the prograp is qiven 
in Sect ions ILZ 2nd ZV. Sect ion V exp3 ains tne csmmands used :in 
interacting with th~ system. 
Zxamplas arc qi~en in the text and three sample .tuns are 
provided in the A ppenrlices. 111 dl1 axamples lines that are 
entered by the user dre lower-cgse left- justified and prefixed 
by , whereas output lines are uoper-case, prefixed by > and 
indented, 
.c 
nr. 9 introductory presenta tion of the model- 
theocetic senlantics OX PT(' (Friedman, Moran, and War'ren, this 
fiche), a simpla lrodel in this notation is de.veloped and use.1: 
Appendix P shows the use of the coinputer program to develop the 
model. and interpret formu-las in it., h user may want a modgl 
which satisfies a particular set or^ formulas; Appendix B shows 
the development of such a model duricg the interpretation of 
those formulas. In Appendix C, we develop a modal as a counter- 
e~ample to a formula criven as a thoorom in I'TQ (p. 265). 
A programmers description of the interpretd tion systi.. is 
providei in P@r-an (N-J farth~ominq) , ReatSera who n:iyht wish to 
adapt this pcsyrda to typad lambd,r calculi with other types ace 
raferrird to ':oran (N- 7, fort b.coming) 
I'll@ syst+m P:uil;ls mcdfls anfiint-erpr~ ts f o~mulas ir, them, 
Before b7i~cussLnc; the pdrticukazs ~f our proqram, go Dreser,t here 
th? ur,ier?ying for921 tbeorv. ,he? t~rsid intensional logic in 
the interprstati.on syste~ is that of :ontague (1 37: 1573). *. fi e 
haw faun? 1 (1975) hi~lpfuL as 3 saurct. for 3 formal 
trea+,me;:+ of i:lt~r:;ion.i1 l~qic, but have modifled his natation to 
meet dur needs, 
Z&ah&hgf ul 'x&g3ssioris 
A* ----- - 
T 
,h~ ~ygg~ of intac~i~~al lcaic are defined as follows: (1) F 
an.i'"'I!~ sra elercart3rv types, (2) rhc'nsv~r a and b are types, 
<a,b> is ty?e, an3 (3) wherever a is a tvp?, <S,a> is a type. 
For each ty+ thcr2 is a set of constants a a set. of variables. 
The follawin~, ar 1 mly tk~ follcwing, arm geazinaful ---I --. expressions ----- 
(3E1s) : 
1) I5vt.r~ emstant of type a is a 2P of type -. a. 
2) ,very v?zi;~hlc of type g is a 32' of type 2. 
3) If A is a 3,i of type - a ir~d V is a variabl~ of type 
(LAa-ADA V,A) is a HE of type <b,a>. 
b ~f A is a MF of type <b,c> and E? is a YE of type -, 
then (A B) is a MF: of type s. 
If A is a of eype <c,<b,d>> and 8 and C are ME'S 
of types $ and ,I c then (A B C) is a ME of type - d. 
(This 3xpression and ((A C) R) will lave the sank 
meaning ,) 
,if A ar.d B are :!E,s of the same type, (EQUAL P E3) is a 
YW of typz IS. 
f F ar,d Q are :*iEts of type TS, so are (NOT P), 
(ANP P 0) , (5 P C) , (.T!PLIF.S P Q) , and (IFF P QJ . 
Xf F s a ?I.: of type l'S, SCI are (NEC2SSkFILY P) , 
(FUTUk.1 P) , an8 (PPST P) . 
if ? is a of type TS and V is a variable, then 
.*i+ - 
(911;~u-iS V i') and (FOE-AIL V F) are aEts of type TS. 
If A is a NT of type 5, (I'NT'A) is a Mi of type <&a>. 
I!! A is a U.2 of type :S,a>, (SXTJ) is a PIE of type I a. 
- 
Hodels of Intensional Wqfi 
Be ---I. -- --,,-,,, 
Fodels 
----- 
Let A acd S be noc-empty sets of entities apd poicts of 
reference, respectively. A fram &sed 2; 5 is an indexed 
family of danotatlbn-sets, (D-a) a E typx?, uhere 
ti) DE=A - 
[ii) D - TS = {3,1) 
(iii) D-<a, b> is a-subset of 3 a bada I 
(iv) D-<S,a> is a subset of D - a 
S 
For the elementary type d the set of pOss~a&e denotations is the 
set of entities. For the ~lementary type IS the denotation-set 
has the two elements, (false) ar.4 1 (true) . For a complex ty?e 
<a,b>, the dtnotation-set D - <a,b> is a set of total f~ndtions 
with domain D - a and ranqc D n h. We Asfine P S to he S, so that 
I 
the special. C~SG D - a - is handled by the qen~ral rula. 
A ----- rimdel I.. 3 war on - 4 --- and rrrr- ixJ is a pdir C (2 - a) a saps F> where 
,, I 
1) (D-3) BE;~&~s is a Frame based an A apd IxJ, where I is 
a set of p~ssihle wcsl~!s and J is an ordered set of 
nomznts in time. 
2) F is the hsaninq function which assigns to ezcn LOQIC~L 
constant ~f type 2 an elzment of the denotation-set 
D - <;,a>, 
Zv3luation 
----c----- 
Evaluation is a rcla tionship hatueen. meaning£ u1 sxpresslons 
and models. We A%fi~!e recursivaly the value or i--rr-r-rr- denotation 
dTB:Y,i,j,j] of a meaningful expressior! B with respect to a model 
3 and .i, j, and g, where is 3 mole1 on A and IxJ, i EI, j EJ, 
and, g is a= variable assignment, q assiqns to edcn variable of 
type 2 an elem~nt of P - a. 
1) If E is a constant, then d[B:H,i,j,q] is F(B)(<i,j>), 
2) If B is a v'ariable, then d[9;?l,ir j,g1 is g (B) . 
3) If H €?:I - a and V is a variable of type b, then d[ (LABBD.4 
v B) , j g] is thaf fulr~tion h with domain D-b such 
that whenever x is i h that donlain, h Qx) is 
d[~;~,i, j,qt Ir where qt is a variable assignment like CJ 
except EM the possible differance that gt (V) is x, 
4) ~f ncYE - <arb> and C ~b!r-a, tben (I[ (B C);M,i,j,j] is the 
valus of the function Bit j, for the arqument 
d[ C ; :I, i ,.j .J 1. 
5) ~f E E~~-<dj<crb3>, c E 32- c and DEMX-d, then d[(B C 
9) it, j, is d[ {(I? D) C) ;J.i, j,g]. 
5) If R, C E II?-a, d[ (EQUPL B ) Hi, j g is 7 if and only 
if d[s;a,i,j,gJ is d[~;~j,i,j,g]. 
7) If P, C) EME-~S~ then d[(NOP P),,, is 1 if and only 
if d[I';:~:,i,j,g] is Similarly for AND, OR, IMPLIES, 
IFF, 
If P EYE - IS, then d[ (NTCF:SADILY P) ;M,i,j,g ] is 1 if and 
only'if d[P;Y,il,j',q] is ? for all I'PE I and jt& J. 
~[(~UTUFS P),j is 1 if and only if d[P:M,i,jq,q] 
is '4 for some j' such that j d[(PAST P);i.l,i,j,g] is 
1 if and only if d[P;E?,i,j!,g] is 1 for some j1 such 
that j1 < j, 
9) If PC Mg - TS and V is a variable- of type a, then 
a[ (THEFL-IS V P) ;?!,i,j,q] is 1 if and only if there 
exists Y ED .I a such that ,j, is 1, where gq is 
as in 3. Similarly for .d[ TPOP-ALL V PI:E,i,j,q]. 
I?) If B EKE .I) a, then d[(IAX);-ti,i,j,g] is that function h 
with doma in IxJ such that whenever <i ', j E IxJ, 
Standard Eodels 
-.--u.IIICI*r).-r --I--- 
A atandaha ffaag bdsed qg _-_ dn3 _ S is a frame based on A and 
S in which all possibl~ functicns xcur in the denotation-sets, 
D a D S 
that is, - <atL)> = 3 - fr - and Z! - <S,a> = Lp " - d- A standard model 
Il-(l- -- 
is a mod31 hast3(1 on a standard frame. 
General Yodels 
---.lr- -----rrr 
In a genegal model (4-xroddl) , the denotation-sets of! the 
frame are less ccnstrainel. As (350~~, 5 - 5 = k a,n.d I) - TS = {(?,I). 
However, for .3 complex tY FG <a&> we have 
D a 
@ + D-Ca,h> n h - . 
- 
I ~b is furth~r required that the 
denotations for all taxpressions be in the model. This means in 
effect that thz functions h which are the denotathns of LASBCA- 
expressions and IS IT-~~xpressicr,~ IRUS t $xist in the appropxiate 
denotatior!-sets, The definition of evaiuatior, in a 3-model is 
exactly as in a sta~darrl luu3sl. Not+, howwer, that LAMEDA- 
abstraction and auantification arc restricted to the denotation- 
sets of the model, 
Named Modeis 
----- ------ 
The models used in the computer system do not correspond 
exactly to the standard or qeneral models of formal logic. We 
therefore introduc2 a r,cw formal defihition of 'named models', 
This dezinition allows a model that map be smaller than a y- 
mod@l, but expands toward a q-model when new functions are 
A named mo;iel (n-model) is based on a frame which need not 
be closed undzr valuation, The valuation function d is a partial 
function, undefin~d where the valuation function as defined above 
take$ a value not in the model. 3 .Ir <a ,b> D I bD--a art& evecy 
element has a unique name. A named model need not be a g-model; 
howkver, a lcoverinq q-model' must exist, The coverinq g- model 
is the closure of the nMmodel unbr the condition that the 
f unckions requir-d for evaluation exist. LAM BDA-abstract ion and 
quantification in an n model art. restricted to the named elements 
in the denotatlon-sets, 
Dyn8mi.c Barned Yo3els 
- ---- --- -1--- 
The models use3 in our interpretation system arc dynamic n- 
models r They are not closed under the valuation function; 
however, whenever a denotation of type <a,b> is created by 
evaluation of an expression with LAMBCA or IIT, the dyrqmic n- 
model is imnediately expanded. The function is named, added to 
the appropriate denotation-set, and all functions with zhis 
denotation-set as domain re expanded to include values for the 
n4w arqument, LAKBDA-aQstcaction and quantification in a dynamic 
n-model are r3strictet.l to the current named elements in the 
dsnata.t:ion- se t s. chis has tht? consequence that they cannot be 
precisely defined inde~endentlv of the order of evaluation of a 
formula, 
A dynamic rr-anole1 may, b~ thought or either as one expanding 
n-model or as 3 sequence of n-mc.;l.~ls. i:t is not yet clear which 
view wiLl he most productive. 
Finite Kodels 
------ -----I 
While the ictensic~al loqic has in6iditely many types, only 
a finite number (xcur ir. ex~r~ssions of PTQ and hhus only a 
finite number of r:-.ts ~f possible llznotaticns arc neel2d. In the 
current versiori ot *.ha interpretation system the sets A and IxJ, 
and h~nce all d~~a.otaticn-sets~ are finite, In the finite case 
the nntions of standard n~odul and g-model are -the same, under 
somt weak conditions. we have introduced the distinction becquse 
we think of our dynamic models as 'potentially icfinite' , and 
fi~d the not,&or. of c:overins d a-*mcd,el, - sugyestive. One might think 
of the g-model as a representation of 'reality1 and an n-model as 
a finite r~~presentation of the svst~rn's knowledge, A dynamic n- 
model is a representation +-hat is forced tc expand toward reality 
as the system needs f uifcher knowle~lye to carry out its- tasks., We 
plan alsewhere to ci>nsid%r t h~seq rnodsls further, both formally 
and as possible psychological models. 
Models &g ug astern 
C, ------ 
This system accepts only finite models. A finite model can 
4 
reveal the principles ir~volved in intcxprtj~dtion of formulas, and 
most ~f the interesting problems it1 the eva3uation of formulas 
can arise there. fu usinq th~ system in resea~ch, we have 
encountered no problems related to size, However, even a small 
stgndard or nil model is too large to b@ practical, The 
closure property of these models causes the inclusion of elements 
that may not he needed, Dynamic named models are practical. 
They need include only those elements whose use is ant; cipated, 
and elements can be added to the model to meet neu or 
unanticipated uses, 
The functions in standard a~d general models are total, The 
functions in named niodels are also total, although they may he 
incompletely (partially) apecif ied, that is, the value of the 
function may be giver, for only some of the arguments. The 
unspecified values fqr a function are regagded as determined, but 
unknown to the system. If the interpretation of an expression 
causes a fuxction to 6b ap~li~d to ar. argument for which its 
value is unspecified, the interpratatio~ is suspendeti and the 
user is prompted for the needed value. This approach using 
partially-specif ied total f u nctions and dynamic mode.1~ contrasts 
with a~proaches using partial functions in static models 
(Kutschera, 1975) . 
.In a nnnied ml, a D - set is a subset' of the set of all 
possible fupctions of its type, with s dynaiuic model, the user 
can enter n function of type <a,h> that. has a valua not in I! I b; 
this caris+s the elament to be a3tl'~d to D - b. Similarly, the 
a\ldition of at: ?l~nt.nt to D-a causes the expansior, of the 
specifications of a11 current functicnS ct type. <a,b?. 
In d Iynamic model, it may be reasonable to have two 
functions with thz sane specific3tian; 2n as yet uqspecifled 
value may be different for the two functions, or they may have 
rliffer~~lt valutacs for some aI11-clument not ye+ in th~ model, 
?h~ dt3110tatior: of a LAMEDA-expr~ssion or ar, IKT-expression 
is a function an3 if t'ndt functi~n is not an element of the 
mod~l it is added. If an element is added to D-a during the 
interpretation of a LAFIRD3-expression of type <a&> or an 
argument to which it is applied, the body of the LAEBDA- 
expressior! is in terprgted for this new - alement and the 
specification of the denotat lor, m- the ZA2:ECA-expression is 
expanded to, includz this argumenb and its computed value. 
This ability to expand t-he modal dynani,cally during the 
interprstation of formulas qives tile US-?'~ a second means of 
constructinq picdels: starti~g with a minimar outline of the 
model, the user interpro ts expressions describing the desired 
model. when pro~npted for unspecified values, the user can 
respond with elltries that will make the expression true. 
The model can also be expanded under' the direct control of 
the ust;r, Elenlctnts can be addlad to the model or pnspecified 
values of functions can he ent:~re\L 
I?iPLE?!FNTATIQN OF NAMEC EODLLS 
III. ------------ -- ----y ------ 
Names for ~YES~ gid gsgss 
Am -,a,, e-- 
Semantic types play a significdnt role in the interactions 
batweer the user and the system, but the names of complex types 
as constructed in PTQ are cumhersou\a. Fcr exantple, words in the 
syntact.$c category TR'Vr/ZE (e.g. lint and @aboutt) ar2 translated 
into logical constants of type: 
f (IA V/Tg) = <<s,<<s,<Xs,e>, t >>, t>>,<<~,<<s,e>~t>>,<<s,e>, t>>> 
To facilitate interaction? the system uses new type names that 
are mean iny ful, simple, and easily distinguished from each other. 
The conventiou is to use the names of the syntactic categofries as 
names for the corresponding semantic typez, i.e., for syntactic 
category x, the name of the correspondinq type, f (x) , will also 
be x. This can be done here without confusion becaose the 
syntactic categcrias do not play any pa~t in this svstem. Where 
PTQ uses special symbols, e.g., iV, IV, for the cogpound 
syntactic catqories, 5/@, - ,V/TZ, we also use these special 
symbols, Flpwaver, there are types that ja not corcesponil to 
syntactic cat~.qories, e.rl., the types fat the intensions of the 
typed that corraspond to syntactic catoqories; the name ue use 
for one of those is the corflhi~~ation of the names forits 
component types, u. y., <S,IAV/TE>, 
It is possiL:le to have several names for the same type, for 
example, E(C%) = E(:V). In such a case, anothsr (neutral) name 
is ~eederl - tile conv?rttion is that this name is formed by 
combinimq the types using an equal sign as a slzparator (2. q., 
Sn'=Z'V), Type narn?s such as CY and IV will be referre? to as 
names when it is necessary to distinguish them from the 
SU~~YE~ --I-- --- 
oaer type 11ame5 ( CN-3V OX: 2) Ihe user can usually 
refx to a t-vpe lrsinq &tiler a subtype or type name (in the case 
of €(CN] = Y(XV), hy Ch, IV CX CN=IV), whichever is most 
natural, 
When the uscr is prompted for a type, the preferred resnonse 
is one of these new type nan;es. However, the user may enter any 
equivaknt form, For exanple, IAV=?V/IV, <<S,IV>,IV>, ant! 
<<S,<<S,Tb,TS>>,<<S,I>,TS>> a,l1 name the same type, Since a type 
and its suhtyues ah1 have the same comFonents, these e'quivalent 
forms refer to the type, 
Names are also assigned to th2 sets ojf possible denotations 
of each tv~5. 1h~ riame for a sst of possible denotations of a 
type is formed by concatenatinq D and the name for that type. 
The Cull type name must be used hem, not a subtype name, That 
is, the nams D - Cti is not recoqniz~d by the syqtem; it expects 
DL - CN=ZV insttad, 
PU, g Logical Constants and Variable g&;~~fjggg 
me -c --I- YIIICIIIW..I.(t- 3*-- ------w 
The system contains the tensed intensional logic used in 
PTY, Th~rr is also an extensional version without 
intensionality, modality, or tense; we do not discuss it in this 
paper, TWutypes arlsl those occurring in formulas that are 
translations of English sentences or: are meaning postulates. The 
types and s~~btypes for intensicnal models are: 
S 
E 
<St &2 
CN=f V: <<S,E>, TS> 
SUbTYPES: CN IV 
<S ,cN=~v>: <+,<<s,E> ,TSW 
SUBTYPZS: <F,CK> <S,IV> 
(5 ,TS> 
<S,<E,TS>> 
IAV=TV/IV: <<S,<<S,E>,TS>>,<<S, E>iTS>> 
SUBTYPES: IAV IV/IV 
<S,LAV=IV/iV>: <S,<<S,<<S,E>,'i:S>>, <<S #E>, IS>>> 
SUBTYPES: <S,IAV> <S,IV/ZV> 
<<Er TS>, <Z,TS>> 
<S,~<E,TS>, <P, TSS>> 
7.E : <<S,<<S ,E>, IS>>, TS> 
<S,Z"E>: <S,<<S,<<S, X> ,'iS>>,TS>> 
ZV: <<S,<<S,<<S ,Z>,ZS>>, TS>>,<<S ,E>,TS>> 
<s,Tv>: <S,~~C,~<S,<<S,E~,'~~>>,TSL>,<~S',E>,TS>>> 
<E ,<E ,W>> 
<S,<P,;<E, I!'s>>, 
IAV/TE: 
<?s ,<<s ,<<s ,v>,~~>>,2~>>,<<~, <<s,E>,Ts>>,<<s~E>,Ts>>> 
<S,I~/TE>-: <s,<<5, <<s,<<s,E>,'~s>>,-~s>> ,<<~,<<s,E>,Tc>>, 
<<S33>,TS>>>> 
<E,4<E,TS2,<EfZS>>> 
<S,<E,<<Z,TS>,<3,TS>>>> 
TS 
The logical coEstants are formed by capitalizing the words of 
which they are the cranslaticns. For: examrle, the WOE,\ N~alktg 
translates to the constant dtWBLK't, li'trt? logical constants are; 
TY'PE F*: J, I:, E3& 3. 
TYPE CY=TV: 
SIIRTYPP: CC: XAN, WO::Ah', PACK, IS, PFN, UNI:CC3h-, PEICE, 
TSM Fi FATrlFE 
SUBTYPE ZV: 3, WALK, TALK, EISE, CHAKGE;, 
TYPE IAV=IV/XV: 
SUI3i=YP,E 1AV: EXPTCLY, SLCtWLY, VOLUKTAFILY, ALLEGEDLY, 
SUBTYFE IVfIV: ?FY0TOp UISH-TC 
TYPE 2V: FIflD, LXE, SAT, LCVE, EAT,", SEEK, CONCSIVE. 
TYPZ ZAV/TE: Ih, ?.EC3T, 
TY PE ~V/IS: ~~L;LVETT~~AT, ASSLS?&IEiA T. 
79 permit an unr+stricttd n~tffber of variables, certain letters 
are dasianat~d as variabls prefixes, and a variable of type I* a is 
a variable prafix of type - a follc~ed by 2x6 or more digits. The 
variable pr+fix ,, 
TYPE. ?: U, V, 
TYFL <S,Z>: X, Y. 
TYPZ <S,C>J=ZTJ><: F, 0, 
TYPE <S,<Z,iS>>: E. 
P 
"PE <3,2>: 3. 
TYPE <S,<Z,<Z,7S>>>: S, 
'TYPE <S,<d,<<T,TS>,<F,TS>>>>: G. 
TXP? <Z,TS>; KO 
Changqs to thz built-in logical constacts and variable prefixes 
can be acco~plishei wLth the ccmnands in Section V. 
The loqic is bullt into the system with a saries of 
declarations yivinq the types, logical constants, and variable 
prefix~s, and an ord~ring of the types. qhis ordering, which 
need not contain all the types, gives the sequence in which the 
system will prompt the user to enter the sets of possible 
aeaotatiahs, The built-in loqic can easily he modifies or 
raplac6d bf chnnginq th~sta decld-saiions (Ncrrac, N-7, 
Eo~t hcominy) 
Sets of ~osskble Denotaticns of Corng&?i? 212s 
C* -- .I- -I-- L- ----..I)----- 
A set of poss'ible denotations cf a complex typa <a,h> is a 
set of functions of type <a,h>* EacK' function is entered by 
givinq its name and specification.  eve^ thouqh functio~s are 
understwd to be total, functions can be entered with partial 
specifications. For each set of functions, the proqram prints: 
1) the name ot the set P_<;l,b>, 
2) the ndse of the set D-a that is the domaic, and the 
names of alewnts in the domain, 
3) tne name of the set D - f: that is the range, and the names 
of elements iri the range. These are the names to be 
used as values in entering the fu~ction, 
4) tha logical constants whose possible den'bt ations or 
denotatio~s of their intensicns are in this set. 
Follbving t-his prelimina~y information, the program asks for 
the name for the first element :o be entered. This name can be 
