SITUATIONS AND PREPOSITIONAL PHRASES 
Erik Colban and Jens Erik Fenstad 
University of Oslo 
Institute of Mathematics 
Postboks 1053 Blindern 
N-0316 Oslo 3, Norway 
ABSTRACT 
This paper presents a format for representing the 
linguistic form of utterances, called situation 
schemata, which is rooted in the situation semantics 
of Barwise and Perry. A treatment of locative 
prepositional phrases is given, thus illustrating the 
generation of the situation schemata and their 
interpretation in situation semantics. 
Introduction 
A natural language system aims to provide an 
overall framework for relating the linguistic form of 
utterances and their semantic interpretation. And the 
relation between the two must be algorithmic. In this 
paper we pursue an approach which is based on an 
algorithm for converting linguistic form to a format 
which we call a situation schema. 
A situation schema has a well-def'med formal 
structure, suggestive of logical form. This is a 
structure which is different from the standard model- 
theoretic one; we will argue that it is a structure better 
adapted for the analysis of the meaning relation in 
natural languages. A situation schema is effectively 
calculable from the linguistic form and we believe 
that it provides a format usefull for further 
processing, e.g. in the construction of a natural 
language interface with a data system and also in 
connection with mechanical translation systems. 
The general structure of situation 
schemata 
We begin by explaining the general structure of 
the situation schemata and how they, are rooted in the 
situation semantics of Barwise and Perry (Barwise 
and Perry 83). 
Situation semantics is grounded in a set of 
prinutives 
S situations 
R relations 
L locations 
D individuals 
The format of a bas/c (located)fact is 
at I: r, al,...,an; 1 
at 1: r, al ..... an; 0, 
the first expresses that at the location 1 in L the 
relation r in R holds of the individuals al ..... an in D; 
the second expresses that it does not hold. 
A s/mat/an s in S determines a set of facts of the 
form 
in s:at l:r, al ..... an; 1 
or 
in s:at l:r, al ..... an; 0. 
We can think of a situation s as a kind of 
restricted, partial model (data base) which classifies 
certain basic facts. The set of primitives <S,L,R,D> 
may come with some internal structure, e.g. the set L 
of locations is or represents connected regions of 
space time and thus could be endowed with a rich 
geometric structure. We shall see how this can be 
exploited in our analysis of locative prepositional 
phrases. 
A situaion schema is a complex feature-value 
structure computable from the linguistic form of the 
utterance and with a choise of features matching the 
primitives of situation semantics: 
"REL 
ARG1 - 
AEEm - 
LOC 
.POL - 
Here the features REL ARG1,...,ARGn, arid LOC 
correspond to the primitives: relation, individuals, 
258 
location. POL, abbreviating polarity, takes either the 
value 1 or 0. The values in the schemata can either be 
atomic or complex feature-value structures. The value 
of the LOC feature is always complex. 
The interpretation of a situation schema is relative 
to an utterance situation u and a described situation s. 
The utterence situation decomposes into two parts 
d discourse situation 
c the speaker's connections 
The discourse situation contains information about 
who the speaker is, who the addressee is, the sentence 
uttered, and the discourse location. The latter 
information is necessary to account for the tense of a 
sentence. The speaker's connections is a map 
determining the speaker's meaning of lexical items. 
The meaning of a sentence ~ 1 is a relation between 
the utterance situation u (=d,c) and a described 
situation s. We write this relation 
d,c \[srr.,h\] s, 
where SIT. t)lden°tes the situation schema of 01. 
Remark. In other works, e.g. (Fenstad et. al. 87), we 
have developed the mathematical study of the 
structures <S,L,R,D>; in particular, several 
axiomatization theoremes have been proved, providing 
a complete inference mechanism for a multi-sorted 
logic based on a semantics of partial information. 
Since the model theory of these sU'uctures seems to 
be a natural formalism for a (relational) data base 
theory, it would be interesting to build a PROLOG- 
style system based on the proof-theory which we 
have developed. 
