Two alternatives for handling preferences in qualitative choice logic

Abstract

Reasoning about preferences is a major issue in many decision making problems. Recently, a new logic for handling preferences, called qualitative choice logic ( QCL), was presented. This logic adds to classical propositional logic a new connective, called ordered disjunction symbolized by × ⇒ . That new connective is used to express preferences between alternatives. Intuitively, if A and B are propositional formulas then A × ⇒ B means: “if possible A, but if A is impossible then at least B”. One of the important limitations of QCL is that it does not correctly deal with negated and conditional preferences. Conditional rules that involve preferences are expressed using propositional implication. However, using QCL semantics, there is no difference between such material implication “( KLM × ⇒ Air France ) ⇒ Hotel Package ” and the purely propositional formula “ ( Air France ∨ KLM ) ⇒ Hotel Package ”. Moreover, the negation in QCL misses some desirable properties from propositional calculus. This paper first proposes an extension of QCL language to universally quantified first-order logic framework. Then, we propose two new logics that correctly address QCL’ s limitations. Both of them are based on the same QCL language, but define new non-monotonic consequence relations. The first logic, called PQCL (prioritized qualitative choice logic), is particularly adapted for handling prioritized preferences, while the second one, called QCL + (positive qualitative choice logic), is appropriate for handling positive preferences. In both cases, we show that any set of preferences, can equivalently be transformed into a set of basic preferences from which efficient inferences can be applied. Lastly, we show how our logics can be applied to alert correlation.