chose& alm~st arbi trarily. There are a few illegal names, but 
they are refused by the system. Tile following cannot bc used: 
the name sf ~cdther clerner3 of sng set; the nae of any of the 
rn*rv~ 
model conrponcar.ts (2.q. 'T"NL~II~;S'~ } ; tha nant? for a type, a 
set ~f: pOssiI11v d~notarions, cr a uoint of referaxe; the nalne of 
nuaEet OF a 
a comnan:l; a n.3rnr in with th.2 character ='* 
system atom (T, E;X) . 
After the Ilant9 for an elemqnt is +r.t.crt?d, the prlograax leals 
the user throuylik its specifi-cation, and then asks for the name of 
the next element. indicate the end of a set of el~ments~ tne 
user responds ritn XIL* *hen the specification of a set is 
tzrminated, tne pro~ram displays its Elements and then requests 
specificltion ci +[LC next set, 
> 
w V-l * '-q. 
THEY MILL 6; It,. VFLtlES CF F FdF ~k12 Li36rCkL L'JP;S?Z.A~A.. 
> J, Y P, 3. 
> 
> D - S = (If, 12) 
> I! - 3 = {Jc!, US) 
> 
> 
R-7- 
2N *-? ~-41:~ ?c~ L~>yt~?, (3IL = SC F052) , 
* 3 {j 
S~ecificatio~ of Fucctions 
3. - ---- - ------- 
,qfter the Iiafi~ fcr a function has been Pr;r;er9d, tk.0 proqram 
guid~s ths uzer throiijii its .cp~cifacatior.. For sach element in 
the ~Q~RS~R, the proqram prints its raa% ar,d its specification 
and the user rcs~owds with the raac of tJln corCespGr,ding value. 
ff the function is to be unspeci-fied for. this argument, the user 
enters NIL, Pny element entered as a value should already be in 
the model, However, if en element that is not yet in the model 
is needed, the user may enter the name intended for that element. 
The program detects this as a potential error and asks the Jser 
for instructions (see F below) r 
> 2NT2.E; bAX2 FCF ELEI!FZU'T. fNX, .KO MOEE) 
*aQ 
> ENTLF X VRL~JE QE NLL FX FFFC'?~ AFGUMEN?: 
> 11 = <fI533Z,"H3N> 
*jo 
> 12 = c~za~,ko~> 
*jo 
> A?' 9?? TSF PC. 
b ****I3 <SIC> - ISCIVIDUA'L CCh'CT2I:S 
> coeji~g: D-s = (21, 121 
> rA3GC;: D r' = (JO, UN) 
> A{: = [?11,53>, <I2,JUY) 
> k3 =, {<I? ,UM3, <12,US>) 
When the specificat ion of a function is completed, the model 
is checked oAr an uquival~.nt fU11ctlon. TFI such' a situation, 
there would be two names. for the Sam+ Olernent and, in functions 
for which thiq element is an argilment, a valuq will be specifieii 
for each name, Tf these values are nct the same, the 
interpretation of an .expressi3n Can depend cc the name used. To 
prevsnt this, on€ of: the equivalent elements should be deleted or 
mod5f ied* 
Functions Used Before Thej R_rg se~hried 
3. --------- ---- ----- 
During th~ sp~cificntion of a function, tile value for a 
particular argument is entered by jiving the name of an element 
of the 'range, If the uses enters a name which is not in the 
model, the program 3sks for clarificatian, f f the user- chooses 
to specify the tzlc>mrnt immmediately, the specification of the 
function is sus;,pended vhei-le it is eritereu. For exampie:* 
FNYLF NAiiE FCF FCEi:?,KT., (N$L = 0 ?!OFE) . 
0 SUCU LLLYFF*'i.- iLYPLAI?+e 
(??-WR'OI:G;NA!!Z; 2-WILL . BE EYTZiiBC LLIZ5; 3--EST$& NOW; 
4 F,rfNCZIC?& AS IlHSP';,CIT:ILD FC5 ALL ahGU?lENTS). 
THIS ELZI:?l\'T SF- D i?i=IV 15 A 'irllbiCfICN F$c?~ C <S,E> TO D - TS, 
YHP IS, FSUP IND?VICIIPL C(?NC991TS IC TFUIf? VALUZS. 
--C 
****C C!!=IVVm SETS SF iN$TVICUAL CC~~CLLIS 
< 
DCZIIN: D - <S',F;> = (AO, k3) 
5F;NGL: k, n ~-5 = {I. t 11 
ti., = -[) 
015 = {A .43 1 
P? = (AS) 
- 
1f the user ch~oses to delay tile f;ltry of the new element, 
the spacifiqtion of the ftlnction continues uninterrupted, When 
the entry of functions into a set is finiShed, the user is 
prompted to enter the sp~cifications of the 3eferred rle~ents. 
T 05 
SETSF A VALUL 3? NIL FOF ZACH ArGUMENi: 
A3 = {<I% ,30>, <I2, JO>) 
**MARKING - C C;3=IV CONTAINS EQUIVALEEJT ELrE12ENI'S. 
v 
EQUIVALE!~ SLSNEKTS: El, F5. 
New Elements in 2 ggmlh 
Fm --- ------ a- 
If in entering a model or adding to one, the us& enters 
elements ir&o a set which is the domain of some previously 
specified tunction, the specif lcatzon of that function will need 
to be expanded to include the r.ew elecnrnbsb The system will 
suspend its curr~nt projtzt and prompt for this# swpansion. 
> EXPA?j%I?\'G XL,Et.2?:T75 LE; P - CE=IV = {SETI-WALKs'i;S, 572'2-.WALKEF.'S, 
> .SFT=XE??] 
> reEY AFL FIII;CP:ON~ -FECE: r-<s,, 4) TS 5-7~~ 
> 
CI ... - 
,HA2 25, rr SX i~CIiiLDU?.L FCNCEPiS TO i'i\U;t! 'VF.L:U.SS. 
> 
> 
- 
D - <S,E> = .(IC-JG, -C-YA 8 *, Ice-PI, IC-K~) 
> D - TS = {", 1) 
> 
> 
- 
HEM P.T;CTU?:ENTII IN 9 .*CSrF>: - C-ti:, TC-?:A. 
> FOF EACH OF THP, FOLLONIKG PUSCTIC;XS, LNT~X A VALUJ 
> OR SIL FCF B~cti CIF XFCI ZFGLJKENTL 
> 
> .GXP.Ah'CI?iG G SECIFICkYIGN CF Sf'V*~Gs'ALfCEf S = {iC"30] 
> ILO-RX = f<fiIr91>r CI*;f?I>) 
* '3 
> TC*~F. = < 4, <I2,hF>f 
* 1 
> 
> EXFANDING ?~?LCIPICATION CF sZl.2-WALKEFS .. fIC-%A) 
> :c-ar cq (<:I ?EL>, -<T~~EI>I 
* s 
> TC-.NA = {<:I ,Ex>, <IL,XA>>, 
*2 
> 
> ZXPAZJDLkiG SPEGI FiCA'iIC?X CF STT-.:?ZN = [IIC-JG] 
> ICChE31 = {<IP,PI>, <f;,RI>y 
*I 
> IC-NA = (<II,BA>, <I~,EX>) 
* 43 
> 
> **** C CN'TV 1w SS 25 GF INDI VTC7JtiAL CCNCZFTS 
> 
e 
GOU~I"~ :2-<S,,> = fICmJO, *Cka?:A, IC-PI,'IC.*HA) 
> F;; flG3: " 3 c {i",* . ] 
> SL.TI+~T;~K~:FS = {:cm JC~ .~C~~~JAJ 
> SZT2- ~?A~R:!?s = s(IC**Ff, T.CL BI] 
> StT- #'2k = (Ice J@, ;C--EI) 
Nealliu Function 1 
. as --a 
In a model, the meaning function F assigns to each logical 
constant a function that is the denotatioir of the intension of 
that constant. If th? constant is of type ,I a the value of F is 
of type <S,a>. After entering the .sot D rn <S,a>, the user is 
prompted to enter the value of F for each of the constants of 
type a. 
> **J:*ZE~.EFINC TUI F~~ICTXQ~; - F FOE -LOGICAI CONSTANTS OF TYPE E 
> THE ,VALUES -01 F Fdb *THEST COPJ$TANTS AFE bX.Pt:ZNTS OF 
> D - <S,E> (JE!bXV;LGrJAL i'tIKC2FTS). 
> 
> LOGICAL CQFS'IAXT?: (7, , I?, Na 
> D - <S,E> = {kt ,2A3) 
> 
> FOF 3AC.H (I"O!lSIAliT, .ENTEE THE VALUE C'F. F (3P hIL: 
> J 
*a! 
> ;-I 
*a3 
> B 
L3ni1 
> N 
*nil 
Yo check is malie that a constant satisfies any meaning 
postulates, since it car, be interestin7 to investigate both 
models that do an'd do not satisfy them, The user car, find out 
whether a meaning postulate is satisfied by interpreting it in 
the modd, 'as is don2, for exam~le, in Appendix C. 
INTERPPEZA'TiION IN =g& 
IVe --,----------- ,- 
An irrtansional mod~! is hsed in eva1uatir:g neaninqf u) 
expressions ot intunsro~al Icgic, Xhese expr~ssions may he 
written directly or they may be obtained using other related 
computer pray rams. Fot each Enqlisfi sent%nce our-parsinq system 
produces the set of derivation t;"raes that give the structure of 
the scnt.ence. C~ur translator applies the rules T1-T17 of FTQ to 
obtain a msaninqful -xpression in intensionat logic. The 
erpression obtaiced is the 'direct tra~slation' of t Re parse 
tree; a normal farm is obtained by application of lambda- 
reduct ion and extension- irite~siori renoval. The interpretation 
system works for acy of these meaningful *x~ressions. 
Yeaninqf u1 expr2ssions are it t uitb respect to the 
dynamic n-mod21 an3 two parameters: a pint of reference and a 
variable assignrn~~t , whose initial values are provided by the 
user. 
During thd ir. terpge tativn of rneariinqful expression, the 
interpretatior. of each of its sub 3x~ressicns is printed 3ach 
axpression and the curr5r.t values a£ the two parmeters are 
printed as cvalllatior, begins, md the expression and Lts 
dznotaticn ar;t minted when t 'r,e evalluat-ial is ci)mpletdd. 
* (walk x3) 
> 
7- +- 
~;AF~~SSPOS I'S OF ?YPI 'IS 
> FFFE VkhIABLFS: 33, 
> OK? 
> 
> 
p .,hAUEi 7 n9- P43IBT UE ZEFLFEYCE, (NIL = NC 3iOFE) : 
*i2 
> PYIZER A VALUE; FOF LACH VPFZAELB (NIL =CAVCSL) : 
> x-3 
*a0 
> 
> INITIAL VAL IE,RLE ASS ZG'NKENT Gl: X3=k?. 
> COYPUTING DPGOTATION CF ' (VALK X3) FOR I2 AID GI, 
> : DEEOl'iiIO$ OF WALK IS P~J [AC) 
> : DENOTAmIOIi OF X3 I$ A? = {<Il,JO>, <I2,JO>] 
> DENOZATXON IS 1- 
The interpretation of a LAMBDA-expression or , a quantified 
exprassi.cn requires a series of new variable as'signments, one for 
each possible denotation of the bound variable. These variable 
assignments are generated hy the system and ace just 1ik.e +hQ 
previous assianrnent vith the exception of the assignment for the 
bound variahle. Thhe system ,alsc generates a name Gi for these 
assignmznts, 
Zach function in the n109aL is total, but it nay he only 
partiaAly specified. If a function 1s applizd to an argument for 
which its value is unspecified (kIL), fhe system suspends the 
interpretation nnd prompt6 the user for the value. Similarly, if 
the rneanipq function F is ufispecified for a constant in the 
expression, the system prompts the User for the value, 
> e :. CQYFUTXiiJG TATTO! OF (XAiJ X) FGT; I3 ANE G5 
> * 
. 0 
I * : DErJOTAI OF 9hN. IS SZl-MEN = (IC- SO) 
> 
.. 4 
' L 
a : ckWO2ATION OF X IS IC-?A = {<II,MA>, <IZ,MA>) 
> 
. 
. u + : i TH~'V%L'JE OF S?T*?X?3 
> 
- w 
w . 1tX's UHSPECIFIEC F THE< AFGUYEST IC-MA 
> 
* 1. 
. -a .. : [ 185 P~O~SI~LE VALUCS ASE: 
> 
e * 
* e :] c-PS = (c; 11 
> 
e * 
0 = I 
> 
.1 
a • : 1 LNIEF 'rI.1E VALUE* CF SET-MFN FOP: 
Two functions are XQUAL only if they have the same came or 
they have the same full spa~ificatior.. Tuo functions with the 
same partial ,;pecifica4Aor, car~st be said to be equal because 
they ray lif fer in so~t. of their as. yet unspecified values, In 
t~sting the equality of partiallv specified f.unctions., the system 
prompts the LL ?or ench of the ucspecified v-alues until the 
specific3tion~ ara fcund to be d~fterznt. The user may respond 
the system may ~zonpt for the'vdlu~ later:. This allows the user 
to avoid syze5fyina d value- for a particular argument when the 
functions Arc going ta he \Inequal for: some later argument. 
> INIT IAL VAFIFiS'i 3 ASSIGSKFNT GI: Y=IC2, X=IZ I, 
> COPP,UX;NG,2EhOTAT?O~I OF' (ECUAL X Y) FOF 11 AND G1 
> : DENOTA~ZION .SF k I3 C = (<Il, NIL>, <I2,JC>; <I3,NIL>) 
> : DZliOTACrOK Y IS IQ = {<I1 ,YX,, <i2,50>, <I?,KA>$ 
> : IC1 ?C FOB ilF(:U>iENTS: I?, 13. 
Interpretation ot an ex~r@ssion beginning with Fa&-ALL, 
TNEAQ-IS, N3CESSAF;LY, FUTUFE, or PAS2 calls for interpretation 
of its hotly with rpspuct. to a series of variable as~ignments or 
points of refercnCc>. ~ntprpretation of the cexprc.ssior. stops as 
soon CIS the valu~ of tile ~x~f~ssioj is determined. This is also 
true for @xprrssi~n~ with the loaical connectives AND, OR, or 
IY*ELIES. 
Zni erprrtation cf ?ak?!P~A-ex~r~ssioj~s and INT-expressions can 
add r,ew elements to the model, The aenotation of a LAYBDA- 
exprassior,, Such as (L'AYP~R X (WALK X)) + is a function Elhose 
aFguments are the possible denotatiurlz that can be assigned to 
the variable, .XI an1 whose values are tound by interpseting the 
body of Lhe expression, (i4AL.K X) , for those assignments to the 
variable. If this function is not already an element of the 
aod~al, the user is asked to came it and the new element is then 
aJded to the model, Denotations for INT-expressions are 
generated in the same manner, with ths points of reference as the 
domain of the functbion 
> : CO:<PUTIKG i~~~~orrl~~or~ OF (LAP~BCA P ( (EXI? PI (INT ~9) 
> : FOF 11 XiD GI 
> * D613OZAPIOY 9i (LAMEDA P ((EXT P) (INT J)).) ZS [CIl 
> . : BIJT IS ~;OT AN ~EI~ENTI IN TIHE- KGDEL, 
Ney alernsnts can be added to the mods1 during interpretation. 
by beirq given as the previously unspecified value of a function 
or hy being the int~rprctatior of a L~EP~A-expryssipn or an INT- 
exprwxxion. As part Of the ad3ition sf a n@~ element to the 
model, the system nrompts the user t.0 expand the specifications 
of the functior.~ to whose dom~in the alemeqt has been added. 
However, t11~ addition of an element mdy cause the expansion of a 
f unctiar~ that is t 112 d~diot ation af a LA:1FCA-expressio~* liathet 
than ;~s~;urning that tha user. will carrt.ctly expap3 the Cenotation 
of the LA:iF3il-ex~re~sicri, the system first has the user expand 
all th~ functions in thc ~.~odcl, and then it expands the LAERDA- 
expr.ession by intarurntinq its bod'y for the g.sw denotation of the 
LP.?!BDA~variable, and adds th~ dan~tatio~ to She model if it is 
new, 
In interpret inq a LA:!?3A-axpr~?ssion o r a quantified 
expressi.cn, th+?rq may b? no possible derlotations for th~ bound 
variable, i.e. +hc ?-set is capty. ?he system assumes that the 
user intend4 some as yet unspecified function to he in that 
D I set .and allows the usir to name tha+ function, This function 
is entsred as king unspecifiec? for each of its arquments; the 
user is ~r:ompt~i for vzlues as they are needed. The user may 
choose to leave +!I? 3 - set empty, in which case the denotation of 
the exp~es~ion is true for universal qua~tif'icatior., false for 
existential quantification, and a fu~ction with an empty domain 
for a LASSDA-expressior. For a LAEBDA-exprqssion that is applied 
ti) an argument, this latter course has the effect of delaying the 
interpretation of the LAMBDA-expression until af te~ the 
interpretation of its argument, 
> CO3PUTIIG OESOTATIUN ,6~ (THEliSu IS E (EOR-ALL X NECESSARILY 
> (IFF (WALK X) ((EXT Z) (EXT X))) ) ) ) FOR I2 AND G 4 
> : TIIE:A AARY NO POSJiBLE DENOTATIONS FCE THE BOUND VAFIABLE 
> : F* 
> : UNSP3CXFLED FUNCTI.CN PFING ACCED TO D <S,<E,TS>>. 
> : ENTZB NAXE FOB THIS ELE:?(FNT (KIL = POF~': ADD) : 
*prop- walk* 
> : *NEW VAFIA3L3 .11SS9Ct'h'HEah'T 2 ;'~PEc~P-WALK*, 
> : COfiP1JT3:NG PLNOXAT30N OF {FOEtALL X (NECESSAEILY (IFF 
> : NALK X). ((ox7 E). (EXT X))))) POF I2 AAD G2 
At first consiii~ration. this treatrner! t of LAKBDA~axpres~ions 
seems inefficient; it would Seem morc efficient to interpret the 
body of the LX:?ELA-~xpressicn cnly for the argument to which it 
is applied. kiowever , th.; logic includes meahingf ul expresgions 
in uhich a LA:9BilA-expressior. is not arplied to an argument. It 
is Also possible for the argument of a LAMBDA-expression to be 
anoth~r &~EA-ex~c~'ssion. 5eaningf ul expressions of both these 
forms are qene~dtet in PTC* Furthermore, even where this 
simplification is applicable, this simplification is a syntactic 
reduction an5 ahauld be performed before the expression is 
interpreted. Theref ore, when interpreting a LAMBDA-expression 
applied to an argument thz system assumes that the usGr does not 
want this simplif ica tio~. 
USIYG TH& SYSTLY 
V@ rr---- 
Introduction 
A ---- -------- 
This systam hcts a simyle, i'lexiblr ccmaand language which 
supports the Ceeds of bcth th&.rovicr and. the experience4 user. 
The novie+ can follow 3 direct path through the system, simply 
respondinq to prompts as they are jiven. Pith the prompts he is 
rzminded of tll~ relzvant past entriss that Esrm the cantext for 
his current decisians. The ~rcropts follow an ord~r from simple 
to more complex sb that the buil3ing blocks are always available 
when they are zsedzd. The systenr &hec)ss all resoonses for 
errors, an if on? is foucd, the use$ is advi3~d and allowed to 
make a ccrr~ct ectty. 
Thc advarced user ~;e~d not follow the direct path. The 
order af ;'ntry -oc 4 rodel can be varied to corresposd more 
qatucallv td the proh1c.n at hand. The mo.ic1 can also be changed 
in order; to sxten~l the model, o cor'rect errors, or to explore 
alteynat ives. ~r, impx+ar.t and exl;.f smely useful feature of the 
intefaction is thlt the user may i~terleave model-buil8ing and 
f~rrnupa" interprefa tlCn. The epeFediCication of a function may be 
dzqer~ed until t tl e f unct ion is 3ctually needed in the 
intergrl2tation of a formula. 
Interqctinq with the Program 
B* .I.---- -11116- -I-L *-w 1-- (1-1 
The commands in thjs system art. LISP function ?ails; the 
command and its opprands (if any) are cncloked in parentheses: 
QN'T FEP) 
(XNTER 14Bt'EL) 
"r, 
(P'SPLkY C-SFTS) 
3% System is implrmente~l in1 :?~~S/LI,P and is currently 
dvailable only at the University of Yichiq~ri To- use this 
system, run the LISP iritrrpreter dnd use the function EXSTORE to 
load the program *from the tile WFF: I-t;TE'FD 
#$run *lisp 
* (restore shof:  inter^) 
Rormally in XTJ/LISP anqh hrdcket-s are Buper-parent heses 
andWconrsas ~LQ separators betve~n eltnients in lists, Bowever, we 
use tilsse characters in type names, e.g., '<S,E~~, so they have 
bzen cedefined as normal characters, 
Entering a nodal 
C -- - -*--- 
The entry of the model fcllcws the order implicit in its 
dsfinitioc, First the sets A of entities, I of possible uorlds, 
an8 J ot moments in time are entered. From the possible worlas 
and mooents in tile the system generates t"ha set of points of 
reference IXJ, rhe ssts A dnd IXJ determine tbe frame far a 
standard model, 
The models in this system ire named mo3zIs. The P-sets for 
tire elementary types a:~ +he saw 3s in a stondacd no$lcl. Each 
D -rr set df a complclX type is entered by tht u&cc with na~ds for 
taac11 function entered iri the set, Interleavsd wirh the ectry sf 
the D :Gets is the spccificaticn of th~ meaninq f unctior: ; the 
- 
values of 'i' for 1oirFca.l constant:; ~f %I type are s~~~~ified as soon 
4s + 11i-l 3 - set eo:~t(ii!lk:lq the , values is +r"ctrare.i, 
(2~~zy;~y~~) , rC ,h~ hyst~m first dsks whether an icte~sional or 
opportunity to chanqv tit3 built-ir; hqicallcur,stact-s before the 
specific3tios of F hcq7insc Wxt the user is pronpt~d for the 
elpm~nts in thtlstz lises cap he ruabt~~~ ox +strir,ys oE characters, 
.- 1 
lists, ;::P aomerrts ir: time Art: ente-.=?d in orler, sarliest to 
latest, 
* i 
> 
- - 
r0 YGrJ iJISH LO 2!!,4hG3 ;I--fS ?.I LQGICAL L'CSSZA:311S? 
* n 
> 
> 2LXXI!D?F: CC1:kAq LANSCXE ~U"z3 13 EE?AFA.TTS I3 ~ISTS, 
? 
7- i".-- - .y -,- - 
Y 2121 -2F ;:?u:IA&Ls. 
*(jo un) 
> 
I -7-- r 
8- IS F E"55FI9iE WOFXrF, 
* (bere) 
> 
T--*.;; -2- -\ 
ENTZF LIJT OE ,I'??12?if5 -I.... r :.\CFE44S1SG C5CFY 
* (khen now) 
> POIll'iS dI' EXF35if:CL (LEiDICFS) : 
S 11 = <41khE,PIiEE3> 
> ~i = <NI:R,,WM> 
> 
> 
> ;rltrlt*r:+FN;TE~,1KG L? CF f3 - <S#b> - I?lDIVIDUAL CONCEPTS 
3e ,el.trya ot C!ir snt.s of possible denotations is ordered so 
that hefore a D-set is ~ntered tile D-sets which are its aOrnain 
and itsn ranqe are ente~ed. This otdering is built into the 
systgn~ as pa~t of: the fy-pe specificbtion. This ordering also 
cause7 tke syst~m not to prompt the user for 40 - sets tbat haue 
empty dornai~.s. !kither will th~ system ~rcmpt the uspr for any 
D I set ~ot in this ordering, 
1ks syst~m can co1.tai.n only one mod21 at a timt. If ihe 
system 31rea(!y cantair,:; a motiel, the us~r must deleta it, using, 
Interkrctidg 22ani~gful Exaress'ions 
2. -- 
7- 
------ --- ----------- 
"he comfn3n11 2NTZF 2 starts tb~ lrlter-~retation of meacinqf ul 
e~pressions. ;he user is ~rcrnpted for a meaningful egpression 
and th~r~ far a pci~t of reference (if usinu an intensional model) 
and an initial variable assignment (i.f the expression contains 
€tee variablcsl , The system interprets the meaningful expresion 
with respect to kh~ current model and the yivan point of 
kaference and varlabla assignmart. 'Ihc user i then prompted for 

