Multivalued logics and Topics

There are several practical problems of knowledge representation where it is more natural to talk in terms of the set of sentences related to a given topic than to make explicit all the sentences in this set. A problematic feature of classical logic is that if we want to represent this set by a small set which is closed under logical consequence, we can generate sentences related to new topics. For example from p it is possible to infer p _ q, even if q has no common topic with p. In this paper we compare several multivalued logics in order to give a formal characterisa-tion of the relationship between topics and sentences. We give a uniform presentation for the semantics of the four valued logic suggested by D. Lewis, for the D. Bochvar's three valued logic, and for classical two valued logic. We present theorems that allow to compare their possibilities in terms of characterisation of propositional variables that occur in senet-nces. The main result is that Bochvar's logic is more suitable than Lewis's logic to characterise sentences that are logically equivalent, and that are formed with the same propositional variables .