Topic/Focus Ar'ticulation a~d l~te~sio~al Logic 
Tomes VLK 
P.O. Box 55 43401 Moat 
Czechoslovakia 
Abstract 
A semantic analysis of topic and focus as two parts of 
tectogrammstical representation by means of transpa- 
rent intenslonal logic (TIL) is presented. It is poin- 
ted out that two sentences (more precisely, their 
teotogrameatlcal representations} differing Just in 
the topic~focus articulation (TFA) denote different 
propositions, i.e. that TFA has an effect upon the 
semantic content of the sentence. An informal short 
description of an algorithm handling the TFA in the 
translation o~ teotogramsstlcal representations into 
the constructions of TIL is added. The TFA algorithm 
divides a representation into two parts corresponding 
to the topic and focus; every part is analyzed 
(translated) in isolation and then the resulting cons- 
truction is put together. The TIL construction d~sous- 
sad here reflect the scope of negation and some of the 
presuppositions observed. 
I. Introduction: TranBparent intenaional logic 
One of the current tasks of semantic studies 
consists in finding • procedure translating the dis- 
ambiguated linguistic meanings of sentences (see SOS11 
et el., 1986) into the constructions of Intensional 
logic. The core of such procedure was developed (Ylk, 
1987), but a description of this procedure exceeds the 
scope of the present paper. The aim of this paper is 
rather to present some ideas used in the algorithm 
handling the toplol~oous articulation within the 
translation. 
Sufficient means for the semantic analysis of 
natural language are given by Tichy's Transparent 
intensional logic (TIL), Referring to exact defi- 
nitions to Tiohy (1980) and Katerna 41985), we repro- 
duce here only a brief characterization of TIL. 
Let o = ( T, F } be a set of truth-values, let L 
be a set of individuals (the universe of discourse) 
and let ¢U be s set of possible worlds (the logical 
space). Then 
B : ( o, ~ ,~} is an episteaic basis. Then 
(i) any member of Bite!a type over B, 
(ii) if ~,~,,.,~ are I types over B, then 
(~'"\[~) is n type over B, where 
(~- ~) is the met of (total end partial) 
functions from \[, X ...x ~ to ~ . 
(iii) the types over B ere just those introduced 
in (1),(ii). 
Any member of type ~ is called an object of type ~ , 
or an ~.-objeot. An object is an ~-obJect for shy ~ • 
For every type a denumermbly infinite set of 
-variables is at our disposal. 
The constructions are the ways in which objects 
can be given. They ere detined inductively: 
(1) any ~-objeot, and alma any ~-vsriable, is 
an ~ -constructlon (called the atomic con- 
struction}. 
(ii} let F be 8 (~ ~ ~}-oonstruotion, X, 
a ~;-conatruotion for i=l,..,n. Then the 
appliostion \[F Xt Xt ... X,) o~ F to Xt, X,, 
... , X~ is an ~-conetruotion. 
(£ii) let Y be an ~-construotion and x,, xs,... , 
x. dlstlnot varlables of types ~,..., ~ , 
respectively. Then the sbstraotlon 
\[XXl Xe ... Xm Y\] of Y on xl, xl,..., x~ is 
s (~ ~,..~)-oonstructlon. 
(iv) there are no constructions except those 
defined in (i)-(iii). 
Let us characterize some important objects of TIL. 
For every type ~ we have objects ~, T~ ~ of the type 
(o(o~)), such that (i) and (ii) hold: 
(i) \[~ X\] - if X is empty class then F 
else T 
(iS) \[TT ~ X\] =~ ~y. ~\[X y\] 
For every type ~ we have the ~-singulurizsr Z~of the 
type ( ~ (o ~ )), which is defined on eingle-elemM)nt 
-classes only and returns the single element of the 
respeotlve class. Propositions are objects of the type 
(o~). 
The following notation will be used through- 
out the paper. The outermost parentheses and brackets 
will be sometimes omitted. FurthermOre, • dot viii 
represent s left bracket whose corresponding right 
bracket is to be imagined as far to the right as is 
compatible with other pairs of brackets. The notation 
with an apostrophe will be used in the following 
meaning: 
X' :fix w\] if X is of type (~) for any 
/ 
X otherwise 
where X is a construction end w is a particular 
-variable. 
We write ~ x.Y in place of ~ Ax Y and ~x.Y in 
place of Tr~ ~x Y, 9 x.Y in place of \[I t ~x Y\]. 
Logical connectives and identity will be written in 
the standard way, e.g. a & b, e • b in place of 
(& 8 b\], (=~ s b\], respectively. 
2. The topic/focus articulation 
The procedure lie divided into two p@rts: into the 
.eeic ,l rith. hm dli g such phecomene ee 
Of quantifiers, eev~r.II klnds of reference, .n~ s~on, 
and the TFA algorltjhs b~ndllng theitopio/focus/artlouF lstion (TFA). The, B.ic .lgor, h. r  rs/v' y 
applied to all subtreee of the dependqnoy ~\[H, and 
returns the constructlon(s) corresponding to the sub- 
tree. The TFA algorithm divides the d~ndenOy trH 
into tic porte corresponding to the topic and*to~ the 
focus, respectively; either part is translated by the 
Basic algorithm, and then the resulting construction 
is put t~ether. 
