Information States as First Class Citizens

INFORMATION STATES AS FIRST CLASS CITIZENS Jorgen Villadsen Centre for Language Technology, University of Copenhagen Njalsgade 80, DK-2300 Copenhagen S, Denmark Internet: jv@cst.ku.dk ABSTRACT The information state of an agent is changed when a text (in natural language) is processed. The meaning of a text can be taken to be this informa- tion state change potential. The inference of a con- sequence make explicit something already implicit in the premises -- i.e. that no information state change occurs if the (assumed) consequence text is processed after the (given) premise texts have been processed. Elementary logic (i.e. first-order logic) can be used as a logical representation language for texts, but the notion of a information state (a set of possibilities -- namely first-order models) is not available from the object language (belongs to the meta language). This means that texts with other texts as parts (e.g. propositional attitudes with embedded sentences) cannot be treated di- rectly. Traditional intensional logics (i.e. modal logic) allow (via modal operators) access to the information states from the object language, but the access is limited and interference with (exten- sional) notions like (standard) identity, variables etc. is introduced. This does not mean that the ideas present in intensional logics will not work (possibly improved by adding a notion of partial- ity), but rather that often a formalisation in the simple type theory (with sorts for entities and in- dices making information states first class citizens -- like individuals) is more comprehensible, flexi- ble and logically well-behaved. INTRODUCTION Classical first-order logic (hereafter called elemen- tary logic) is often used as logical representa- tion language. For instance, elementary logic has proven very useful when formalising mathemati- cal structures like in axiomatic set theory, num- ber theory etc. Also, in natural language process- ing (NLP) systems, "toy" examples are easily for- malised in elementary logic: Every man lies. John is a man. So, John lies. (1) vx(man(x) lie(x)), man(John) zi (john) (2) 303 The formalisation is judged adequate since the model theory of elementary logic is in correspon- dence with intuitions (when some logical maturity is gained and some logical innocence is lost) -- moreover the proof theory gives a reasonable no- tion of entailment for the "toy" examples. Extending this success story to linguistically more complicated cases is difficult. Two problem- atic topics are: Anaphora It must be explained how, in a text, a dependent manages to pick up a referent that was introduced by its antecedent. Every man lies. John is a man. So, he lies. (3) Attitude reports Propositional attitudes involves reports about cog- nition (belief/knowledge), perception etc. Mary believes that every man lies. John is a man. So, Mary believes that John lies. (4) It is a characteristic that if one starts with the "toy" examples in elementary logic it is very dif- ficult to make progress for the above-mentioned problematic topics. Much of the work on the first three topics comes from the last decade -- in case of the last topic pioneering work …

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