are 31~0 available* 
A second rncati103 of qivinq a meanincrful exyrussion is to 
entar PF~T'VWUS thereby [;la kinq the previous expressioh the cunrent 
0112 This allows +he 11ser to, qet . out af INYEfiP, change the 
modrl, inn then rept?at the int~rprrjtatior~ of the same axpre?;sion. 
Also, if the txpressiori is syntactically incorrect because of an 
undeclared luqical constat cr variable prefix the user car mqke 
the needed addition and then re-intor prct th'e expression, The 
previous erpr&ssion use3 hy ZNiEbF can also be set by th,e 
auxiliarvm furictisrl TYFc 111 OE SXP (962 Section J) . 
A third met.l:od invoLvcs UT~~J t LLSF systep directly. 
Between commands, a k~owledq~able s can create and name 
s.xyr\;ssicns usinq LISE, 
C 
dese expressions can be enter~~l during 
xNm-- &lhP by giving th4i~' names. Nd~nell c XPLPSS~ORS are useful for 
dcalinq vith r - sxprarcsions: r-xprassions can ba hvilt UP fr~m 
sub-expr~~sictls usins the%tanitart3 LISP functions, or they_ can he 
moaifica tima of oth'er expressions (e .g. by replacinq "$XFKIf with 
t'FI:i3ft). k'amed expressions alsv vdn be easily decomposed into 
their: sub-expressions. This is uscf61 for verifyin? that a 
cKange ic th~ rrrol.lel produces the intehiTed change in *t kl e 
interpretation of that sub-exp~t:ssiori, Names for expressions 
cannot he anything that muldpha mistaken fot an expression, that 
is, the aamr cannot ba a logical co'nstant cr a variable. 
* (se-tq mpl- j (qpotc (tnerf-is u (necessarily- (eqdal j) ) ) j ) 
> (9129E'-IS U (NGiESShhLLY (QCrjPL U J))) 
* (int erp) 
> 
> ENTER PIEAN'INGFUL B.YPZLSs?c?l (NLL = I:@ VORP) 
*mPl-j 
> (THEF:P"iL 'rJ (NTiFS3 A5ILY ('EQUAL (1 J) ) ) 
>' EIPEBSSIC?~ IE ,OF TYPE TS 
> F~EE VAR~J~LFS: SOKL 
> 0 K ? 
-2 
-I+.LI Saving -I.I and --ill.-I--- Gesturi~g - a ----- :!ode1 
?lTSy?.lSF includas 3 facility tor s%a.vi ng and reseorinq the 
internal korm of -2 3aPa struct~~rs. Ths current mod~l is a list 
nqmed 3ODZL; it car, be savd for,latcr use with the command 
(CIttCKPCZNT mo&ol. f ilprarns ?;ODtL) 
This cotnmand uill tarmi-nate the executioc of the program, and 
therefore only oornp1~t.z modcls shauld b~ savsti. Nhgn the model, 
is hter r~stored, char;q~E can ht. finde ogly with the commands in 
th? folJowing sections, 
AFt5r rest0rir.q tnc- prcqram, the user can r.es.tore a sayed 
mofiel dith the :ownan3 
(FSST"I3RF model. f il~r.a~e) 
If the-system alrta8y contains a model, that model must be 
d~leted with the commsnd 
CD'ilEZ'i? FOCLL') 
h;for~ the saved modal is restored because restoring a mdeJ. does 
not completely re pip lac^ a previclls mcSQ1. 
-..)I 
The mod~l can be changed by adaing or deleting functions or 
by modif yinq the sp+cifications cf possible denotations or by 
modifyinq the specification cf4 tho meaninq function F. The set 
of tygrs, and the sets. euf ~ntiti35, possible worlds, moments in 
time, and points of reT+rencr bc chanqed. 
Addition of Eunotioris to t1:a mo3~1 is inif;:i,&t~d by the 
command ACD (or d21iS2) with the cperand !Cl_SLTS (or. D-SET, 
FUNCTICNS, F'JNCT'GIJ, DENC7'IATIC\3Sr of LiENCTk'TXUN) . ThCS system 
prompt ths user for the +yne ~f the  function^ *to,-be enf aded and 
then follcws t&e promptinq sequence used in thg ,initial entry of 
functions into t-bat D - set. The user is then prompted. for the 
type bE the n~xt group of functions to be ~ptered a'nd this 
sequence is repeated uctil all the new furictions havs been 
*(add function) 
> 
cl . p -"- R" 
i TYEL GF J-LZ3ESTS PE ADDE'C (KXL = KO HOKE) : 
*4s, e> 
> 
> +*~*E~~z:EL.-T::G :-~:y;zl;~~ CE' 9 - (c -0 j -. ~~~~~p~~i COC:~~T,C - 
> Xq2Y REE F~!&cTI,)A~ 0 D - 5 ,.TO L-F',. 
> THJ*? IS, F'?Oh P4>INTS PF FEFEFEwGE TO EFl,,~ra, T'T-' '- 
> 
m 
THEY NSLL 3 L H vuuny CF F F~E .THE LGGICAL COKSTRNT-C: 
> J, 3; B, ?;a 
> 
=, 0,s = 1x1, 221 
> I2 - 3 =- [53; HA, 51;. NA] 
> 
> 
- 
EHTEF A FCE .7ZE?:;-Ii; . (4IL = ti0 &OFF) 
*icema 
> ENTEF A KALrJF C,?.. NZL, 29"rFACH AiGULEN';:: 
> fl = K*71 > 
*ma 
> IL = <1,2> 
Functions 2r.a .lelcted fron the modef ,kith the command DfTdTE 
and the operand PUXCTIGSS (or FrJn:C2:OE:, PZKOTAXICYS, DPROTATIOF) . 
Th$ us~r is prompte.1 for t h.? list of functions to he deleted. 
l'he*functions in tnis list mav be ir, any order and of any mix of 
* (delet.~ -f unctio~) 
> " CE' F~TJCT~O~:~ TQ EF 31 LEmI;,T: 
* (set I- men). 
> 5.ZTl-?IEE,~ DZi.E.2P2, 
The specif Icat ior;s of fur,e;tior,s car: he modified with the 
command 3i)OIFY and op~rm2 FU-KC';: 151; S (or F1Jl;C TIOK 
DENOT?,TTC)Y S , CiN0TA';'Ic)E') The system rsquests the name of the 
function to ha mod-i-Z-ied, an4 then 'iia list cf ar-gurnerts for which 
the value of tile furiction is t-o be changed. The sp'ecification of 
t1Qe r.2~ values for these arguments follows the metho4 used to 
origi~all-y specify '*,he values, This seaup-hce is r=lpeatted for 
each of th~ functions to be ~odiEi-2~i. 
* (modify function) 
> EN1?"!zF F'JSC'iTQK TO 8E '.!CDIFIIQ (YTL = FIOFB) : 
*1'3 
> 
- 
HIS .ZLZ:IILNi' OF D -. IAV=IV/IV S . F ~ZOPI D IIC <~,c~=Iv> 
> TO 0 C??=IV 
> TYAT IS, kh0~ PROFLFTIFS CP 1ND;VIDUAL CONCOPTS TO SETS OF 
The specifi~ation of the waning functioa F is madified with 
the command (XODXFY I?), The modZEication proceeds in st.eps: the 
system prompts the uset for a typz and the list of lpqical 
constants of that type for which ti~c va,lu;j of F is to be chanqed, 
and theh prompts the USPL €01: t.h@ new values in th+t same manner 
as in the oriqinal specification of F. 
* (modify f f 
> 5 1YPE OF L9GICAL CONSTA&CrS WIjC5E VALIJLS OF ? 
> FrZ '20 EE ?.3DIF24P (NIL = ?:C >!OFF) : 
* f: 
> Ti T LIZT 3F ",HEX LOGICAL Cc1;S"INZS: 
* ((b n) 
> TH2 VAL3i.S OF, F 325 THEST CObS'PANTE AFE ELEPZNTS OF 
> D - < (Ik'DIVTDrJAL .CCYCE:FTS). 
> 
>, L3GICAL COES5XNZS: b, N. 
> D - <$, F> = [ICzJ3, 1CmEA) 
> 
> POF EKH CON;-TA~:T ^I H~IEF THE VAL'JE OF F OF NIL: 
> i3 
*io bi 
> N 
*ic- na 
> 
G . &Lsii~l gons-qlt,s 
The lorlical canstants ef. PX &re huilt into th~! System, 
Thesa cdnsCallts can t.2 cilarr~sd luzirlq till. initial t3ntry of a 
model, as nlct of fhz (5hlEi. dCPL,L) ccraand, or lat~r vita the 
 AD^, cNlEF, and CELiT3 ccmma~ds~ 
Ourin,~ entry of 3 n:c~l~l, the system first prompts for the 
type, intensi~nlzl or sxter.sionL?l, of &ode1 to be ehtered, The 
system then asks If the built-in consta~ts are to b changed. if 
so, the ~y~ti~[i prt3=nts tila ccnst:rr,t.s subty~e by subtype, and 
asks for irl~tio!is drid additions t each list. 
> 33 YP'Ct M LSN CIiANGi, Ti 35 !:A UiT LL'GIChL CGXSTAIITS? 
* Y 
> 
> ~7 A&J, V'SDEF - : . Cp? 333 q:X!;?:Qz 2F QCiLZl AS SLZAF-AT3FS IN LI5-5. 
8 ' 
> L~)~;;cAL CQJSTAYTS d~ ? PF;: J,+ I.' ..c c., N. 
> o'(? 
*n 
> EX,, - LIST ;IF cCb+,"'Iil,TS 7'2 El CYF12.VE2 FFCX TiiiS LIST. 
* (n) 
> 
;.STor'F '" " 
, .,,, L-~L CF CQi:SI;AgT-IS TC P? ALrir 7915 XIST. 
*nil. 
> L~G~C~I, Si. ,"F TYPE F PFi: J, 3r 
> OK? 
*YS 
After the nrol~l has heFir. snttl~sd, co-nstants are added with 
the command ADD (~3r rXTI.5) rind the operand LCIGICXL - CCNSTANTS '(or 
Lr3GLCAL - A, Ct'NSTkKIS, 2CNSYA?4T) . Th e additiion procee 1s 
subtype by s~~htype, First, the system prompts tor the list of 
new constants of that subtvpe, and then &for the values of the 
maaninq fu1r~ti011 F for those 'constants, 
+ (add conslant) 
> ENTSE XYYi 81: LOGICAL c'ONSTA?ITs TP DL, ADDED (I = NO ;tv;OEE) : 
*iv 
> J.J2GI:C4i CPNbTXKTS OF TYPP TV A5E: FUF, WALK, "'AX*$, FIS,P\, 
> CHANGE, 
> EETAR LTsT 2F ZCINSTKhTS TP P'F ACCFD: 
* (swim) 
3 
> 1 VPLUIS OE F FJE THYSF TCNSYASTS APE LLX?!LNTS PF 
> D <S,V (E50PEFT5ES GF 1hf1~Idfl~L CONCEPTS) , 
> 
> LXLCkL COESXANS: SSI!l, 
> D-CS,Ch=IV> = (Ct , C1, t21 
> 
b. 
9 FOE ER0!1 CiiNSTkhT, Lw-PR TH? VALUF OF F CF KIL: 
> SWI?", 
4~2 
> 
> YSTEE TYPF OF i!3GICAL CP35'IaNTS TO F?e 4CI'TD (1 = NO ?!OPE) : 
r 
*nil 
Constants are 3e1tatf9~3 with the command EELH'TS and the 
CONSTANTS, 
CgNSTANI) . The usGr is yrom~t;.d fm the list of cor,stants to be 
deleted, I-" -he constants in +his iist may be in acy order and of 
any mix of types. 
* (delate constants) 
> E5TCelE LIST F ~a)f;TCr;.i, CPNSSfU?';:S 50 EE ChLXTZQ: 
*(m rise chanqe temperature Pelieve-that) 
> CFLZT;3D, 
> FISZ CEL ETZD. 
> CHAKGL ilEZZTLP. 
ChangLhg bgia$le Pp?fixe_s 
11. --rc- 
A set of variahl~ pretix~s is built into the system, 
Ohqrlqes arc ms,lu with the comman~ls ACU, $N?'EE, CFLETZ and FIQDZFY 
and tile operand VAGIABLE - EFEFTXIC (or VAkZkErLX - PbF'FIX, VAFIABLRS, 
VA51 PDLX 2;' Ff kFFXY St ~FbZFIX) , 
h a9.di.t io~ 1 d~ltti~tl OF vacZab1t. prefixes proceeds as 
tor loqlcdl corstdnts, CXC-CU~ thdt prefixes ara qivan only- for 
semantic types, and not for c-rlbtynes. 
mh-? cbmmanl 1:J?:FY allows thr use5 to replace the current 
prefixes of a type in a single ste~, rather than goin,g through 
the two Steps of addino and deletjnq prefixes, If only some sf 
the prefixes ot a type tire to he chanjad, the list ~f +.he 'newr 
> 
> ENYE, TYPF OF VASIAl'+Ll FEFFIYFS I? E?E FF- SFi (?;:I?= KO ?:OR,7) : 
*<s,<e?,ts>> 
> XtFVIOU5 P: -FIX":S WEFE: 
F 
---.IT.- 
FSTFF LIST OF N3V VASIFEI E rh:r,.f,,c: 
* b') 
I. QineJhyiig tke jcdyl m$ &jt C~sm~or.zn+s --I- - 
Sim~le ?isplays 
LYI ..-.I- -*.I 
Ths basic informatior! about a compo-tept or element of the' 
model can be disrlay~il by enterirg its :lam (wirhout parentheses) 
inst eaJ of ;3 c~innan ,I, For exanple, dnterinq FLNIITIPLC:I 