The toplc/focus articulation (TFA) plays a cru- 
cial role in analysis of the presupposition, of the 
scope of negation and also of the so a4alled exhaustive 
listing (ale Sgsll, HaJlcovs, Pansvova, 1~, RsJiaove 
1974,1984). First, its Importance will be shown on an 
extremely simple 'toy' example; we will then discuss 
some problems in detail in connection with other exam- 
pies. 
Informally, the topic of s ~entence ix whet the 
sentence talks about, and the ~ocus is whet the 
sentence says e~ut the topic. A for~l definition of 
topic and focUS ai tic parts of the tsctogrmmmetiaal 
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/L u!~ ~.986)~ 
l,e~ t ~,' 'Lv'7 to /Ind the construction ~orresponding 
~:4:.~ daff_I~:, (i~S)o Af%i=~)i' {:.he division Of the TR into topio 
i~A,i{ 5!l\]~fl~il ue {\]~{; 
i'opi~<i. = ~o >,y \[~iu't ~ Cha):')~oe~ },'\] \[o~)to :~onatru~tloa 
l,'oc, tt~J. : H~i'y b "ooastre~tton 
:(~,d;uiLlvo\]y~ i:hi;i ;h~ a~it uhat we= need, The ioou8 is to 
u~J~gx't ~Joi>iethln{~ ;~b<mt the topi~ but here the fouus 
ii~ only ~ c~unt~x'part of ~n indlviduuL Intuitively, 
tllc, ~'+~'(iJ.~ of (2t~) i~ theft ladiqid~al that Charles ~et 
.~nd ih,+ "{gi~e~ declaz'~u abo~t this individual thrat it 
i.t~ ~Ixy,. The \[~otiutx'u6rtiol|~4 .~iu~t be £ni'ther ilodifiedo 
'l'opl~2 :; k(% q ~o fief" Chor.~o~ y 
{thg;t :l.ndividtitd. tlmt Charle# set) 
(the px'op~;'x't 7 (~ heia~ ilary) 
'l'lA' t3~ney~a'~h3t!o~ e~:~Ys(~.*~it'~dtnt~ to (ia) i~ obtsined by 
,.Opplit~tls~i Og t;'~Ut*2 {;0 {OiiJ.O2~ 
(2') (~=) 
}.~. \[),..R:4iary\] \[ ,} ?.Her' Chax'le~ y\] 
Ana!oo.i6al\]y :~o~' (2b) '+~+ get 
(2" } (b) }.I. " \[FO~l~Id2' 'l'ODii\]2' \] 
},*;,+ qy {iiei,' Chav\],er~ y\] £ iiary 
a*m :{os' ( 2c ) 
Topit:~ ~: >,v, .+, " \[igc.t ' Clmx'ic~ y\] 
TopÂe2 = },,eo ,,y0 "' {flet' Charle~ y\] 
(2') (¢;) ),v~ \[ Fotmu2 ' ={'op:Lc,2 ' } 
~;+o "IV \[" oIcd:' {\]:ha~'le~-~ y\]= Rary 
Du the~e ~oau'Lru~tien~ re£1et3t presuppo~itimb 
~a'ti~n ~_~m~ ~,a.<haeutl~e li~tlnq a~ observed in (2~=e)? 
The ±oLa=op~#*'.,~tcz" (t~iat~u\].~rizer) Js net defined on the 
oupty ~la~t~, io~Vo the ~ propo~£t.ton~ (2'a,b) are unde o 
girted ±~ tho~e pomdlble vorlds ~|lere Chsrles met n¢\]~ 
b*~dy~ and (2~) i~ eadeflned in tho~e pou~ible uorldo 
~'he.vo Chavie~ uet everybody° Al~o the two ~ope~ of 
n¢,~atiu*~ ~orro~posding to the contextually boend and 
toni-bound operatox' el neg~tiou are di~tingui~hed by 
{2q~} ~nd (2'*~)o I~ (2'a) mid (2'0) the equality sago 
%hat Ramy ~are the only one individual ~ith the given 
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iaeverthelese~0 *~t lea~6t t~o obae¢~t!en~ to these 
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pre.q~:n'L ll~ tha bpeaRer%~ ~A.nd, The con~trnetion 
~Jheuld be ~b~tituted by 
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•172 
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~, "fF~A DtT~_ip:itJ,Lk~t;~ 
~<~ d (o 2+ ..,!,) 7 -+D" ~~.: 
i75 
The following ~unc%ione are used in the deaoriptio~; 
CB t-DepTree -> Bool 
HB L DepTree ~> Booi 
HBNeg ~ DepTree ~> Bool 
Tree L Edge ~> DepTree 
Fun ~ Edge "'> Functor 
H : Fun~tor-> Construction 
RooEdge : Edge ~> Bool 
A-Edge : Edge "> Bool 
DivEdge : DepTree -'> Edge 
DelEdge ~ DepTree Edge -> DepTree 
PutVar ~ DepTree Edge -> DepTree 
Translate: 
GetTyp : 
DepTree -> Construction 
Contruetion -> Type 
The meanings of the fanction~ are as follows~ 
CB(dt) return~ true i£~ the root of d% i~ oon%e~. 
