命題自己認識論理における決定手続き

抄録

Classical logics such as propositional logic and first-order predicate logic are called, in general, monotonic logic. On the other hand, logics which can invalidate old conclusions when adding some new knowledge are called nonmonotonic logic. Nonmonotonic reasoning based on such logics is of great importance for the realization of commonsense reasoning or incomplete knowledge reasoning in knowledge information processing system. One of the interesting approaches to the nonmonotonic reasoning is D. McDermott and J. Doyle's nonmonotonic logic. However, there exist some problems in their logic. In order to avoid the problems, R. C. Moore then reconstructed an alternative nonmonotonic logic, called autoepistemic logic. At present, autoepistemic logic could be regarded as one of the most promising formalizations of nonmonotonic reasoning. Autoepistemic logic is on the basis of the notion of belief and is intended to model the beliefs of an ideally rational agent reflecting upon his own beliefs. This paper consists mainly of the following three topics. The first is to survey Moore's propositional autoepistemic logic. The second is to redefine the stable expansions which are the possible sets of the agent's total beliefs for a given set of premises, in terms of the fixed point relation with respect to a certain operator. The third is to give a decision procedure by using a tableau method, whether or not a formula appears in all stable expansions, and to prove the correctness of its procedure.