Universal Logic

General description: The notion of preference occurs across many areas, such as philosophy of action, decision theory, optimality theory, and game theory. Individual preferences can be used to predict behavior by rational agents. More abstract notions of preference also occur in conditional logic, non-monotonic logic and belief revision theory, whose semantics order worlds by relative similarity or plausibility. In the tutorial, we will present various languages to express preference. More importantly, preferences are not static, but they change triggered by incoming new information, or just changes in our own evaluation. We will present several approaches to model the dynamics of such changes.

Prerequisite: Basics of Modal Logic.

Introduction: epistemic dynamics*: First we will review the basics of
epistemic logic, both in its standard and its dynamic versions. A few typical examples will be presented to show the process of information
update by exchanging information. The same methodology will be used to deal with preference change.

Betterness based preference change: The notion of preference will be introduced as an unary modality, using a semantic relation of 'betterness' in Kripke models. After setting up the static logic, we will analyze what happens to the model when new information comes in, leading to a dynamic logic of preference change.

Constraint-based preference change: Next, we define preference in terms of a constraint sequence, a concept from optimality theory. In case agents only have incomplete information, beliefs are introduced as well. We propose three definitions to describe different procedures agents may follow to get a preference using beliefs. Changes of preference are explored w.r.t their sources: changes of the constraint sequence, and changes in beliefs.

Value-based preference change: Finally, a more quantitative approach will be taken to represent preference, using an evaluation function on worlds. In this richer setting, incoming new information may raise your evaluation value towards some options, but it can also reduce them. A semantics and matching logic will be presented to describe preference change in this manner.

Finally, we will present a comparison of the qualitative and quantitative
approaches presented in our lectures, and discuss various translations between them.

The abstract models presented in this tutorial can be applied to many
areas beond preference per se. We will discuss a few instances in belief revision (plausibility change), deontic logic (commands and changing obligations), voting theory (preference aggregation), and game theory.



	Dynamic Preference Logic Fenrong Liu Institute of Logic, Language and Computation - University of Amsterdam - The Netherlands Institute of Philosophy - Chinese Academy of Social Sciences - China
				References (1) A. Baltag, L. Moss, S. Solecki, 'The Logic of Common Knowledge, Public Announcements, and Private Suspicions', GILBOA I., Ed., Proceedings of the 7th Conference on Theoretical Aspects of Rationality and Knowledge (TARK 98), 1998, p. 43-56. (2) H. van Ditmarsch, W. van der Hoek, B. Kooi, "Dynamic Epistemic Logic", Springer, Berlin, 2006. (3) J. van Benthem and F. Liu, 'Dynamic Logic of Preference Upgrade', to appear in the Journal of Applied Non-Classical Logic, Vol 17: 2, 2007. (4) D. de Jongh and F. Liu, 'Optimality, Belief and Preference'. Tech Report, PP-2006-38, ILLC, University of Amsterdam. Also in S. Artemov and R. Parikh eds, "Proceedings of the Workshop on Rationality and Knowledge", ESSLLI, Malaga, 2006. (5) F. Liu, 'Preference Change and Information Processing'. Tech Report, PP-2006-41, ILLC, University of Amsterdam. Also in "Proceedings of the 7th Conference on Logic and the Foundations of Game and Decision Theory", Liverpool, 2006.
	General description: The notion of preference occurs across many areas, such as philosophy of action, decision theory, optimality theory, and game theory. Individual preferences can be used to predict behavior by rational agents. More abstract notions of preference also occur in conditional logic, non-monotonic logic and belief revision theory, whose semantics order worlds by relative similarity or plausibility. In the tutorial, we will present various languages to express preference. More importantly, preferences are not static, but they change triggered by incoming new information, or just changes in our own evaluation. We will present several approaches to model the dynamics of such changes. Prerequisite: Basics of Modal Logic. Introduction: epistemic dynamics: First we will review the basics of epistemic logic, both in its standard and its dynamic versions. A few typical examples will be presented to show the process of information update by exchanging information. The same methodology will be used to deal with preference change. Betterness based preference change: The notion of preference will be introduced as an unary modality, using a semantic relation of 'betterness' in Kripke models. After setting up the static logic, we will analyze what happens to the model when new information comes in, leading to a dynamic logic of preference change. Constraint-based preference change: Next, we define preference in terms of a constraint sequence, a concept from optimality theory. In case agents only have incomplete information, beliefs are introduced as well. We propose three definitions to describe different procedures agents may follow to get a preference using beliefs. Changes of preference are explored w.r.t their sources: changes of the constraint sequence, and changes in beliefs. Value-based preference change*: Finally, a more quantitative approach will be taken to represent preference, using an evaluation function on worlds. In this richer setting, incoming new information may raise your evaluation value towards some options, but it can also reduce them. A semantics and matching logic will be presented to describe preference change in this manner. Finally, we will present a comparison of the qualitative and quantitative approaches presented in our lectures, and discuss various translations between them. The abstract models presented in this tutorial can be applied to many areas beond preference per se. We will discuss a few instances in belief revision (plausibility change), deontic logic (commands and changing obligations), voting theory (preference aggregation), and game theory.