Sweet SIXTEEN : Automation via Embedding into Classical Higher-Order Logic

Introduction. Classical logics are based on the bivalence principle, that is, the set of truth-values V has cardinality |V | = 2, usually with V = {T,F} where T and F stand for truthhood and falsity, respectively. Many-valued logics generalize this requirement to more or less arbitrary sets of truth-values, rather referred to as truth-degrees in that context. Popular examples of many-valued logics are Gödel logics, Lukasiewicz logics or fuzzy logics with denumerable (or even larger in the case of fuzzy logic) sets of truth-degrees, and, from the class of finitelymany-valued logics, Dunn/Belnap’s four-valued logic [1,2]. The latter system, although originating from research on relevance logics, has been of strong interest to computer scientists as formal foundation of information and knowledge bases. Here, the set of truth-degrees is given by the power set of {T,F}, i.e. V = {N,T,F,B}, where N denotes the empty set (mnemonic for None), T and F the singleton sets of the respective classical truth-value, and B the set {T,F} (for Both). This work presents an approach for automating a sixteen-valued logic denoted SIXTEEN. This logic has been developed by Shramko and Wansing as a generalization of the mentioned four-valued system to knowledge bases in computer networks [9] and was subsequently further investigated in various contexts (e.g. [8,10]). In SIXTEEN, the truth-degrees are given by the power set of Belnap’s truth values, i.e.