':h~ com~nn;9 32"-WLAY -w Su'fdLFE - IBZra3 takes as its (arguae~t one of 
the followinu: 9 - SETS, FirKCTICSS, t1:c name of a set of pos$ibl~ 
denotations, or thd narnc. of a p~sslble de~mtati~~~* "he display 
of a possihlt' Jznotatio~ qives not* ozly its specification, hut 
also tha list 0,: runctio~~s i~. which it is user! 3% a valuz. 
* (display - whete -&sea cp6) 
> BJ = 71. 
Auxiliar~ Commands 
J* -------- -------- 
Dis~lay the comna-iids 
-.I.--.) .-- 111.". --"--I-- 
f be user can 82xasine the ava ilahle system comma.nds with the 
comm3nd DISPLAY ~nd drip of thl-tae operands. if the operand 
LtC:<?.AN1?5 is us~d, thC system wili- pz;i,r,t the names of the 
comaiands, 7he ppcr=in-l CCX?:XACSF.OP~FASDS also prints the oossible 
operands for za~h cvmmand. When the? nams of a coamand is the 
operacd, its possible arguments are print~d. 
forma of runctiocs 
chansl~r tpe out~ul ---- -- -----_-- ---- 
';hG output forma$ for functicns can be changed with the 
corpmand s~s~~-*I'N - FdFYr\T. Unless char.ned by tha ussr, the system 
uses FULL format: funrtions are priritrc?, as sets, properties and 
-. 
relations. ,n the TE3SF fdrmat, tile conversion 3f functio~s into 
sets, properties and relations is dolie only en the top level; if 
the first compcneDt of a relation is a set, the systeh will print 
the name of the function qivinq that set rather than the set 
itself, Th3 third forma-t is QFD7FAL - PFIFS and in this forfiat the 
functions a re printed as sets of ofdered pairq 
(c'arqumt?nt:, value>). Tile COB~~C~ prompts +hg bsur to enter the 
came ot the nek tormat, 
Checkus L& &y&e of 2 _o?i~_rs_s_ig$ .11--.- - LI 
The well-formedness and type of an expression can be ch~cked 
with ttlc comma1111. "YPS - (3F - SXP, "te prdn~ptinq dont by this command 
4s the same as the first Far? of T:4TEE-P. It alsd shares the 
P3EVI9U3 expression fzature with +LhTE?P. 
Fesettiny th~ pri~t 1i.m 
-MI----- --u c---- ---- 
Tf the user ahnormally ter~inates INTFFP in the midrile of an 
interpr.station, the characters used in the icdcn ting scheme will 
be frozen in the print line, thqt is, they will be printed out at 
the beg ihning of subseauer, t lines, To remove these characters 
invoke the coamand R5525- FFIt~T-LISL. 
This session pdrailals the development and use of the Simple 
model given in ~riedman, Coran,.and Warren (this fiche). lp this 
model, there are two entit,ies, JQ arrd @'N, an8 two points of 
reference, I1 and J2. JC 'walks at- both points of r~ference, UN 
walk$ only at 12. In 12, the indipidual ccncqpt for UN has the 
property oi *uniccrnkood*. 
& 
tsrun *lisp t=, 
~stovs ~nterp) 
* en t ex. npd44) 
'I" 
> a3 YOU w;l~~ AN T,EITE:~~S~:G~~.L, rror!~~~ 
"Y 
3 DO YQU WISE' 'IC, iHAhtiE 4 rEFXUL:'? LOGICAL CONSTLNTS? 
*n 
> 
> F3EfNCEF: , COX?>P CCr!kiOfin FE USED AS SZPPAFTVi*.S IN LIS*TS.. 
>" I"NT?r LiS"1F i,,,T;ITPELCI) 
*(jo un) 
> 3YTdL LIZ% OF PiiSSii)I.3 kOFLI'!:. 
* (here) 
> rdNT7F LIST F 0. 3h3 I, ih' INCLEASXhG CEDES, 
* (then POW) 
> 29IN':S I? F5C (TYCICES) : 
> 11 = <iil;.sF:,-~~~> 
> I2 = <f~<rnY,HO%> 
> 
> ****iCETTLI?IiG 2 CF C -. <C % ,5> - INDIVIDUAL CCNCFPTF 
> TIiEY ARX FO!JCIIJKS FCC:! D - I 13 D - r,, 
> TYAT IS, FF3E PCINTS GFi FFFEFE&OE LQ! ENTITIES. 
> TrLY KiLi Pi: 2Iil'. VALUES OF F ?3F IEie LOGLCXL COKST4h'TS: 
> J,* 3, B, s. 
> 
> a_$ ~II, I%$ 
> C - E = {JO, 3x-j 
> 
3 ENTPI; P4Ar.z. '*" FCT ,. I I. (KsIL = KO XCEZ) , 
5 7 p' 1. fl' 
*a0 
> 
-- 
z?l+TliFl VALUT. 93 SII FOF EnCF! AEGUE5f;';': 
3 I? = <I~~FL,?:HEY> 
*jo 
> 12 = <HEEE,VCW> 
*jo 
> 
-I- -7 
LC Eh~r2Z9, 
> 
> Ei;IoF 3 C LLdTTzh'7. (E'ZI. = HC P!OirE) . 
da 3 
> EhTER k Va&Ui C5 SIL FOE EPCH kEGUCE53: 
> El = <HEFi,I,Nf;:;> 
*un 
> I2 = <HEFE,NOW> 
*u n 
> A? EKTEEED* 
> 
> EhT3F NAPE FCF 3LEfiFN'f:* (NIL = NO R0FE), 
*nil 
> ***#I2 <S,E> * INDIV1:DUP.L CCKC9PIS 
> ~~?IAIK: D - 5 = 1 I:) 
> FANGE: " D_r. =, $JO, r~$) 
> A3 = [<TLJO>, Yf2,JC>) 
> ~3 = [<2l ,TI?;>, <T~#UN>] 
> 
> ****ENITFiE;G T:iL. FUYCTIION F FCC *i&GICi\L CGBSTAETS OF TYPE E 
> THE VAL G F FCX; '1''fiESE CONSTAKTS ALE ELEEZNTS OF 
> D-<St F> ,(TNPIVID';TAL CC'JC!?r"!:S)'e 
> 
> LUC~CAL CQSSIA:ITS: J, v , PC -I 0. 
> I2 - <5,F> = (.aC, A?) 
> 
> FOF E4CE CJKSTX:??, !YST?F* THE VALUE @F F t'T NIL: 
> J 
*a2 
> .* M 
*a3 
> E 
*nil 
> N 
vnil 
> 
> +**+F6;Eh IEG L OF C,CN=&V -- SET5 OF IE31VID'JPL 
> CoYcEPTS 
> TYEY Ah3 F3NC~IONS FkC3 C <S,Y> 'IC O TS, 
ba 1 
- 
> TtiAl IS , F63K ISFIVIDUAS C3?!CLi?lS- ?\j-~i UTE VALUES+ 
> TH5Y WIZL I3X t:HE OZ:;CCATIOh'S. QF 1 LGGiCRL CCYSI'ASTS: 
> IYq?;, Wi)E,hS, PXZK, FISH, PYK, U?~ICCEB.; PPICL, I~EPEFATT~FE, 
> FUh, WALK, .rfAIK, FIST, CHANGF. 
> 
> C -<s,w> = A, 43) 
> D-ts - =. (11, 11 
> 
> 
r .- *- -- 
A FOT ,Ir,,:,t~?. (NIL = KG KCEE), 
*bO 
> 3 A VALUE OK N'IL TCR EACiI AFGU?:ZKT: 
> A3 = (<.Ll,JCI> <G 80>) 
*'I 
> A3 = [<It,tTlj>, <I2,Vf;>f 
*; 
> 55 EN'13hED. 
> 
> C~TPP fi4:It: 7Cf ;Ld\'YlLI. (SZL = NO ?OBI;) . 
*b15 
> 
w 
tY"Zg A VALLTJtu CF NIL FCS ZFCH AFG'JK5h-T: 
> k = {<Ii,JC>, <Z?,JC>) 
*I 
> A3 = <IN <Ii,vS>] 
* 1 
>b el5  ken, 
> 
2 ENTFF N'AEB FOF SkEEE+Z. (NIL = NO EOGF). 
*nil 
> ****D CN=IV - SETS,, OF IPIMVTPUAL CCNCEPTS 
> COYT~N: c <s,r:> = (~2,~ A?) 
> FAYGE: ' n-TS -... = (,?I 
> B = (t) 
> ul5 *= A, A39 
> 
3 * ELEPV2N12S OF D I <C,ClI=IV> FE;OP.d!3T~ES OF 
> ~NDI-VJD~JAL CON~EPTS 
3 TIiEY Ahk FUNCTI!WS 0. I> - S TO t) CN=I.V, 
> rs, F~OK POIN:C OF IE?EK~E;NC~'TO SEX CF IKQIVIDIJAL 
> CONCEPT$*, 
> TAEY WILI PF, 7ti? VALUES CF F F3F TItE LOGICAL CON$'?,.\PTS: 
> BAN, WU~AN, PAFK, FISH,. FLH, c, PRICZ, IEE*~:FBA~TJFE, 
> FUN; WALK', TALK, FISL, C'FIAVGP. 
> 
> 3 - S = (11, 32) 
- 
> &CN=-V = (Dl,' "5) 
> 
> ~XTE~ KA5F FCF ELEb:F,?.JTs (1JIL = 1;n tic&?). 
*cG 
> EYTb3 'A YALUE, OIt NIL 0 EACH jZiiGU?IEKc'T: 
> 11 = <HCFL,~HE.N> 
* b0 
> I2 = CHEE.S,NCW> 
*b! 
7 NO SUCH 2LEMENG's E~FIAIK. 
> (1:HFCKG .~~AHI'; 20WILL BE iNTF21,3 LAlF; 3-d.NTEE yn rd '; 
> -2 EYNCTICN AS USFPECIFTEAF FOF ALL AFGtIMTfEJTS) , 
* 3 
> THIS PLZJ5PKu2 OF D C?!,=ITJ IS P F3!iC'?LOEd FFCE C <S,E> TO D-TS, 
> THAT IS, FFQP ~:.;C~VIDI~AL CCKCEP';~ TO f~gzg VXLUES. 
EK5F A VALUE OE NIL FCF EFCY &FGWEKT: 
AL = {<L"4.t30>, <fZ,JG>I 
> B'O5 =* CAP, A31 
> bl = [A31 
> 
> ~ESUES SPZCL~~C~TION CF ep 
> 
> C" &NTESTD. 
> 
> 3Nt.l$F GA:!'r. FLF FLF?lLKT. (NiL = Eun iYCFE)* 
*cl 
> ENTEi? A VALUL ?F EIL F('F FACV fihGU?ik;XT: 
> 11 = fi2FI.: ,TIiZ,V> 
*b15 
> 
1.3 , 
,c - <t-IEFF,NCW> 
*bIO 
> NO SUCH ELi;?:EY%. LXrIAIK. 
> ("t*WhdNG NXt!T; 2-HILL PsF :dYPCEi?~3 4 3% LNI'PF NOW; 
> EX VJhCIrO?! $5 11KSFECIFiLC FOI. ALL AFGUISfSSTS) , 
+ 2 
> Cl' E?ITESiI'* 
> 
> F EAI..? FGZ rrxi-s~.~ (rrr~ = ~cl XCFE). 
% 
~42% 
> 
3 ,h 'm- ,L" V,3LiJESOi? YTL FOS E3CH kFGU?i2hi: 
3 11 -; <H'CFf',::tjr?;,.> 
*a 
> 2XPSCTZJ2 7,: ? CF TYFT C 1;=IV, EUYFOI'SD 
> 9N FLP~ENP OF TYPE (5,l.b. EN'TC7 &SW NAIF. 
* bC? 
> 
. . 
113 S'JCFI 2LFYTSLw L X P Z .ST 1; . 
> -4 4; '7-jt',TLi F.1 ESTET LC L ; 3-5h'IEF- *Vb'?'Su'; 
> Fm FUhCIIGa' rJl:SPFC3FIbG FOE ALL AXG"J!FNTS) 
*I 
> ZSTXZ," L'\3F(T LC? KA!I"C:< 
* b: 
> I? = C:j,iS?, SCW> 
* b.5 
> YO SUCH FL>>iEX,.. 2XPLAZK. 
> 
--? - 
(I-.WKF:;G $$):F.;' ~*-N,LL EF EYTT.;i.LD LAZ35.; X-E~IISF. BOW; 
, t -1 
3 2 FIJSCTIC3 rJN?FFCI:FI+Z FOS ALL AIiGU5ESTS) *, 
* 2 
> 
-F,- - 
CC LNIL-~LC~ 
> 
> ZSTLE Sk2-2 PC? 3L3?42Kr, (EIL = fIChZ). 
$nil 
> %***::~:.f~~l:a rj!;SF:c:i;lFr: EIEh'T$l\ITS j, pj. 
> 
> 
-ha+\ 
TFIE3E L OF,-& - C?a=IV FFE i.'Uh'C':I~?;$ FF;h ij - <S,?> TG D - 3, 
> TY4.I;: 15, FFG!: i';:CZVICrJl'L CCNCFP'iS TC IFUIf-i V.3.LUr"S. 
> 
> D - <S,i..'> = -431 
> 335 = , 1) 
> 
> iNT3FE13!; Bq 
Y ~t DE;.T3R VALUE OF Nil FGF ~RCH A~GU~EN~: 
> ALP = {<XI ,JO>, <Z2,dO>) 
*I 
>" A3 = [<I?,UNY, <v,U621 
+J 
> Elb ?NSoFi?D, 
> 
a ENTEEIY~, ~5 
>* '~JTSR A, VALUE' QF NIL FOF8 EFCH XEGU3ENT: 
> Ac = [<TI ,LO>, TIi,JO>] 
* 
> 43 = {C51,UN>r <IErUt'~l 
*I 
3 ~25 .~PITEEEC!, 
2 **WRPMLNG - F5 LS :hi FA?E A5 B7 
> 
> **** C - CLJ*-IV e* SZTS OF INDIVICrfAL CCMCFPrS 
> DO~?A;'N.: D_<S,~> = fAc, .A31 
> FXNGL: Ui.'TS = {", 'I]. 
> n, = fi 
> B.15 *= [S\-+,:, A?) 
> 'B1 . = . (A3). 
> 131 4 ,= .(A91 
> ss = 143) 
> 
3 **HbF'T\TING - ', C - CNrIV CQKTAZNS EQULVALEN1; ?LSKENTS. 
> EQUXVALZNT 3L@?KTS:. El, P5, 
> 
> **** C <3;CN=LV> 4FFCPEiiTPHS OF -l.l~CTVIDl!AL COKCEP'IS 
>. EN il-5 = {I?, I21 
> EA N& : I D c C:J=IV = fPQ4 ,C.15tr I31 B li . E'.) 
> C' j<II, [I>, <Izr {A3)->) 
> Ch [Ecllt, [Au, L3) ), (12, [F.tj)>) 
> c2 = (<I+, 2, <IS, {\?I)). 
> 
> ****ESTFE.IWG qti3 FU?~~TXD~ F FGF LOGICAL CONSTANTS OF TYPE 
> CM=IV 
> ?HE VAL~ES OF F FOE THFSF CQhSTfi-KS'S Ag?? ELLPFKTS C? 
