Deduction in many-valued logics: a survey

Until the late 1980s research in many-valued logic (MVL) focussed on theoretical issues in proof theory, algebra, expressivity, axiomatizability and, on the applicative side, discrete function minimization and simplification. The first papers with practical implementation of deduction systems in mind came up in paraconsistent/annotated logic programming [18, 76] and in automated theorem proving [55, 108]. A partial survey of the results up to 1993 is contained in [58]. In the past five years deduction methods for MVL got more and more refined. Recent results can match those in classical theorem proving with respect to depth and attention to detail. They are not confined to mimicking improvements of deduction invented in classical logic, rather, specifically non-classical strategies are started to being pursued. As can be seen from the references list of this article, there is considerable activity in MVL deduction which is why we felt justified in writing this survey. Needless to say, we cannot give a general introduction to MVL in the present context. For this, we have to refer to general treatments such as [153, 53, 93].