Nonmonotonic inferences: Classical conclusions in an intuitionistic modal framework

Abstract

We introduce a conceptual foundation for nonmonotonic reasoning which integrates an intuitionistic plurimodal logic with classical logic. The need for a multilogical system arises once we understand that to legitimately infer less than certain conclusions, we make two different kinds of assessments: an external one (what are the alternatives) and an internal one (which logic should govern the set of beliefs). We exploit this scheme to capture in novel ways basic nonmonotonic systems such as autoepistemic logic, default logic, one of the best known interpretations of negation-as-failure, as well as some conditional logics of normality. Among the aims of this paper is to explain why there are substantial overlaps between these systems and also to settle some problematic features that are of concern in logical investigations on common sense reasoning.