Relations among nonmonotonic formalisms

Abstract

Our book has two main themes: nonmonotonic formalisms based on the language of propositional logic (default logic and logic programming and its extensions fall into this category) and modal nonmonotonic logics. Until now we have not discussed the question of interconnections between them. We will do so in this chapter. First, we will show that several modal nonmonotonic logics studied in Chapter 7 can be regarded as generalizations of default logic. An important consequence of this result is yet another semantical characterization of extensions. Even stronger results can be obtained for logic programming and, in particular, new characterizations of stable models for logic programs and stable answer sets for logic programs with classical negation are presented. Next, we show that default logic with weak extensions naturally corresponds to autoepistemic logic (that is, the nonmonotonic logic kd45). Finally, we introduce the notion of truth maintenance and briefly discuss its relation to logic programming and modal nonmonotonic logics.