Oblique objects and adjuncts 
In the next section the general theory will be 
illustrated by the analysis of a couple of sentences that 
contain locative prepositional phrases. In this section 
we make some preliminary remarks. See (Colban 85) 
or (Fenstad eL al. 87) for more details. The PP's we 
consider here are all attached to a verb (not a noun 
phrase), and will be divided into two classes: oblique 
objects and adjuncts (Kaplan and Bresnan 82). An 
oblique object fills one of the argument slots of the 
verb if one considers the verb to be a relation with a 
fixed number of arguments. In e.g. the sentence 'Tom 
handed the book to Anne" the verb handed is a 
ternary relation with arguments Torn, the book and, 
one migth say, Anne. However, we will consider the 
third argument to be something that has to be in the 
relation to to Anne. An oblique object is thus a 
constraint on an (unexpressed) argument of the verb. 
This way a verb may have several oblique objects 
without the number of arguments necessarely 
increasing. In the sentence ''Tom sent a letter from 
Norway to France" both from Norway and to 
France are constraints on the same argument. 
Adjuncts function normally by restricting or 
modifying the relation expressed by the verb. 
Examples are: "Tom played with Anne " and "Tom 
ate in a hurry. " Sometimes the location where the 
relation takes place is modified and not the relation 
itself. In e.g. 'Tom ran to the car" the location will be 
restricted to be in the relation to to the car. This 
relation will hold if the location is a curve Izacing the 
trajectory in space-time that ends at the (location of) 
the car. 
The situation schemata in the examples below have 
been produced by a parser for LFG-grammars. 
Usually, f-structures are produced by such a parser, 
but we have written a grammar that causes situation 
schemata to be produced instead. 
Examples 
Examvle 1: 
¢1: Peter ran to the car. 
The situation schema S1T.~I is: 
"gEL ma 
ARG1 Peter 
I,OC 
IND 
COND 
IND2 
"REL < \] 
AI~I IND 2 
.AP4~210 
"REL to 
AP4~I IND2 lIND 
IND1 
/ /A I mD 
| LPOL 
LSPEC THE 
.POL 1 
.POL 1 
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The PP is here taken as an adjunct since ran is a 
unary relation. The values of the ARGi in the 
schemata can either be direct references to individuals 
(e.g. Peter) or /ndeto-m/nates with or without 
associated constraints (e.g. 10, IND1, IND2). The 
indeterminates have to be anchored to individuals or 
locations in such a way that the conslraints hold in the 
described situation. The ARG2 in the second 
constraint of SIT.O I'LOC'COND is: 
COND \[REL car 
ARG1 IND 
LFOL 
LSPEC THE 
This schema tells us that IND1 has to be anchored 
to an individual a that must be a car. The SPEC 
feature can either be used to pick out the unique car in 
the described situation or to make a generalized 
quantifier out of ARG2. The situation schemata are 
hence open to several interpretations. 
The LOC feature in this schema has the structure: 
l IND IND2 \] COND {---} 
The location is tied to a location indeterminate 
IND2. The COND feature is a set (notice the set 
brackets) of constraints on IND2. The first one 
expresses that ND2 must be anchored to a location I 
that temporally precedes the location that 10 gets 
anchored to. By convention 10 is always anchored to 
the discourse location I d. This constraint accounts for 
the past tense of ran. In the second constraint the 
semantics of to tells us that 1 must be a curve in 
space-time that ends at the location of a. The head- 
relation run in SIT.~ 1 asserts that the individual 
named Peter is in the state of running along the 
trajectory 1. An interesting project would be to furnish 
the domain L of locations with a set of "primitive" 
relations which could be used to spell out the meaning 
of the different prepositions. For the moment the only 
primitive relation on L that has been accounted for in 
the axiomatizatlon of the structure <S,L,R,D> is "<", 
the relation "temporally precedes." 
A more precise interpretation of S1T.O 1 is: 
The relation d,c \[S1T.O1 \] s holds if and only if 
there exists an anchor g on S1T.~ I'I'£X~, i.e. 