tually bound. NB(dt) returns true iff CB(dt) x~etax'n~ 
~alse (NB(dt) = ~CB(dt)). NBNeg(dt) returt, s true iff 
the contextually non-bound operator of negation is 
connected ~ith the root of dt (contextually bound 
operator of negation is handled by tile Basic, algo-- 
rithm)o 
Tree(e) returns the dependency tree suspended on 
edge e. Fun(e) returns the ~unctor of edge e. H(f) 
returns the object o~ TXL realizing relationship 
('Cause','Aim'). R-Edge(e) return~ true iff e is an ~~ 
Edge. A-Edge(e) returns true Iff e is an A.~Edge. 
DivEdge(dt) returns the dividing edge betwee~ %he 
topic and the foous of dr. 
Functions DelEdge end PatVar realize dividing of 
the dependency tree. DelEdge(dt~e) returns dependency 
tree dt" without edge e (edge e is' removed fro~ dr). 
PutVar(dt, e) ~eplaoes the tree suspended on edge e in 
tr by a variable and return~ the resulting depende~l~y 
tree. 
Trsnslate(dt) returns the construction o~ TIL 
corresponding to dt to which dt is translated by the 
Basic algorithm. GetTyp(~) returns the type of 
c,onstruction Co 
HOw we can describe the fello~iag prcoedu~e~: 
TFA 
FA 
TA 
FR 
TR 
,- the main procedure (function) 
- verb in the rogue, dividing A-edge 
verb in the topls~ dividing A-edge 
- verb in the fo~ue, dividing R~edge 
verb in the topic~ divldlno R-edge 
TFA : DepTree -> Constrsotion 
TFA (dr) = 
let e = DivEdge (dt) in 
(A-Edge(e) & NB(dt) -> FA(dt)~ 
A-Edge(e) & CB(dt) -> TA(dt)~ 
R-Edge(e) & NB(dt) -> FR(dt), 
R-Edge(e) & CB(dt) ~> TA(d%) 
7; 
If the dividing edge is an A~edge and the verb belong~ 
to the fo~ue the tree is handled b 7 function FAg Th~ 
tree suspended on the dividing edge ie replaced by a 
variable, the topi~ and focus are ~ranslated sepafste-- 
ly and the resulting construction is put togethe~o F 
is the sonstruction c,orrespondlng to the focus and T 
is the construction corresponding to the topic~ 
FA (dr) 
let e ~ DlvEdge (d%)~ 
'i'~ 'l'z'~n~late (Tree(e)) 
in 
if NBNoo(dt) %hen \[ k~., ~ I\[F ~ T~3 :~ 
to the topi~ tile tree ii:~ he,idled by fs~t-!.on TAg The 
%~ee J.s divided in the s~:~:~e ~.~unnc~r as iL~ \[:Ao The 
resulting con~tx'~tion i~ UOX'e ~e~plica%ed th~=~ i~ :~'A 
bee~u~e it he~z to reflect p~-e~L~ppc,m.itlon~-~ ~id c,~h~I~u ~' 
%ire l;\[~tingo 
TA (d'h) :: 
i ,° ~ '~x'~.~'~,~.~.~te ('i'x'ee(~)) 
is% 
in 
else \[ Aug Y \] 
I£ the dividia~ edge i~ ~n ~edffe ~nd %he ve~% belongs. ~ 
to ~he ~'ooa~ ~he %re~ i~ trundle'ted b F f~'.~'ti~n FRo 
l~ere %he flividln~ edge is x~esoved ~~o~.~ thc~ %re~ ~vA 
%ioL~hip bet~en the %opic, and fo~,a~o '~'h~ p~opo~itioL~ 
en~-~l~x'ed by function YX'o '~'h~ rel~%:\[on~\]hi~ bu¢,~en 'hhi> 
%lOne 
FR (dr) = 
let e = Div~dge (d't) 
T = Translate (T~'ee(e)).~ 
P ~: H(Fun(e) ) 
in 
else \[ Me \[P' F \[Tr ° T\]'~\] 
I~ the divldinff edge i~ ~n lb, c~dge w~d %he, ve'xb b~long~ 
~'ho ~,ree i~ divided in %he ~ ~.nn~' ~.-~ i~t b'hL A 
r~latlonshlp betwee~L the topic, ,'~LLd fo~;n~ Ji~ ~:\[thln th~ 
sconce O~ neO~%~on here° 
let c~ ~ DivEdge (d%.) 
F = °l'~snslate (Trec~(e))~ 
in 
724 
Although many problems are open, it is mn that 
the topi(:Ifocua articulation has an effect on the 
semantic content of the sentence and, therefore, it 
can b~ analyzed by means of formal semantics, 
k_cknovled~sment. 
The author vishem to thank Prof. Petr Sgail for 
support o~ this york and veluable discussions, 
his 

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