Encoding Choice Logics in ASP

Choice Logics are a tool to express and reason about preferences. A choice logic extends classical propositional logic by adding non-classical binary connectives which express a certain form of ordering over interpretations that satisfy the connective; examples in the literature are Qualitative Choice Logic (QCL) which introduces the concept of ordered disjunction and Conjunctive Choice Logic (CCL) where an ordered variant of conjunction has been proposed. These logics have in common that interpretations ascribe a natural number, called satisfaction degree, to formulas; the lower this satisfaction degree, the more preferable the interpretation. In this paper, we present a general framework to capture several such logics and show how choice logics defined in our framework can be encoded using Answer Set Programming. (ASP).