Handling Qualitative Preferences Using Normal Form Functions

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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 "x". That new connective is used to express preferences between alternatives. QCL was not designed to handle conditional preferences, even if it is possible to express an implication with a preference on the left hand side, for instance (Air France x Virgin => Hotel Package). However, using QCL semantics, there is no difference between such material implication (Virgin x Air France => Hotel Package) and the purely propositional formula (Air France or Virgin => Hotel Package). Indeed, the negation in QCL gets rid of nested ordered disjunctions. Furthermore, the negation in QCL misses some desirable properties from propositional calculus. In this paper, we present a new semantics for the QCL language that addresses those problems. We describe a general framework for handling qualitative preferences. That framework is based on normal form functions that transform general QCL formulas into basic choice formulas, which are simple formulas (ordered disjunction of propositional formulas). We formulate the properties of our normal form function that overcome current QCL limitations.