~0): ld 
g(IND2) < g(1 O) 
andanextensienf ofg that anchorsIND1 
such thatf(IND1) is the unique individual 
such that in s: c(car),f(IND1); 1 
such that 
in s: c(to), gtlND2),f(IND1); I 
ins: at g(IND2 ): c(run), c(Peter); I 
Note that relations between locations can easily be 
extended to include individuals among their 
arguments. This is done by introducing a function 
/oc~f from D to L mapping individuals on their 
locations. A relation r between locations is extended 
to a relation r' where some of the arguments are 
individuals by letting: 
r', .... al, ...; pol ~f r ..... loc.ofla i), ...; pol. 
Examole 2: 
(;2: The book was lying on th~ ~bl~. 
The situation schema SIT.02 is: 
"REL lie 
IND IND1 REL book \] 
AROl COND AI~I IND1 
l LPOL 1 
LSI~C THE 
"IND 
AR~ COND' 
IND5 
REL on 
ARG1 IND5 
lIND IND4 
,,I 
.POL I 
r o o2 \]\]\] 
/COND 1/A 1 IND2 
L LLARG2 IO 
,POL 1 
260 
The PP gets here two readings; one as an adjunct 
and one as an oblique object, but we have omitted the 
adjunct reading since it isn't natural. The relation lie 
takes two arguments: ARG1 end ARG3. The 
indeterminate IND2 must be anchored to a location 
that temporally precedes the discourse location. IND1 
must be anchored to an individual al which is the 
unique book in the discourse situation, and ~ must 
be anchored to an indivildual a2 which is the unique 
table in the discourse situation. SIT.~2.ARG3.COND 
forces IND5 to be anchored to an individual a3 such 
that the relation on holds between a3 and a2. The 
relation lie will hold between al and a3 if al is lying 
and the locations of al and a3 are the same. 
A precise interpretation is: 
The relation d,c \[SIT.02\] s holds if and only if 
there exists an anchor g on SIT.~b2.L(X~, i.e. 
g:lo)-- td 
g(IND2) < g(l O) 
and an extension fof g that anchors IND1, IND4 
and IND5 
such thatf(IND1) is the unique individual 
such that/n s: c(book),fllND1); 1 
andfllND4) is the unique individual 
such that/n s: c(table),fllND4); 1 
such that 
in s: c(on),/(IND5)j?IND4); 1 
in s: at g(IND2): c(lie),f(IND1),f(INDS); I 
REFERENCES 
\[1\] J. Barwise and J. Perry (1983), Situations and 
Attitudes, MIT Press. 
\[2\] E. Colban (1985), LFG & preposisjonsfraser i f- 
strukturer og situasjonsskjemaer (Norwegian) 
Cand.scient thesis, University of Oslo. 
\[3\] J.E. Fensta& P.K. Halvorsen, T. Langholm, L 
van Benthem (1987) Situations, Languages and Logic, 
Reidel. (Preliminary version: Report 29,CSLI, 
Stanford University). 
\[4\] R. Kaplan and J. Bresnan (1982), Lexical- 
Functional Grammar: A Formal System for 
Grammatical Representation, in J. Bresnan (1982), 
The Mental Representation of Grammatical 
Realations, M1T Press. 
\[5\] S.M. Shieber(1986), An Introduction to 
Unification-Based Approaches to Grammar, CSLI 
Lecture Notes No.4, Stanford. 
Final remarks 
This analysis has been implemented on a XEROX 
1109/1186. Other fragments have been implemented 
using the D-PATR format. In a study of direct 
questions (E. Vestre) it turned out to be advantageous 
to use a DCG-grammar and a PROLOG- 
implementation. The spirit of the algorithms are 
however the same, unification and constraint 
propagation (see (Shieher 86) for a general 
discussion). We are now studying the problem of text 
generation based on situation schemata augmented by 
certain pattern information. 
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