> I?-<S, C%=IV> (J3OOEEFL-ES CF Xf:DZTVIDUXL COKCEPlS) ,, 
2 
> iocrcn~ COHS"~?E;IS~: A,. , FAI K, FZSH, PEP, UXICOFX I 
> PRICZ, I.E~PEBA-~'UF, r.11~. WALK, TALK, ETSE, CHALGT. 
> D-<S,CN?IV> = {CJ, C1, C23 
> 
> FOP EACH C3NSERilTr YE THE Vj:LUE GF'F CF NIL: 
5 EA6 
*nil 
> 'alOt<AM 
*nil 
> P A'E; iZ 
*ni'3 
> PIS ti" 
*nil 
> TE?I L? E FATUFT 
*nil 
> " RUN 
*nil 
> WALK 
*cl 
> TALK 
* n i-1 
> R IS c 
* ni4.? 
> CI.IAh'CE 
*nil 
> 
> 
- 
****1(FTT? I?;\; L 8'1: C Zfiv=~vl/IV #- FELJT-ZONZ .(TH 
> EXTE'NSICN) as?- wx:~ ;~r?~v~r OIL car.cpprs AKC EE.OPEE.TI~P CF 
> INDIVIU$4L COSCFP'IS 
> TBhY Ah E FtlVC?i@!JS 7FO:d. D-<S ,CrV=IV> T3 La - CX=IV 
> TtiA? I, FSCY PLCFZFTTES- Qn I~?iIIVXCUAL ZQKCPPTS '20 LCETS OF 
> INXVIC~TAL ~O~CEPTS. 
> PHFY WILL BZ-THS'QZFiCTAPICES 133 THE L3GICAl CGNSTXK?S: 
> iiAPICLY, S$JWLY, VCLU?'1RFILY, ALLEGECi,Y, TE~;-To, wT-C~YTO. 
> 
> D - <S ,Cb;=;V> = {C?, Cl, C2) 
> D - CN=IV = 8, 315, B'I, F'?, P3) 
> 
5 dETXR 6A\:2. FCF ;"iS:.hh.E. ("L"= KO ?!C.F:) 
*3C 
> , A VACrJE i>i\ UIL, E'cF t ICY X3LU:.CS?': 
> ct. = {<I1 ' , I %,3].>) 
*nil 
> il = (<:I, I:-, a7]?, <I;:, {qr)>) 
*b12 
> YO ~YCH EL?:-:E&T. EX:~LAIK: 
> (1-aF;Oh'~ PAYE; iyWT&k EE <Y'TFFIi) LE~S, 3-ZNTFF GOY'; 
> 4' FYElC,TIOS ;.5? rlN-CPECIFIrD FOB ALL ARGUUEE:TS~ . 
*2 
> 
-* - 
LL = {<I?r [])r (Tir t,k31>1 
$nil 
> 31 s~~L~u~L. 
> 
> 
\- 1" "*- 
kt .,F EAYF FQ: EL: ST; ~NIL. = sc :ioFr) . 
*riil. 
> . +: Uy .5?Pc;FIzD ELEZ'I., Is' 6 12, 
> 
> D <S,E> = [WC, A3) 
> D-TS - = 11 
> 
> * -El2 
> ENTSP A VALU: OP NIL FCS EACN AF<XI~!!!:NT: 
> Aor = {<91,JO>, <IZ,JO>] 
* 1 
> 
'/ 
k3 = I, <12,UN>) 
*3 
> ~12 Fwresr9.- 
> *rWARNINl; - 131; 15 THE SEFF. $5 I??? 
> 
> *t*aC. Cl*=IV - .3i.:TS OF TNtIVZEUAL CQXC?rTS 
> ~32Si;h': D-<.S, F> = {Ar, A31 
> FANGE: D - TS = [$, *1] 
> B; = {I 
> 515 = {A), ~21 
> bl = ~n33 
> Ell, = t.4 '1 
> ~35 = Ck3) 
> PI2 = (AS) 
> 
> **WAFKING I- C-CN=IV CQKTAI!IS FQUIVALENT FLEMPPITS,. 
> ZQUZVAL'~NT ;~LL~I.~z;:NIJ: h31 ; ~5. 
> XOUIVF,LLf;T EL3KLKTS:; -E~Q, E12. 
> 
I.$ ****C - -3AV=3V/IV • - FLLATICIFS t9'K EXTEh.SlO?l) BETWEEK 
> INXIV;pU,L C3LCTPTS kh'3 PFOPTF7II.S OF TEP~VSDUAL C~NCEPBS 
> DOYAI?1: O - <S,CN=IV> = Cni, C21 
> EANG~: U- cr;=~v = (147, a's, et, 5 135, ~121 
> 3u t=: {< I), CG? r <{A"), *CI>, < { C2>) 
> 
3 ****E?jlE5ING .ZLkNtS?'5 QF C <S,iAV=IVjI:V> - 
> ~-PLATIONS~I$-LBTEE:SIO~; PPS.~%;~N ILDIV:LUAL CONCLETS AND 
> PROF?BTSSS OF INDIVIDCAL CCYCE#IS 
> ?HEY A FfJMCIIdNS !?FOP: 14-S 0 C-TAV='LV/IV,. 
> THAT 'IS, SQE. POISZf OP FEFP~ ZKC~ TO '3 ~LAPIOXS (IN FXT&$SION) 
> DETdEZS 15 DiVISr)AL C3NCEF'IS FWD 23OPEF YIFS OF IND~VIDUAL 
> CO!iCTPTSi 
> THZF W9LL 32 3H5 VAl,U+,S C+J F F9E IHZ LOGZCAL COKSTANTF: 
> FAPiDLY, SLOWLY, VO~UhmAF.ILY, ALLEG~~LY, T5Y--TO, XICH-TC. 
> 
> 9 s = [Jt, 121) 
> D~IAV=~:V/IV = [D:)~ 
> 
> fXT5F l;AK"-" FCF ZL7i.,L'fJ'f. (Nli = SC l.;G&?) 
*SO 
> 
-m .- 
Ehrat X VEPE 03 !JIL FOlj EACH AhGUMtST: 
3 
.T.3.-? fp 
I1 = <nsr,, 
*a9 
>' 12 = <H+?FZ,NCW> 
*n il 
> - 1 t!!';fFLD, 
> 
> ENTZF, NPXE FOE' fLEL;~NT, (SIL = SO KObE) , 
*nil 
> ****Dm<!?, .fi\V=IV/IV> - FlF,'LATICNS*3S:S*IKILNSIdN BETWEPK 
> ZNDIVIDUAT# CCNCZPTS Ah6 PFGFEFT1:LS SF ZNL'I:V2DUALd~ONCEPTS 
> DQH3N: f) S = {I 1; 12) 
> FF\NGd: D-IAV=IV/IV* = (D?) 
> s: = I,, or>, A CI>, < c;>)>, (12, 
> 
> ***+FNnFZNG ?tii WXC?ICh E FCS LQGLCAL t'6SSTkN17S aF TYPF 
> IR~IV/IV 
> ?tit VALWbS OF P FCF; THEYE COSS"I'4BT5 AFE "LdI-:SN'rS Cp 
> D - (5, SAVrIV/ZV> (FdLATf:CKS-T,l.~-mIEu*ISNSLC~ EL lNDiV3bUAL 
> CCNCSPTS A4C TT2PEFI;l.S 17F ISCIVI~~TAZ CCNQPPTS). 
> 
> LQGLChL C?hSTAS:?: IArTDLY, SLCWLY, VJLGNTASTLY, ALLEGEDLY, 
> ?3Y-?:O, VZS!i=-TG. 
b n - <s,r%v=~v/m = 
> 
> 
a? r P 
FOF EACi! CO:iSTXNT, ;8,rJn THE VALIT? OF F'CF SZL: 
> i? XP? GLY 
*nil 
> SLOWLY 
*20 
> VOLUNTA3ILY 
*nil 
> ALL?.GEDLY 
*nil 
> TFi Ye* TO 
*nil 
> UXS i3- 22 
*nil. 
> 
> **$.*EP;r,lzFIfi:; ZLSELZli*;1$ J r TE - SETS cF Pp3FEgI;ES (IF 
- 
> INDIVICUAL COKCFPTS 
> ?l.f.IZY A?? FU,"ICTIGNS PECK i, <S,CS=IV> IG I) 'PS, 
- 
- 1111 
> THP? S, FSO:: Pi;OFt,FTI?S CF I,SLIVIDrJAL CCNCEPTS Td T9UTF 
> Y&*tUZS, 
=r 
> .C - <F,:E;=';V> = ICY* -Y 0 C1, C.2) 
> E - TS 3 (", lr] 
> 
> 
-1 7-7- 
,;t. WA?'E*FC' L (?:I1 = 210 30FZ) , 
*nil* 
> 
> +**+ r;j- A H~C ,..-hG 7 LLt,\lki;Z'S @F 2 - < 2 > F; OPCS,~TIdYS 
> TACY A32 FY3CT-38 ?EO?! 2 5 73 D is; 
- 
- - 
> THAT TS, FFO:. PCIULS F hEFEFft;CE,Y CTFUTi! VALUIS. 
> 
*nil 
> EYT~Y XDEL T"'JKIEATEP 
> 
* (display vodel) 
> THE MQD~L TS; 
> 
> ENTITXFS: (JC LJY) 
> 
> POSSTRis, WGL'EPS: (HYPE) 
> 
> YUKZNTS I13 1:: (XE1EN NCW) 
LF%**C <Sax> INDIVIDUAL CC'KCEFl'S 
BlP = tiit) 
~2~2.4~" AS F VAC~JE iti Frl~C110ES: Cl. 
> cr = 1-1, , <12; ln3) 
> CI = {<1I, [A,, A3)'>, <I& 1P9]>) 
2 (-2 = ((11, 1, (12, (A31>1 
> 
2 ****I3 DIAV='TV/IV nw FZLATICKE (Xh EXTbXSICPi) BETWEEN 
> IN'DIVI~UAL CONCXPTS AN3 PP0E'FiI;III:S CIF IhDIVT3UAL CSNCFPTS 
> DOi9RT.N: D - d3;\,C'N=lV> (C', C'It CZ} 
> RRNGd: D - C'N=IV = B F?S, 57, , P5.,B12) 
> 
> ~1- = [<{), C'>, A C1>, <{I, C?>) 
> &;l,P?AES A E: VALT13 IX FIJf;CTIOli%: E.3. 
> 
> ****rlF - <St ZAV=2V/dTV> I* 55LAfICNS*.aXS*IE3,1b~ST~h; FFTWEXN 
> XFJCSVID~AL C~XC*~'PT*TS RKC FF3PFKC;~I QS zrrrvvrcaAr earscwrs 
-4, 
* - 
> Dc?AIN:& C -.. S = CAI, 12) 
> FANG'L: 9 - PAV=IV/IV = {'I1) 
> 
= , (<.{)*, c >, €@-I, 21,' , C",,)), (12, (3)) 
> 
> ***~LoGT:cR'% CC h,r';a::Ys: 
> TY*E S: J, 3, E, 3. 
> "YE EUNIIV: - 
> S!.IE?YPS i3Sz >!Ah, k'C?!'ANr EZIFK, FIS:I, i"Lh, UN3:CL?5htr PFICE 
> 
9 1 I, 
.,A EEi AUUF. 
> SU9,"YFZ' LV: J, GALK, TALK, SISE, CHAhGZ, 
> TYFF 37 V=IV/IV: 
> SU;31YPF ZTV: F"nTJi3LY, SLC,%LY, VCLiJKT'qFZLY, .ALLEGZDLY. 
> 5UBTYP'i: IV/ZV: ZF Ye TCI, I~ISLIP TC. 
> TYPii IV: FFSD, LdSL, FAT, LPVS, CAT?, SFEil, Cq3NC?XVE. 
> 
r- 
AYPZ IAV/ZF: EN, ASCY'I* 
> TYPE X V/IS: T;~LTEVE-*? t!i.T, FS52FT-*THi'=. 
> 
> i F'oJ&Cr'- AA311 (Xf; CFCT F?4 FAZF C) hS 
> 7 = <,A <:;,,a ?>,* <rrNICC';;Ntir>, <WALU3C1>t <S+iu'ULY,E?>) 
> 
> *V**VASIABL'~: ?Z;FF:X:-:': 
> 
- 
TYPE 2: U, V. 
> lYPF <T,F>: Y, Y, 
> TY?? <ii,Zh=IV>: F, c, 
> 
3- 
TY Fk,(S, , <I,,-TS>>: 1,. 
> 
h 
IYE"S,T5>: 3. 
> 
- 
,YPi <Y,<L,<:.,'I;>>>: S* 
> TYPZ <S,<E,<<i ,?S>,<T,f :a>>>: G, 
> TY2E (5, TS>: s. 
> 
> F3P JF: \,CD.EL 32iiCFIPi:TJZbl: 
> 
*jinterp) 
> 
> 
7 -y.l-?-. 
- .- 
?.c" 
3 Ti LAIZFZ~~I@?; (yzi = YC ?!".c<;L : 
* ; coinen+ - J~~Ec+ t rans1dti.c; ot ai~t~:!. walksM 
+((lambda p ((~xt p) (irt j))) (int walk)) 
> 
- 
3X???Z5iC!< IS GF rYPi -q .. Cr 
> h? EE VXSIABLCS: YOKE 
> OK? 
*ok 
> 
> 8S'I";F PQSF2OO FEPLi. E'aJC2 (NIL = NC PCFP9 : 
*il 
> 
> IKITIAL VaRIA3EE ASZ TGNEENT GI: NIL. 
> COXPUTIXG DkEIC'TATSON 0"E" ( {LAfiBDA F ( (ZXT P) (INT, J) ) ) (INT 
> WBLK) ) FOE 1' AYD GI 
> : WO?a&TJ7IIT;G D3NGTA1:kO:J CF (LAYBBA P (EXT P) (INT J) ).) 
2 : FOE 71 XNP ti1 
3 : 2 *NiW VA~IAFLP, ASSIGEINFMT 2: PzC'). 
> 
a 
O : Co2,TUiIN;; QENCITATION ~l?' ((TXT P) (IKT J)) PCB XI AND 
> : G42 
> I I : CQXTUL'ING L,SNCTFTIOM OF (3x7' P) FUF I'I AND ~2 
> 
. . 
I w : ~F,~~STATLO~T OF P iS f, = ($-I?, { > <T2 (~"ji)] 
> t a : DBYCTATICN 25 PC* = [I 
> 
m 4 
r 
: Cdi.tPrlTTN", DENQTATTON dF (IRX) FOE 11 AND G2 
> 
.I 
: DENCXAPIOE: IS A ' = [<$I ,J0>, (12, JO>) 
> 
. 
- : ilEtlO'2AlION IS 4: 
> * : WN3-l VV~IL~BLL ASSfG?;P!EY'I S3: F=C1. 
> 
m 
t, : 9 GF;1KOTATICN 01; ((?XU>) (7 J,)) FOF 11 AN3 
> 
: G2 
> : COi*jFUI'iNS I'EST(7TPTION OF (5 P) FOE I3 AND G3 
> 
-. 
a . : LESOTAZ13El F' P IS C = [<XI, {A\ U)>, (12 
> 
4 
* : , ~3~1 
> 
.I 9 
e : ilENCTATIi?S IS DlC; = (XJ , A31 
> 
0 9 
b : co::.:r::~~~ DENCTATIGN C)Y (IKT J) FOF 11  ED ~3% 
> 
- 
a 
e : DENQT?IICS ,S AC* = {<I4 ,JO>, (12, J@>) 
> 
0 *-IC+'1 J 
* : ~LS~~A~ICEYI 13 1 
> * : *Kt3 VP'rZ9EiE AS5"IGE:?TVT Gtl: P=C2, 
> 
: CO8PUTiNG DPNOTATICN OF ((EX? P) (IN2 3)) FOF I1 AKD G4 
> 
1 0 
. 1 : C9t<PU21S"C; L'EP1'3'?AIT(.lh4 c;F (LXT P) FOE 11 AND G4 , 
> 
e * 
. : IFNOTATION GF P IS C? = [CI;, (I>, C12, (P3]>) 
> 
* 
: DE:~012&13:0N IS Ft = [] 
> CQ?:PhlI:I.NG I:Eh'OTATT:C?F 3F (If;: J) F3F 11 AND G4 
> - : 3EbCTAXGh 15 A3 = 11 ,JO>; <IZ,YO>) 
> . : ilEk.(C3ATZilPI iS 
> 
0 
: IPENOTAIIGN L7F (LA?!ECA ? ( (1 F) (IST J) )) IS {Cl) 
> : u I5 0 Ah Zl7VEFX I:; i :$CC.EL. 
> 
r lr- 
. h . XAKF FO? TlJIS FLLZENT 111 C - TZ: 
* j*1 
> : DEHCTAIIS~: :S J"l = {CI) 
> : CC?!PUTING 351;i0i> Zi(>N OF ILL*, " kALK) FOE INAND GI 
> :- 1)380TPTIOE; TS- C% = [<I1, v:, A33>, < (A".)>) 
> PEYD'IAIZGN IS 1 
> 
> 25 2OXEJT OF* SEFki ENCF (KIL = KC ?{Of;p) : 
*nil 
> 
> 68TiF ~~'~ANIsG~uL. EXFF~SSIC~ (5;L = !iC p:~pF,): 
;comment - rtdliced £om of "john walks'' 
'PY 
> 
