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Modal Logic for Belief and Preference Change A MODAL LOGIC FOR BELIEF AND PREFERENCE CHANGE A DISSERTATION SUBMITTED TO THE DEPARTMENT OF PHILOSOPHY AND THE COMMITTEE ON GRADUATE STUDIES OF STANFORD UNIVERSITY IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY Patrick Girard February 2008 c Copyright by Patrick Girard 2008 All Rights Reserved ii Modal logic for belief and preference change ILLC Dissertation Series DS-2008-04 For further information about ILLC-publications, please contact Institute for Logic, Language and Computation Universiteit van Amsterdam Plantage Muidergracht 24 1018 TV Amsterdam phone: +31-20-525 6051 fax: +31-20-525 5206 e-mail: [email protected] homepage: http://www.illc.uva.nl/ I certify that I have read this dissertation and that, in my opinion, it is fully adequate in scope and quality as a dissertation for the degree of Doctor of Philosophy. (Johan van Benthem) Principal Adviser I certify that I have read this dissertation and that, in my opinion, it is fully adequate in scope and quality as a dissertation for the degree of Doctor of Philosophy. (Marc Pauly) I certify that I have read this dissertation and that, in my opinion, it is fully adequate in scope and quality as a dissertation for the degree of Doctor of Philosophy. (Krister Segerberg) Approved for the University Committee on Graduate Studies. v vi 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. vii viii Acknowledgements Johan van Benthem has been the best mentor I could have hoped for. Even though he is permanently on a worldwide tour, he has always made himself available with lengthy and wise answers to my numerous distressed and stupid questions. His frankness, positive or not, has always been the best guidance. I would not have published papers if it were not for his amazing skills at polishing them - or co-authoring them. For all your kindness and generosity, Johan, I thank you! Having Krister Segerberg on my committee was a great honor. His modesty, simplicity and sense of humor has made his company most enjoyable in our various encounters around the world. Besides being one of the best logicians, he is defi- nitely the best chef among them; my best American Thanksgiving was spent with his Swedish family! Krister, thank you! Marc Pauly has introduced me to the field of judgment aggregation and motivated me to pursue Preference Logic. His criticisms about my work have forced me to carefully motivate my research and have put my feet back on the ground on several occasions. Thanks Marc! My thesis would suffer from logical deficiency were it not for the teaching of Solomon Feferman. It has been the greatest privilege to learn Logic from one of its founders. Likewise, Grigori Mints has taught me the mathematical skills without which I could not have undertaken such a project. I want to thank him also for advising me during my two first years at Stanford. Stanford’s philosophy department has provided me with the best intellectual and social environment for the pursuit of my studies. Jill Covington has been my savior on various occasions with her unbeatable administrative skills and benevolence. This is also true of the other staff members: Joy Rewick, Eve Scott, Sunny Toy, Joan Berry, Alberto Martin and Evelyn McMillan. Stanford’s philosophy department is among the best because of its faculty, whose dedication to students is beyond expectation. I wish to thank in particular Michael Friedman, Thomas Ryckman, Lanier Anderson, ix Mark Crimmins, Nadeem Hussain and Krista Lawlor, but also everybody else with whom I had the chance to take classes or interact over the years. I would also like to thank Vaughan Pratt for chairing my defense. A graduate degree is not something that is accomplished in isolation. Colleagues and friends are crucial for survival, in good and bad times. I have been surrounded by the greatest students and learning philosophy with them has shaped my intellectual life and given me the necessary moral support. Darko Sarenac has opened my eyes to various aspects of life which I would have missed and kept misjudging otherwise. Our discussions about logic and philosophy, sometimes while climbing walls in Yosemite or Squamish, would always teach me so much about what I did not know or understand. Thanks Darko, as well as your adorable family, Chloe and Catherine. Robert C. Jones is the best human being I have known. His kindness, generosity and loyalty have made him the best friend I could have wished for. He has ingrained in me the importance of living the best life I could and to be considerate to every animal residing on this planet - including humans. Thanks Robert! Jesse Alama is the best roommate I ever had and a compassionate friend. Tyler Freeman Green is the smartest ski bum there is and an appeasing friend. Tomohiro Hoshi is smarter than everyone looks like and a friend full of surprise. Audrey Yap is the living proof that women are smarter and stronger than men. Alexei Angelides is an α-friend and Alistair Isaac is a very strong crab-fighter. It was illuminating to learn set theory with you guys; thanks! I also wish to thank Peter Koellner, Randall Harp, Laurel Scotland-Stewart, Tim Blozer, Darren Bradley, Simon May, Ben Escoto, Patrick Forber, Shivaram Lingam- neni, Facundo Alonzo, Damon Horowitz, Manuel B¨achtold, Didier Jean, Angela Potochnik, Michael Weisberg, Jesse Cunha, Binh Danh, Robby Richardson, John Paschal and James Porter, who have all been important friends in the last 5 years. I have conducted an important part of my research as a visiting researcher at the ILLC, University of Amsterdam, where I spent 10 months in 2006-2007. The ILLC has given me the best opportunities to work on my thesis. Olivier Roy is a dear friend and has been, without really knowing it, my second advisor during the last 2 years. It has always been a great experience to organize events and collaborate on papers with him. Merci Olivier! I wish to thank Eric and Lauren Pacuit, Fenrong Liu, Leigh and Jill Smith, Jelle Zuidema, Jonathan Zvesper, Raul Leal Rodriguez, Sujata Ghosh, Jakub Szymanik, Joel and Sarah Uckelman, Kees de Jong and Fernando x Velazquez-Quesada who have all contributed in making my life better. I also want to acknowledge the Barderij, whose cheerful staff and crowd warmed my heart in those cold Amsterdam nights. Back in Qu´ebec, Alexandre Ethier´ has been one of the most influential person in my life. He has taught me how to live with passion and I always found motivation to do so in his enduring friendship. Merci Alex! Pierre-Alexandre Rousseau has taught me to never stop believing in my dreams and that there is no defeat. Jessica Brousseau and Fran¸cois Leduc have been loving friends whose liveliness rejuvenated me every dinner we had together. From McGill’s Department of Philosophy, I wish to thank Storrs McCall, Michael Hallett and Stephen Menn, who have all contributed in giving me the necessary background to pursue my studies abroad. Jean-Charles Pelland and Ben Curtis are two good friends and I always enjoyed and benefited from our philosophical discussions. From the UQAM,` I wish to thank Mathieu Marion for his enthousiasm in organising logic conferences in Montr´eal. I would like to acknowledge the financial support of the Fonds Qu´eb´ecois de la recherche sur la soci´et´eet la culture (FQRSC), scholarships #85863 and #109941. Finally, and most importantly, I would like to thank my family. Even though I have been far away from them in the last years, I have always felt them close to me. My parents, Jean Cheeseman and Michel Girard, have always encouraged me with all their love in everything I have undertaken. I could not have completed my thesis if it was not for my sibling’s love and support: Fran¸cois-Michel, Sylvie, Liliane and Isabelle and their troupes: Fran¸cois Lepr´evost, Bruno Chatelois, Charles Sylvestre, Laurence Blais, R´emi, Louis-Philippe and Andr´eanne Lepr´evost, Michelle, Marion and Fr´ed´eric Chatelois, F´elix-Antoinne and Catherine Sylvestre and finally Mathilde Girard. My aunt Shirley Cheeseman is like a second mother to me and I consider Gudrun Jakubowski to be my sister; both their presence has fostered the cohesion in my family. Infinitely many thanks! My thesis is dedicated to Fr´ed´eric Chatelois, who was born during my first year at Stanford.
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