Date: March 1998
Pages: 211
Non-monotonic systems are introduced as a framework for analyzing non-monotonic reasoning. Such systems are defined as parametrized inference operators in a way that is compatible with Tarski's characterization of classical reasoning. The generality of the framework is demonstrated by presenting non-monotonic systems for the leading non-monotonic logics such as circumscription, default logic and autoepistemic logic. Various translations between non-monotonic logics are studied within the framework. Non-monotonic systems associated with the non-monotonic logics under consideration are shown to be preserved by these translations - including new translations between default logic and bimodal autoepistemic logic presented in the work. The standard semantics of non-monotonic reasoning - stable and stationary semantics - are generalized for all non-monotonic systems. Various properties of the semantics such as cumulativity and computational complexity are addressed. Moreover, it is established that the translation functions presented preserve these semantics. Finally, a new semantics called cautious semantics is obtained as a systematic refinement of stationary semantics. Cautious semantics is analyzed using the methodology developed in the work. A comparison is made with similar approaches in the literature. Applications of cautious semantics are considered in the fields of logic programming and consistency-based diagnosis.
Keywords: nonmonotonic reasoning, semantics, cumulativity, computational complexity