Modal Logic for Belief and Preference Change

Abstract

In my thesis, I show that Order Logic interpreted over preorders provides a unifying framework for individuals and groups to analyze believe and preference change. Order Logic is a modal logic with three modalities complete for the class of transitive and reflexive frames whose fragments and extensions yield various formalisms to analyze the dynamics of beliefs and preferences. The analysis proceeds in two steps: 1) I give static logics for belief and preference and 2) I introduce dynamic modalities to analyze actions over models. I investigate four kinds of doxastic and preference logics: Relational Doxastic Logic, Binary Preference Logic, Ceteris Paribus Logic and Group Order Logic. The actions I consider are of two kinds. In a first time, I integrate three well-known dynamic actions. The first one is public announcement, the second lexicographic upgrade and the last preference upgrade, exemplifying state elimination, state reordering and link cutting respectively. In a second time, I introduce new kinds of actions: agenda expansion and agent promotion. All actions are incorporated into static logics via compositional analysis, appealing to reduction axioms. This uniform completeness strategy consists in giving axioms that transform formulas with action modalities to equivalent formulas in the static language, reducing completeness of the dynamic logic to that of the static one.