Qualitative choice logic

Gerhard Brewka, Salem Benferhat, Daniel Le Berre

Abstract: Qualitative choice logic (QCL) is a propositional logic for representing alternative, ranked options for problem solutions. The logic adds to classical propositional logic a new connective called ordered disjunction: A×→B<math><mtext>A</mtext><mtext>×</mtext><mtext>→</mtext><mtext>B</mtext></math> intuitively means: if possible A, but if A is not possible then at least B. The semantics of qualitative choice logic is based on a preference relation among models. Consequences of QCL theories can be computed through a compilation to stratified knowledge bases which in turn can be compiled to classical propositional theories. We also discuss potential applications of the logic, several variants of QCL based on alternative inference relations, and their relation to existing nonmonotonic formalisms.1