Representing Knowledge About Knowledge and Mutual Knowledge

REPRESENTING KNOWLEDGE ABOUT KNOWLEDGE AND MUTUAL KNOWLEDGE Sald Soulhi Equipe de Comprehension du Raisonnement Naturel LSI - UPS llg route de Narbonne 31062 Toulouse - FRANCE ABSTRACT In order to represent speech acts, in a multi-agent context, we choose a knowledge representation based on the modal logic of knowledge KT4 which is defined by Sato. Such a formalism allows us to reason about know- ledge and represent knowledge about knowled- ge, the notions of truth value and of defi- nite reference. I INTRODUCTION Speech act representation and the lan- guage planning require that the system can reason about intensional concepts like know- ledge and belief. A problem resolver must understand the concept of knowledge and know for example what knowledge it needs to achie- ve specific goals. Our assumption is that a theory of language is part of a theory of ac- tion (Austin [4] ). Reasoning about knowledge encounters the problem of intensionality. One aspect of this problem is the indirect reference introduced by Frege ~] during the last century. Mc Car- thy [15] presents this problem by giving the following example : Let the two phrases : Pat knows Mike's tele- phone number (I) and Pat dialled Mike's te- lephone number (2) The meaning of the proposition "Mike's tele- phone number" in (I) is the concept of the telephone number, whereas its meaning in (2) is the number itself. Then if we have : "Mary's telephone number = Mike's telephone number", we can deduce that : "Pat dialled Mary's tele- phone number" but we cannot deduce that : "Pat knows Mary's telephone number", because Pat may not have known the equality mentioned above. Thus there are verbs like "to know", "to believe" and "to want" that create an "opaque" context. For Frege a sentence is a name, refe- rence of a sentence is its truth value, the sense of a sentence is the proposi- tion. In an oblique context, the refe- rence becomes the proposition. For exam- ple the referent of the sentence p in the indirect context "A knows that p" is a proposition and no longer a truth value. Me Carthy [15] and Konolige [I I] have adopted Frege's approach. They consi- der the concepts like objects of a first- order language. Thus one term will denote Mike's telephone number and another will denote the concept of Mike's telephone number. The problem of replacing equalities by equalities is then avoided because the concept of Mike's telephone number and the number itself are different entities. Mc Carthy's distinction concept/object corresponds to Frege's sense/reference or to modern logicians' intension/extension. Maida and Shapiro [13] adopt the same approach but use propositional semantic networks that are labelled graphs, and that only represent intenslons and not exten- sions, that is to say individual concepts and propositions and not referents and truth values. We bear in mind that a seman- tic network is a graph whose nodes repre- sent individuals and whose oriented arcs represent binary relations. Cohen E6], being interested in …

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