DS-2008-04: Modal Logic for Belief and Preference Change

DS-2008-04: Girard, Patrick (2008) Modal Logic for Belief and Preference Change. Doctoral thesis, University of Amsterdam.

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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.

Keywords:

Item Type:	Thesis (Doctoral)
Report Nr:	DS-2008-04
Series Name:	ILLC Dissertation (DS) Series
Year:	2008
Subjects:	Language Logic
Depositing User:	Dr Marco Vervoort
Date Deposited:	14 Jun 2022 15:16
Last Modified:	14 Jun 2022 15:16
URI:	https://eprints.illc.uva.nl/id/eprint/2064

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