> ??;T;:F PCI:;T OF FaFF~FkNCL (&I1 = SP flC1:E) : 
*il 
> 
> :Sf LIFL I X2kTGS2kh'T GI: XTL* 
2 . I:kK?TA?13:9' q!?F (YALK, (TNT J) ) FL~ 11 RND 77 
> : D5WCTXXIU3E; QF WALK 39 $15 = {AC, A3J 
> : ~w. '2 1 P.1'1 7,"AZi&4:: QF [TNP J) XC^P 'II ANP GI 
> 
- - 
: IIF:NL?PA';TOX -3 XI = I <l:,J0>) 
> ' 1 ,'5 1 
> 
> 1?u'"1:5 SOT ST LF FL'FEEFSC5 (3fL *= KG 2CE;Z) : 
*nil 
> 
> 3 ?~":KN1::;GFFli LZSEFLSSICS (SPL = b"G i.:r35E) : 
4 ;comment - ceduc~d form ot ttjciin walks sloulytl 
*,((slowly (int walk) ) (ict j)) 
> "!?XPiiES5IC:< I5 OF TYFi 15 
> 
'1 ... -- -, 
1s.t~ VA~145Lt5: ?;Ct,E 
> CK? 
> 
> 
P;\Y(*r7-. 
1 1; C FkiL?PKCE (XiL = 52 ?lG5L) : 
*il 
> 
> J L vF,SIAPLT AskI(:Kvr4'T .. 21: 311. 
> C CL\I\~A"LC:; OF ( [SLPXLY (2 68LF) ) (IHY 3) ) FOE 
> f"rA?ir, GI 
> : CO?PF.JIZ>c; I'Zb2?-;\TlC's CF (SLCdLY (IF? A)) FOF I3 AND G? 
> 
I bEP;O!:A'I':I2 J3F 2LQhI.Y 45 6: = 
{< () , tt'>, < fA.7) , C1> 
> 
. < [) # C2>) 
> : CO;:i'3=1I?:G PZRS"I"IIOK CF (L3T WALK) FJF 1 AKD G1 
> 
. 
- 
I A ,t. C-? = {<I?, [& *&, A2) >, (12, {A:] >] 
> 
w* P - - 
. ~~~<C..~-LCI?~ As YL = {A:) 
> ~~~pg~=~~ ~:-\!,-J;A- 1~9N bF (Tdi J) FCF AYD GI 
> : D,ZN3'IA,TI13 I-" A = 1 <12,3G>) 
> C <YOTAT IQti 5 1 
> 
> 
- s- - -r% I,-,- 
2NT2q Pi3IST CT . (1411 = ?1"S r",C?E) : 
*nil 
> 
> 
. . .- 
CXT-;E A? 7 el!?~ ~SS;.C?I ( = NC YCFf) : 
*cil 
> D)..L- - ALX* - w t-~,,ya$g: crd 
* (cb.eckpcir,t rnc17el-,r: .? model) 
>ClISCKDDTG: XS3, SOACS=c PXGT 
#sXECUK!)S 77: (IEl*?,T:SQ 
Creating a model that satisfie,. Waning Postulates I., 2, and 3, 
* (enter model) 
> DO YO11 WAK'T ,414 INTEESSOOAL LMCDEL? 
* Y 
> DO YOU dfSiX 9 CH.hE:GE 'THE DEFAULT LCGICAL CONSTAMYS? 
*n 
3 
> FkF3SDr;P: AS CANNO? FF flSGC AS SEPA5AIIOES IN L41$TS. 
> FN'iPP LiZ"i4"F '3NTh.X,FSa 
* (50 ma) 
> EtlTE37 LIZ? CP POFSIbL? WORf,I?\S. 
* VI 
> 33T';Z LIST dF E:OE(ZKT3 IN ~f?"', IN INChEASIhti .CI;DLR. 
* (I 2) 
> POPBTS, OF Fk;FEPE:?;23 (3:TPICES) : 
> ;1 q d,l> 
> 12 = <"1,2> 
> 
> *+**t"E1EJif Zi XVG ELEF"EGmS CF 5, I'h'DIVID'JWL CONCEPTS 
> THEY- AFE FUNCXIOSU TFC?: E S TO D-& 
> 'IBAr' IS, FF.0:. POINIS OF FTF~FFXCE TC 3BTiTI3S. 
> THEY WILL E5 ili3 VALUEc CF F 0 "rHE LCGICjiL CGNSTAKTS: 
> J, ; * Mr 
> 
> E)-S = [I?, -12) 
> D - If;T '= (JO, 9A) 
> 
> 
Tv- 
5NT'IJF :fAI;F FCIE'Xl.tra~KY'. (C:IL = NQ 3CFi.:) 
+nil 
> 
> *EL tLE!?F.;ITS 2F C <S,iS> * G~GFCS~T~CNS 
> 
THFY AT7 F[JII~YLJ?~~ FFOX f - TC D ..I 2s. 
> "THAT TIj, FpOK PQFN~S OF BFFZFZLuCE TG T+FUZti VXLUGS. 
> 
> 3-S = 7 12) 
> D,';S =. I,;, 
> 
? 1 
> EYTLF i XI z~e:ixs\..:. (KIL = hc EO~L) , 
*nil 
> EI4TF P C F 2uSDT.i "T'ETEEIP;A'fED 
> 
* (interp) 
> 
> 
% tt 
PXTdF :ilTA!iINGFLJi EAPF'~SSIOE? (KZi, = NC EOfiE) ; 
* - ;corn-her t meaning postulate 1 for jchc. 
* (there-is u (necessarily L (qua1 11 j) ) ) 
> ZXPFZSSXO3 IS CF TYFt TS 
> ERE5 VP.I;PA@LET: B0:IE 
> OK? 
*ok 
> 
> 
t Pp * 
QN'2t4n PCIN: OF 'ECt,i1 NCF (1;:~ = Kc 2 
*i 2 
> 
> isif 192 YA:L~CLL ;IEsXt;?;?:LST Q;? : ErIS 
> C TI Ft"Si","TXGL (IF (T??F$- ha U i[tbYi:t 5.?XF3k.Y (E3tlAL !I 3) 
> 1) FdF I2 AN1 
> 
I 
* E;ih ~J,5=.?.3~"af 3 G2?, U *\ll"DI 
> : <c::PuTX~~~-.?~SCZA f ITS CF (Nk&r2SS&?ZL4(\t (Z~X.fji3. tf J) ) WQ'S 
> 
b 
: Pf ASP G,. 
> 
* 
4 ; ClP??, (1': T:: \; 2 +,:'Q: ATTlx ,,S C!' (a,?Li&L I1 J) FCC =I7 A?iP 1;2 
3 
1 I * 7 = 
.. I . rh~*"YA:2i?:; a't' TFJC 
> 
t I F 
a 4 1 " VALcy $.'F I? IQ: L~??k~~*9~i~ rb: *%~F~~,b,~?~~ J 
2 
0 v C 
rC 
- • * I + :i: F3-CSI23L VBX"",". AFL: 
> 
I t 
I 0 1 1. - <9,*:bz: = [I 
> 
* 9 9 
a * I 
> 
* . 
$7" '''Z ' g;"' 
I . • I .. .L t. he&- V -4 i rJ k L 4w-. 
(* y c* T ,-7 
B 
> 
I * . 
* * IJ 
+ic- ja -P 
> 
R . 
* I h'' "'l;tt iL':xE&", • . z.iLaLAIh, 
> 
0 * * 
. I 
sq w ' -q1$.- 
(1--ti?(":'- SP..??; ,- nITh EE 139E='r;3 efi--?; 
> 
- q- ,- -* \yjw. 4-rT-- 
I 
-. ..\.RC 
- "$ .t--+ ,\ir.F* ?!l?iCf"7'~'E; AS 
> 
I 
r a * I 3???wL.b* + - 2) * 
%- 
- Fee ,,, ,1\EG",km:;F: . 
* 4 
> 
* 
. 
I. 
. I C3VF - TC-JO FESET, 
> 
I I 
. - II I 
I 
> 
1 
* 
Y 
:* DENCTATIGN OF J IF' * JO 
> 
L 
T : DfMOTAXOS IS 1 
> : DENOTATION IS ? 
> DSS3TATItgh IS 'D 
> 
> 3W:Zp ?QTSXCtF 9EEFE'PENCE: (1JTL = NC %CRE) : 
*nil 
> 
> FNTEP ?! 13.4YINGFrJi i?XPFIS$13tN .(?ILL = NO '~:oBF) : 
*-n i 1 
> SNT;? :iaXT" CC:":?AYC: 
> 
> 
* (ad&@ functio~) 
> 
fir .hiI,Ii TP TYPS GF 1;LE"*Lb~S('TO RE AJiIt2 (hiL = :BO --$OF.f) : 
*Cs, a> 
i 
> *'**ENWLIDG ELSNEh'lS OF I: < > I:'lDIVIDU~JhL. CCNCEFTS 
> THEY AIZ FUMCZiCIls FFG? c - 2 3 l?, 
h- 
-. 
>b THAT IS, rs3Y PCIIYTS GF EF"-F~E~!~CE TO i53'iL7iL&Se* 
> TREY WILL 9,~ TH~ VFLKS C.F F FJ~\THZ LOG~CAL cr31s~aa.r~: 
> J, !<, 8, ?i. 
> 
> D-5 = (14, Z2) 
> 9-3. = (JO, EA) 
> 
> 2$-ilZcS UKZ FCI 'ZLE?AEkiT4 ('EL = 30 EOFZ). 
*ic- ma 
> 
- 
3 A VY-LUE OP NIL Fi)R 2 FLH AFGUKZNT:' 
> 21 = a,t> 
fins 
> I2 = <.1,2> 
* ina 
> IC- XA aN2Sr:E 39. 
> 
9 E8TEF KkifE KF. PL2i".l.:Kil. [NIL =b hO NOF';) . 
*nil 
> *x*dD <> - IIDiVIC7AL CCNCEPTS 
> oonk~': = (17, 12) 
> FiAZJGE: D - Z = (JO, EA) 
2 IC-JO = {<II',JC>, <I?,JO>] 
> IC-!<A = I, <I2,M9>) 
> 
> ENTEI; YYP~ OF ~LL::EKIS TC ZE. AGCED (KZL =-II'C MOP?): 
*nil 
> 
*(modify f) 
> 
-7 
rNTE5 TYPE 13F LflGLCAL COKSTANTS FHOSE VALIJZ'S CF F 
> XFE ~~~45. 1CODIFIZC (NIL T bO TORE) : 
*e 
2) ZNTZF THZ LIST OF ZiiESE LOGICAL CPNSTR4IS: 
* (m) 
> Ti VA.L.UF7 QF F FL5 T'FS CCK$TAN%~ AFF 'EiiSKENl;S OF 
> i'r - < > (INi;iV23nJAL CcJKCEF'I?) . 
> 
> LOGZCIc,L L'Oh'S'I~tli5: !<. 
> 3 - <S',E> = {IC~-"JC), LC-K,P) 
> 
> FQF EACH c'JN539hT, - x!:'r"F TIIF VALUE! CgE F OP ?;II': 
> 2: 
~ic-w 
> 
> rhTaF 2 OF LaSGIC>A. 50KST.?h'T5 WHOSE VALIT55 CP F 
> AZcF- TO 3r. X?CiFI:i3 (IJIL = NC 5:CFE) : 
*nil 
> 
* (in t9r'p) 
> 
> 3NT33 LLA:;I?:GSrJI, ZX*T~~S?LC)N. (XiL = >lC XCFE') : 
ic ;commer.z a+anir.q postulate a for pary. 
* (th~y-1s u (necs;ssarily (equal u m)) ) 
> P\SPFF.SSI:G?; I4 3F TYPE IS 
> ?F:Z 'j,lAFiAELF 5,: SChk 
> 9~? 
*0 1C 
> 
u'y7-F 
> LJ-LO PCIKT CF 'iEFr'CEhCE (EZL =- 'PC ZCRE) : 
+il 
> 
> 
T TtCRT 
LEY+ AAL VAhZA9L5 SF G1:- SILr 
> OPT 'A GF ? ! (?:ECES~AF ~LY (PO?!P L U S) 
> )) FCIi 11 RNC GI 
> : r ;i~k: IJ~.F;I~~LY 45511;3::~~~ G_2: U=JC. 
> r ~!:?UTY>IG $';:W?XTIGI~ On (E~LC~LSSAEIIY +(I\IU,AL U ) ) FOIi 
> : ? kND ~2' 
> 
: cb,,PtlTT:;s - -) v 3L:1'3TATICF CF (LQUkF U ) FCS 11 3x9 G2 
.3, 
> : DEPii:3.:195 OF U IC 30 
> . : D~.~C~A;I~YOF v IS .IA 
> . . DZbCIAIION IS 
> : DEI~U~ATZO~ IS 
> : KEN VAFZABLE kE5IGNL':ENT G3: U=YA, 
> : PUG ~~!O~?'?TIQII CF (NtC1;SSkE.ILY (LQUAL fJAk ??I ) F03 
> : 1"iAW G~Q 
> 
: CO;.rPFJT?NG CZ??r',TA'TICN GF (LQUAL U M) FCli I1 AYD G3 
5 
: DZRG'TATICX OF U IS LA 
b Rf:T,PF PQIhT GF F;EFT<E ZNCE (NZZ = NC :3CRF) : 
*nil 
> 
> E?lTES Pig-xBIEiGF1JL EXPFESION (NIL = NC ECFP) : 
rlr ;comment - ueanicg postulate 2 for man, 
* (forall x (ni?cessar ily l'im~lies (man x) (there-2s u (equal x . 
*(int u)))))~) 
> 3XP9ESS$Cli-,LS 3F TYPZ TS 
> FF;33- VARIAELES: NCEiZ, 
> 3K? 
*ak 
> 
> ZNTZF POIk? CF" ZEFEFEKS (511 = NO EOEF) : 
*i 1 
> 
> INITIAL VFTX.~~~P,~~~~SIGN~ENT GT: YIL. 
> COEPLJTIY G 9iNOTATIOlJ OF (FUF-ALL X (X3CESSAFILY (IKPLIE'S ( 
> A X) (2H3BJ-IS U* (&C!J~L X (I U) )) ) ) ) FG6 11 AND GI 
> : *NFW VAKABLE ;\SSIG?:?FEi? 172: XfICeJC. 
> : C~E~IITITG I? CF '('KLCESSAFILY PIU1PLI:TS (F4N X) ( 
> : THEFd-IS U (kQD!!L X (IEI U))))) FCTi I'I AND G2 
> • : CC?PUTIS$ DYE;O:;(ZCN OH (IXPLIE3 (%AN X) (THfP2-IS il 
> 
. 
1 : (iOC4L X (INT U)))) FCF 11 A&D G2 
> . . : CCli:i:rJnIS$ T,EMO.IP.I:OA UF (3AY XI FSF I7 k?:D G2 
> 
I, 8 - .I 
e - • I '2R3 VALUE CF F 
> 
a a # 
a 8 4 I fS ~~~SFECIFI?~ F31 'IHL kFGU?.Sli'i ?:AN 
2 
.* 
a 
- -1 H PCTS~FL'E VALUES AI~: 
> 
1. a .I * 
1 • 1 .J - <s,cn;=rv> = 
> 
8 C 
* w I t* 
> 
. . . 
8 I I ?SIZE TP*f VAIrfX OF l? FCF: 
> 
* I * 
- . . I 3AN 
*PLOP-man 
> 
a ., 4 
- I a I idC SUCH ELEMEN?,. -EXFLXI$. 
> 
0 a 
. . I (3- 3ECsk"G NAE%; L-ilILL'BE Z.:icjXEEE:D LAT.EF; 
> 
1 8 
8 I . 1 ~PLXT~F ?{Oy; ~<NTPF FU8C?-XX? AS 
> 
8 8 * 4 
e t. I ~~SECIPZEC >FO~ ALL AFGU?:E:KTS) . 
* 4 
1 P (".A) = PECP-%AN = {<il, {I>, <12, {I>] 
j DC?IE P FECET. 
I 
I TiIZ VALUE CF ,FT\dP-bAX 
1I.S ~JhSPECIFIEC FOE THE AEG'JhENT 31 
I P,OSS'IRLy V4LUES AEX: 
) II-CN=IV"= {I 
I 
I AP;XE Pf5E VFLFJE OF PEOP-XAl; FOF: 
1 11 = <l,l> 
I '10. SIICH. ELEMEIST, ZXPLAiX, 
1 (5-KFONG NF6E; 2-WILL EE EKTEEED LATEE: 
1 3~fihTEh NOW; ,4-Eki'TEF. FUNCTION AS 
I fJE$FLCZPIFC FClF ALI 4.SGUP".ENTS) r 
> 
0 0 I 
w t . . I 
\ 
> 
t b 
. * ., : Ct,~OTA!XXC.N CF A LS SFPELN =. [) 
> 
0 0 * 
. : I?g?,TT;\TiON OF X I3 IC-JO = .&<.<51.,50>, <T2,J0>] 
> . : I TF!3 VALUE C?? SFTa*i4r;"X 
> 
* 
. : 1 TTNS2LCIFIEC FCI: TtiE AFiGTJ:<F,NT IC-JO 
