APPLICATION OF INTENSIONAL LOGIC TO KNDWLEDGE REPRESENTATION 
Ton~ Chrz 
FSO Prague, Czechoslovakia 
The system of transparent intensional logic (TIL) intro- 
duced by Pavel Tich~ is used as a framework for a description 
of knowledge representation in n~n - machine con,nunication. 
A detailed exposition of TIL can be found in /1/. 
A language expression denotes an object by expressing 
its construction. The syntactic structure of the expression 
reflects the structure of the corresponding construction (thus 
obeying Frege's principle of oompositionality). To analyze an 
expression semantically means to determine the construction it 
expresses. Ordinary language expressions have often more than 
one analysis. 
The analyses of language expressions (i.e. construct~, 
ions) can be represented by ~-expressions. This representat- 
ional language has the same expressive power (within the frame- 
work of TIL) as the natural language, but has no ambiguities. 
The inference rules of TIT serve as a theoretical foundation 
for the inference necessary in knowledge representation. 
The infinite hierarchy of types in TIL makes it possible 
to work with properties of properties or with relations between 
an individual and a proposition in the same way as the first 
order theories work with relations between individuals. Thus, 
TIL can be considered to be a limit case of the theories of 
order n. 
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A s~stem for knowledKe representation, based on TIL, is 
presently under develo~nent. Its knowledge base contains a 
special atom representing the system itself, and certain proc- 
edures allow the system to determine the truth-value of propos- 
itions concerning its knowledge (this can be considered as a 
rudimentary form of self-reflection). This feature allows the 
system to infer correct answers e.g. in the following convers- 
ation, where x,y are variables for individuals and p is a 
variable for properties! replies from the system are marked 
by >>>: 
(I) John is a boy and Paul is a boy. >>> Hm. 
(2) Is Tom a boy? >>> I don't know. 
(3) If x is a boy then you know that x is a boy. >>> Hm. 
/,4) Is Tom a boy? >>> No. 
(5) x is omniscient with respeot to p Iff 
(if y instantiates p then x knows that y instantiates p). 
>>> I-Ira. 
(6) With respect to which property are you ommlscent? 
>>> Boyhood. 
Not_....ee: Before the start of the conversation, the system is in 
the initial state, where basic infer,no, rules have been 
programmed and grannnar and a dictionary have been introduced. 
but no factual knowledge. The dictionary entries contain in 
most cases only a word, its class and the type of the object 
it denotes. 
The self-referential oapacit~ is one of the strong feat- 
ures of natural language (thus allowing the linguist to de- 
scribe the object of his study). This capacity leads to the 
possibility of paradoxioal assertions (the Liars paradox- as 
far as a modification for artificial intelligence is concerned, 
see Cherniavsky /2/. Havel /3/). In the following example, the 
system is ordered to believe a proposition ~8). which is easi- 
ly performed ~9). Nevertheless, if the attempt to believe a 
proposition (12), althou~l it is"known" to be true (11). 
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(7) Tom says that the Earth is round. >>> Hm. 
(8) Belleve the proposition which Tom says\[ >>> OK. 
(9) Which property does the Earth have? >>> Roundness. 
(10) Paul says that you do not believe the proposition which 
Paul says. >>> ~hn, 
(11) Is the proposition which Paul says true? >>> Yes. 
(12) Belleve the proposition which Paul says\[ 
>>> Sorry I cannote 
Not_._~es In this example, to "believe" is interpreted in such a 
way that the system "believes" a proposition by actual stor- 
ing its ~epresentatlon. Thus, the positive answer to question 
(11) does not imply that the system "believes" the proposit- 
ion. Diverse interpretations of "believe" are possibleo 
The "the" in (8), (10) - (12) is interpreted locally, 
i.e. in the context of the knowledge base of the system. Thus, 
if the system knows only one of the propositions which Tom 
says, then this proposition is th..~e proposition which Tom sayse 
The problem of anal~sls of language expressions (i.e. 
of determining the constructions expressed by them) is not 
the main goal of our research, Nevertheless, a restricted sub- 
set of scientific English (see sentence (5) above) has been 
described by a grammar, which is "almost SLR(O)". (The stack 
automaton accepting the l~u6uage has some states with shif~- 
-reduce and/or reduce-reduce conflicts.) The analyzer gives 
all possible analyses of the input sentence, taking into 
account both the ambiguities of the syntactic structure of 
the sentence and the ambiguities of the individual words. The 
second case is illustrated by the following example: 
(13) John has a ballv 
(14) John has every good property which Paul has. 
(15) John has a brother, 
The sentences can be rephrased as 
(13") John owns a ball. 
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(14") John inetantiates every good property which Paul 
Inst antlat es. 
(15") There is x such that x is a brother of John. 
The word "have" in (13) and (14) denotes the objects 
(i.e. relations) denoted by "own" and "instantiate" in (13") 
and (14"), respectively. (The relation in (15") is dlffloult 
to denote by a single word.) Thus, the analyses of sentences 
(13) - (15) are: 
(13-) Aw.Some ~x.And \[\[ Ball w\] x\] • \[ Own w\] John X 
(14") ~w.Every x p.Oond 
\[And \[Property p\] . And \[\[ Good w\] p\] . 
\[Instantiate w \] Paul p \]. \[ Instantlate w \] John p 
(15 w) ~w.Some ~ x. \[ Brother w\] x John 
Notes The information of the different analyses of "have" has 
%o be stored in the dictionary. Here, to own is a relation 
between individuals, to instantiate is a relation between an 
individual and a property, and in (15) and (15"), a relatio~ 
between an individual and a relation is mentioned (since 
brotherhood is a relation between individuals). Thus, ambigui- 
ties of this sort may be resolved by examining, whether the 
type of the denoted object "fits" into the types of objects 
denoted by other words in the sentence. 
The s~stem is bein~ programmed in 7.7SP and the current 
version has some 2500 lines of source code. The quoted examp- 
les (including the inference of answers (1) - (12))have been 
processed by the system. 
The aim of the present paper is to demonstrate that TIL 
forms a suitable framework for a description of natural lan- 
guage semantics, since 
1 ) the language of A - expressions is sufficiently rich but 
diesmbiguat ed 
2) the translation of natural language expressions into these 
"se~=utic 7 :~)resentations" is relatively straightforward 
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3) the inference necessary in language understandiP4¢ can be 
performed using the inference rules of TIL 

References

/1/ Tich~, P.s Foundations of partial type theory. 
o~ Mathematical Logic 14 

/2/ Chernlaveky, V.S.: On limitations of artificial intelli- 
gence. Information S~stems, 6, 1980 

/3/ Havel, I. M.: Truth-reaction paradox and limitations of 
artificial intelligence. (manusoript in preparation)  
