Multi-valued logics

Abstract

A great deal of recent theoretical work in inference has involved extending classical logic in some way. I argue that these extensions share two properties: firstly, the formal addition of truth values encoding intermediate levels of validity between true (i.e., valid) and false (i.e., invalid) and, secondly, the addition of truth values encoding intermediate levels of certainty between true or false on the one hand (complete information) and unknown (no information) on the other. Each of these properties can be described by associating lattice structures to the collection of truth values involved; this observation lead us to describe a general framework of which both default logics and truth maintenance systems are special cases.