> w : I "i"H& PQSSZDLE VALUE'S AES: 
i 
9 
L ? : 1 C-"; = ={t, 1) 
> : t : I 
. 
> 
V. v r; Tr. - 
w t : I L~V - r~ TfIF VALUE OF SETmP:LK F(3fi: 
> 
L 9 
). : LZ~JO = iCii,JC), <Ii,JO>J 
* 
> 
w 9 * 
. : I 
- -3 m- 
2; 1 t: e: r, = -sz=- ~,sy 
> 
t I. 
'1. : 1 Gc.h'3 SET-SEN h;ESl;i. 
> 
8 0 
t rn . - I 
.. 
> 
0 
I . : 3ESC;k'TIL'U I I 
> 
C 
1 : CC::EIJ'Xsh?IG DLYOTATLCN ZF (1:H*iiFP~-35 U (ZQUAL Y (INT 
- *- 
> . . : u))) *.FJL xi ASC G 
> 
0 * I 
: *:\i"W' VkE I.AtiLS AES~L;E:\XK? 53: X=ZC-JOi !J=JQ* 
> 
I + 7-7 
- . : CQCI?iIIISG CENCfPT1CE.i bF (LQrJFi S (Ahr TJ.)) FOF 
> 
0 . 
.I (r L4YC G.3 
% 
> 
. m . a 
s I * 2Z1";3)nATcCCS C'F X i5 -C-JQ ,, = {<Z~,JC>, <22, 
> 
. I * . 
. : LJ*'S > ) 
-> 
w . . 
a I . 2C,'E!PUiI!;G EEKCZA21Oh CF (I IT) ?9,Fg I? -\AND 
> 
9 1 . .I 
* I .I : 7-3 
> 
-7 
. I .I 
• I 9 I : CFI;GTA?TCS ?F u i Ju 
> 
* - 9 
e . v : t~t:~'i~'Iih'~ CF 'J i9 JC 
> 
. L 
8 rn : 3",f;i,;P."ICN IS IC-JC = {<If ,JO>, <3:2,JC,>i 
> 
0 b L f""3yp(---r-' 
v *. AiuLi zs ? 
> 
. 
. : BLNC*:.I~I~& 'XS 
> 
. : il_E;iOFTATTC!J IS 1 
> 
t 
: CUiXPLJTISG DFhiCTAT~iCA C?. 1 A X) (2HEFFmi:S 11 
> a : (EQUAL-X -(LliL d)-9)) FOF I2 ANlj iii 
> 
- I 
. * : CC,Y1?rJZ=,Y.7 I~EE~c-T>TICN~ GF (frrA5 X) FCF* 112 $NP G2- 
> 
. 
. 9 I TBi VPLUE CF FFL?-?AN 
> 
0 . 0 . 
rn . . 11.5 ~;~~SFECIFILC Fh6 IT?. AFGUXLFT I; 
> 
L 7q cqy 
a 9 I TY& i: L 4-'U~RLrJ VALUES P.52: 
> 
. * w . 
I • 1 3 ..c C-K=IV = IC~:T-..~~~N) 
>, 
* . . 
.I 0 I 
> 
.nCI 
. 0 9 
- . 1 JNLLL~ YTHZ 'IfFLTlE CF FFOr?mF.AE; FOE: 
> 
0 9 0 
0 
. . 1 12 = <-it L> 
*set-rnt'jln 
> 
0 
I 8 . 1 EFOPe1- ?A?? = {<I1 , [IC- JO] >, (12 & {zCwdC)) 
> 
m .I '4 
9 9 I>) 
> 
.I . 
. . .) 1 *f)C>.?IZ F5€IF-fTJY E-ESLIT. 
\ 
/ 
L - 
* * . 
t 
> 
* a 
a . : Dmi3Y.4,'1:-Ff:N OP 8FN IS SET--EEN = {ICmJO) 
> 
.. 
- - 
. 
9 - : DUHJT~TION OF \\X 'IC-JC = i 0 <I2,Jb>] 
> 
L 
9 . : CiiNCTATIOS IS 3 
> 
a 
I. • c COP.PUTI~G CE;NqTATION QF (TH3F9- IS U (EQUAL X (INT 
> 
I 
: U))) FOE 1; AND %2 
> 
. I 
.I 1 • : *N;U VPFIFBLI: ASSIS?i:*.~t:T G 4: X=IC-~d, U=J~. 
> 
I I 
- . : CcXPTJJ?I.NG DEEOTFTION OF (EQUAL X (INT IT)) FOE1 
> 
0 * 
. . . : I2 AMC G4 
> 
m * 
r m m c : 3ErJC1ZATI311 OF X IS ZC.*JO = {<11,3O> r <Fz1 
3 
* 1 
- I : 53)) 
)a: 
9 . a 
. • . : CC'IPUTING CFIPEATIFfi OF (I U) FOE I2 AND G4 
> 
* 1 P 
• . * • q : ~~~o~drrou 0% u IS JC 
> 
e * w w 
. t 9 . : L~LI:OTA'fII:,N 0 U XS JO 
> 8 . a . : DF:Ii)','~TI0E; TS LC-JO = <J (lz,JO>) 
> 
I 
: LE:;2'iATICis& IS 1 
> . : c~xbznm~p~ IS I 
> . : DZYDTA?hU' IS 1 
,> : CFKGTA'X~~ IS 1 
> : *yCr fl5;~1i3~f ASZIC;!;P:EflT G5: X=IC-:tJ. 
> : C041PU?IMG D2t4OTATICN CF (M'X6SSAFILX- (IEPLTES (ZAE? X) 1 
> : ThEEZ-I3 11, (ZQfJAL i (IKT II) ) ) ) ) FG? I?AAND GZ 
> 
I 
* : CO?.PIJTI:iG Dd:;3Tk'IICN OF (IPL1;S (UM X) (THEBF-IS u 
> 
* 
. : (7' X (IN1 U)))) ,FOF 11 AKD GS' 
> 
a 
: COlfF37f 8,; DESOTXTICN OF ('CALZ X) FOE 27 AND G5 
> 
I , 
o t : L~LYG -*v - -3k Ok ?AN T.5 SE%-?Il?h' = [IC11*30) 
> 
* b 
. , o CZ?!OT,XITZ.CN 3F 7. IS. 1- A, <T2,MA>) 
3 
. I 
p : I I VALUk OF SZTc+I,ck' 
> 
8 1 
* i]ZS '9:iSfECIF;I:EI: FOF ZIiE ARGUKEKT iC-YA 
> 
L 
: I P3SLCIBLF VFLfJFS AX: 
> 
* 0 b 
# @ :I D-IS = {?# I] 
> 
* P 
. . * 
\ 
I 
0 a w 
, c.i- 
R a : 1 E?~irb :HE V:iLUT; CF SET-KE~: F0-h: 
> 
m 
n ( IC-.% = {<:'I <12rEf)F>) 
J 
> 
I 
. : 1 3 SET-EEN = (12*- $C) 
> 
7. 
I : 1 Df'h, - Sil-KEN FET62. 
> : I 
> 
r." +? -I- f,. 
. . i.,~hL1AI1u!i IS 
> . : ELKC?AISCS (IS 7 
> 
+? 
t 
: ,CO:?TZIJIIP~~; CZ~,CTAF~~N OF (IEGLIZS (EAN X) (THE~PIS CT 
> m- : (2QUF.L -Y ' (JCI~:. U) ) 1.) FCF IS A-14D G5 
> 
. 
I : CO~~FUZLMG,$~.~;CTPTLON DP (?!AN X) FOF Xi AI:D.G~ 
> 
I 
- 
. . : D3:<3TATLCIi CF YAEj LS S35-!!EN = {ICmJ03. 
> 
. 
. . . : LZN3";AI;LCli CF X IS IC-I.IA = {<II,MA>, <IZ,PA>] 
-> 
. 
: DLYOXATIOL~ IS= 
> 
. 
. : ciq+iorxr~o~ LS 7 
> : DENCTATIOW $5 7 
> DEEOZ2ZIOki IS 1 
> 
> ENTE5pVIP,8~~ir; o,; hkFLi-ZEICY (YI? 5. 110 3C.RE) :- 
*nil 
> 
> sl!$T?,;i XEAKINGFDL EXP6ZSSIOB- (SIL = W MCFI) : 
9 ;comment - mar,ing p~'6\~~1ate for walk. 
[there-is e (for-all x {necessa~iJy (iff (walk x) ((ekt e) ( 
~ext fJ)J)) ) 
2 EXPEZSSTCN 1 0 ?YPi.TS 
> WEE V~~;P~RBLFS: FC,:JE: 
> CR? 
* Y 
> 
> 
-3 ri C * \I 
~,YT:~,,,T"  PUT^ r 'CF' FL:E,\CF ( K 2'1 = TJ T !! c.: r ) : 
4i.Z 
> 
> ,%Y ,. ,,I'Ai*YXFI.FF>k': .- 5 GI:. MI2, 
.. 
> 
I 
.C3?'Prl~IG,$34::~'2XT;3b CF (7:1!Zi.~.- ,4 L (FOFe AL. 9 (WFCZSSAPILP 
> (ZPF (kkih ) ((5x7 1.) (PYTu XI))))) F5h 1: Ah3 ~1 
> 
P' 
1'HES!?;>;: .t3 PZ55I3Lt t:'F)L:CTAAIi&S PCF CTkE GQUSC VAFIABLE 
> : E* 
-. -.. - 
> 
: ;; ,- T 8- xr 
: U'T?PLCA~ &tdi We L VEIKI; q33i'C 73 2 - <St<;,?%>>. 
> "TT!, : FX=' LHZS EiZ::i,vT .(!,&I = nu?; 1.T &Dc) : 
*prop-nlk* 
> 
; < -*- ?yv kt- 
: * V4?IFi3lX. +IbL. -L~h,.;L1.. G2: Z=I:fCP-KALKP. 
> : 0 G ?L';C,A~ZCS Cv -. (FiT-ALL X (NECLSS4P. 3LY (IFF ( 
> : ~~ry r) . X) ) ) 1,) FCF I, A G; 
> 
> 
> 
> 
Jwil 
> 
> 
*nil 
> 
> 
*\ - 
2 h"? CC,'::Ax:I: 
> 
* (displsv ,El~cctlcr,s) 
> IC-JC = {<I?,JC),-<I;,JJ>) 
> 
7 - 
L = I A, <L:,M:>) 
> sLlbv$x; ..,., - frc-~c) 
> S~);t'i--d;tIX535 = CZC- JG$ 
> .. $t'T?-Wj?,jJKXi; S = {IC- ?A) 
> P50F-h:lAY = (<:I, , I, (IC-JO~ >) 
1 
> P~GF--~AE% = [<J, {IC--3C) >, 2, [JC= :<A) >) 
5 s~~~l-.wfi~~'l:~~~ = {JC] 
> ~s~2dg~i~"z~~ =. [%A). 
> FRQP--WALK* (<I4, {JO$~>, I, (E>.)>)7 
> 
* (checkpoint rnodkl-rn~ mor7Cl) 
'#Z;,XECUIiCN T$S~IKALEE 
Conse~g:f'imq CI ecurs?er-zxana~ic tc: 
(KLCESSAIILY (IF? (WCvAK X) (kuYAN* (FXZ X) ))) 
n 
#%run *lisy t:~ 
*(restore i~te~p) 
* (enter' mo~lel) 
> D")O YQrJ YANT . IK?i'!JSZP;:AL ?"ILL@? 
* Y 
> 93 YC3 Id1512 TO ZHF,h'Gji DEB4.lii'I LOGiCAL CCfiSTkN"r? 
*n 
> 
> 
-%y-). - c' 
Fz..~~DL~z: 0 CANKO? EE VSFL AS SEr\FEkTCibS 11: LIzTs, 
> 
.-* % 
3 1 bF r;S'IIYESa 
* (i ma) 
> 3f.iTtF LI57 F XSCZELL LWCFLI?S, 
* ($11 w 2) 
> 23~2s LIST OF t;;;a:~?jxs I TKE, ~r; x~c~r)srsrn~s ~FDFE., 
* (t), 
> FC;ITS 3F FEFFF dXCi (,IE;C:C?':) : 
> t7 = <dl ,m> 
> 12 = <NL,?> 
> 
> G i,LiP!?hIS 9F C <.S ,E> Lp iStlTVIP13Al CC??CEPTS 
> 
. -- 
.~LY irbi PUHCYIGONS FFC% C 2 1,O 9-E, 
> 
- - 
PRAT LG, ~50:' PJISTC OF F?PP?~~LE TO EhTITI.E!5. 
> THSY KZLL i3E THE VALUE,' 0 t F3E XH LOGICAL C3h;STAh'TS: 
> J, "a, N+ 
> 
> D - s = ~rl, 12) 
> D I ? = {K, Ykf 
> 
> EKTI~F-NAEL FOE 2L3IA.LKT. (NIL = KC,/ FQ~J~). 
*pl;es 
> 6NTZ5 A YALUL- QF SA FOF EACH REGUPIENT: 
3 L7 = ,Gtl,T> 
f ma 
> 12 = <'ui2,T> 
*bi 
> PF5S 2?3iEIED, 
> 
ZNT~!: FiRYi FCF FI,7eQT. (KIL = hC ECF~). 
qbiic 
> EYIZF A VJ.IUT CF fiIL YCF EACH AFGUdEN?: 
>- ,+I = <? ,"> 
*bi 
> 12 = <+,q,,Q<> 
+bi 
> 31IC ZK1hEi~3r 
> 
*ma 
> WFiC zY7E53n, 
2 
> 
- \, 'W --- - 
- h7Y.Z FC7 -T%?:I.B';. (KIL = :iC KCIF). 
A,* ,-, 
*n, 1 
> "**'C <,PI> > - I. CrSCEFTS 
> 0:: D .- S = 111, h2\ 
> EAWG3: 3 - 1 = 9, "fR1 
> 
-- - 
S = {<L~,xA>, <T2,Fi>) 
> FZIC = {<Iqt9Z>, <~2~q:>) 
> I = 1 A, <I?, !IF>) 
> 
9 **** EFIS7I:;G T'l J) F ICC:Ii:E\L CZ~i$~A~~~ TyPc E 
> 4 V%LrleS'OF - F' TCit 3 Cr4 7FT 2 C'F 
.- 
> S - (5, -> ('I'!;ZIVZI>.:IAI LC!:CLEYZ). 
> 
# 
> LI?C;IC.~L C J, , F, K* 
> 
- - .. 
C - <,",:,> = qPZ.:;Z, 9: h:i!Lc) 
> 
2 9 k?iL'h SC?;:IIX!;T, I! THE V CI; I; CE EZl: 
> J 
*nil 
> 
*rna$c 
> i' 
*biic 
> 44 
*nil 
> 
> 
.- .a 
, p L; 15 G-T I?\ cs=:v 
P r- 
- >z,"S CFt I:iDIUIPUf.L 
> CCSCLF'i3 
> 
" C 
>,'.q?Y 7 S FUNC?IOS? k5GY D - <Sf?> TTC L - LW, 
> -1nAT 15, F~'J!,~!!CIVJCUFL CCSCEP7S 10 1 VALUES, 
. C1 
2 2ilTY WILL B 5 L! Of 9 IIOXS 2C.F TKF L9G1: C'AL CCIJSTANTS: 
> A, WdEAN, FWK, EISII,. I?rn?, !J~ICOF&; PC, Ii,EPGSATllf.E, 
> F7h.-WALK, fdl~, FISL, CHANGF. 
> 
> 1: (3 ,L> = P, FTIC, ?:AIC)v 
> D-~s - = $7. 71 
> 
> EN"T5-C . FCF FLb-;:;Thy, ffl1L = h?& ECL) . 
> 3ATC = [<Zq,:<h>, <ZGeP4A>) 
+ 1 
3 ke2:;~KsLz; -4:4Tl"l 55. 
> 
3 5HT2c &f\,":F aTZF;$N:e (KNI fl.OFf] 
Ut1i.1 
> 4 U c~.N;:IV =* - qST5 CF INI'XVICOAL CCSCLFTS 
>. 
L ,, C, YALC) 
4 U <S,k> = {?F3;"= 
> 5XtfGlL: 19 - 'is = [I) -, 1). 
> Wi"bA&SLY = {kPIC1 
> 
> +***F:i=F Ifit3 -FLL,?55:5 C7 C - <S ,CV=iV> FFa2EFTIES 9F 
> IEiSIqIIDUAL C:C$CEPIS 
> THF:Y'?A.~Z FUhC IZKS FFC?: L- " 5 TC G-CN=LY, 
> THAT. 12% F;C:* E?T;b??C. CP PEFFF.?'~;O TO SF75 OF I?:I?TViCTTAL 
> COSCZFTS, 
> YtEY WILL E? "HL Vl'c'iUEJ (.'T F "I;: THE LCGT??L Ct'EiSTkflTS: 
> 
-P -%kl 
YAK, WC~A~, PA1 I(, PYCd, TF!J, ITNICCFN; PRICZ, IL.,PZFLT!JI:E, 
> t~!;; 'dFi6, TALK, FISL, CRAKG'C. 
> 
> 
f- 
3-5 = ii 1, LL) 
> D - C?;=IV = (GF: As&S!?T) 
> 
> <h":+F ?+k!,X, E"Cr'* 2L;Yr'NT. (NIL = liC -3OFE) . 
*wo~an ~r~p 
> 2P;TtF A VFLffI 95 :iIP FCF fs..hCH kFGIJK?KT: 
> 11 = <w~;T> 
*wumsr,s~+Y 
> I2 = <12,T>- 
*woman8et. 
> FjGXANPFaF ?!qZi?LE. 
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References

