WHAT IS A NONMONOTONIC CONSEQUENCE RELATION?

Abstract

This paper is an attempt to articulate and respond to a philosophical problem about the general idea of a nonmonotonic consequence relation. The problem concerns the clarification of the target notion that various particular nonmonotonic theories, both model-theoretic and proof- theoretic, are attempting to explicate. Two different general conceptions are contrasted. The first is based on an idea of implicit content. According to this idea, a semantic interpretation assigns to the sentences of a language an explicit content in the usual way, and also an implicit content as a function of the explicit content, ψ is a nonmonotonic consequence of φ if ψ is a consequence in the classical sense of the implicit content of the implicit content of φ. On this interpretation, nonmonotonic consequence is a deductive relation. According to the second idea, nonmonotonic reasoning concerns belief revision; to say that ψ is a nonmonotonic .consequence of φ is to say that ψ should be accepted in a belief state that is revised to accommodate the acceptance of φ. Some specific nonmonotonic theories, and some principles of nonmonotonic consequence, are considered from these two points of view.