J. Friedman. Notes on an intersional logic for English: A unique reduced form for wfts of IL. Univ. of Mich.

J Friedman, D Horan and D. Warren. An interpretation system for Montague grammar. AJCL 1978.

J. Hintikka, J. Noravsik, and P. Suppes. Approahces to Natural Language. 1973.

Richard Montague. The proper treatment of quantification in ordinary English. In Hintikka & al. 1973

Richard Montague. Formal philosophy: selected papers of Richard Montague. Yale Univ. Press. 1974.

J. Friedman. Notes on an intersional logic for English: A unique reduced form for wfts of IL. Univ. of Mich.

J Friedman, D Horan and D. Warren. An explicit finite intensional model for PTO. AJCL 1979.

J. Friedman and D. S. Warren. A parsing method for Montague grammars. Linguistics and Philosophy.

Daniel Gallin Intensional and Higher-order Modal Logic. 1975.

J. Hintikka, J. Noravsik, and P. Suppes. Approahces to Natural Language. 1973.

Jerry F. Hobbs and Stanley J. Foserchein. Making computational sense of Montague's intensional logic. Artificial Intelligence. 1978.

Edward L. Keenan. Formal Semantics of Natural Language. Cambridge Univ. 1975.

Franz von Kutschera. Partial interpretations. 1975.

Richard Montague. Universal grammar. Theoria. 1974.

Richard Montague. The proper treatment of quantification in ordinary English. In Hintikka & al. 1973

Richard Montague. Formal philosophy: selected papers of Richard Montague. Yale Univ. Press. 1974.

D. Moran. Changing semantic types in the interpretation system. Univ. of Mich. forthcoming.

D. Moran. A Programmers' description of the interpretation system. Univ. of Mich. forthcoming.

David S. Warren. A translation program for the grammar of PTQ. Univ. of Mich. 1975.
