Fenrong Liu

Reasoning about preference dynamics

Preface.- Part I Introduction.- 1. Introduction.- Part II Dynamics of Information.- 2. Dynamic Epistemic Logic.- Part III Preference over Worlds.- 3. Preference over Worlds: Static Logic.- 4. Preference over Worlds: Dynamic Logic.- 5. Entanglement of Preference, Knowledge and Belief.- 6. Intermezzo: A Quantitative Approach.- Part IV Preference from Priorities.- 7. Preference from Priorities: Static Logic.- 8. Belief-based Preference.- 9. Preference from Priorities: Dynamic Logic.- Part V A Two-Level Perspective on Preference.- 10. A Two-Level Perspective on Preference.- Part VI Applications and Discussions.- 11. Deontic Reasoning.- 12. Games and Actions.- Part VII Finale.- 13. Conclusion.- References.- Index.

Logic in the community

Communities consist of individuals bounds together by social relationships and roles. Within communities, individuals reason about each other’s beliefs, knowledge and preferences. Knowledge, belief, preferences and even the social relationships are constantly changing, and yet our ability to keep track of these changes is an important part of what it means to belong to a community.

Logical Dynamics of Belief Change in the Community

In this paper we explore the relationship between norms of belief revision that may be adopted by members of a community and the resulting dynamic properties of the distribution of beliefs across that community. We show that at a qualitative level many aspects of social belief change can be obtained from a very simple model, which we call ‘threshold influence’. In particular, we focus on the question of what makes the beliefs of a community stable under various dynamical situations. We also consider refinements and alternatives to the ‘threshold’ model, the most significant of which is to consider changes to plausibility judgements rather than mere beliefs. We show first that some such change is mandated by difficult problems with belief-based dynamics related to the need to decide on an order in which different beliefs are considered. Secondly, we show that the resulting plausibility-based account results in a deterministic dynamical system that is non-deterministic at the level of beliefs.

Modelling simultaneous games in dynamic logic

We make a proposal for formalizing simultaneous games at the abstraction level of player’s powers, combining ideas from dynamic logic of sequential games and concurrent dynamic logic. We prove completeness for a new system of ‘concurrent game logic’ CDGL with respect to finite non-determined games. We also show how this system raises new mathematical issues, and throws light on branching quantifiers and independence-friendly evaluation games for first-order logic.

Preference, priorities and belief

In this paper we consider preference over objects. We show how this preference can be derived from priorities, properties of these objects, a concept which is initially from optimality theory. We do this both in the case when an agent has complete information and in the case when an agent only has beliefs about the properties. After the single agent case we also consider the multi-agent case. In each of these cases, we construct preference logics, some of them extending the standard logic of belief. This leads to interesting connections between preference and beliefs. We strengthen the usual completeness results for logics of this kind to representation theorems. The representation theorems describe the reasoning that is valid for preference relations that have been obtained from priorities. In the multi-agent case, these representation theorems are strengthened to the special cases of cooperative and competitive agents. We study preference change with regard to changes of the priority sequence, and change of beliefs. We apply the dynamic epistemic logic approach, and in consequence reduction axioms are presented. We conclude with some possible directions for future work.

A Two-Level Perspective on Preference

This paper proposes a two-level modeling perspective which combines intrinsic ‘betterness’ and reason-based extrinsic preference, and develops its static and dynamic logic in tandem. Our technical results extend, integrate, and re-interpret earlier theorems on preference representation and update in the literature on preference change.

Diversity of Agents and Their Interaction

Diversity of agents occurs naturally in epistemic logic, and dynamic logics of information update and belief revision. In this paper we provide a systematic discussion of different sources of diversity, such as introspection ability, powers of observation, memory capacity, and revision policies, and we show how these can be encoded in dynamic epistemic logics allowing for individual variation among agents. Next, we explore the interaction of diverse agents by looking at some concrete scenarios of communication and learning, and we propose a logical methodology to deal with these as well. We conclude with some further questions on the logic of diversity and interaction.

Reasoning About Agent Types and the Hardest Logic Puzzle Ever

In this paper, we first propose a simple formal language to specify types of agents in terms of necessary conditions for their announcements. Based on this language, types of agents are treated as ‘first-class citizens’ and studied extensively in various dynamic epistemic frameworks which are suitable for reasoning about knowledge and agent types via announcements and questions. To demonstrate our approach, we discuss various versions of Smullyan’s Knights and Knaves puzzles, including the Hardest Logic Puzzle Ever (HLPE) proposed by Boolos (in Harv Rev Philos 6:62–65, 1996). In particular, we formalize HLPE and verify a classic solution to it. Moreover, we propose a spectrum of new puzzles based on HLPE by considering subjective (knowledge-based) agent types and relaxing the implicit epistemic assumptions in the original puzzle. The new puzzles are harder than the previously proposed ones in the literature, in the sense that they require deeper epistemic reasoning. Surprisingly, we also show that a version of HLPE in which the agents do not know the others’ types does not have a solution at all. Our formalism paves the way for studying these new puzzles using automatic model checking techniques.

Von Wright’s “The Logic of Preference” revisited

Preference is a key area where analytic philosophy meets philosophical logic. I start with two related issues: reasons for preference, and changes in preference, first mentioned in von Wright’s book The Logic of Preference but not thoroughly explored there. I show how these two issues can be handled together in one dynamic logical framework, working with structured two-level models, and I investigate the resulting dynamics of reason-based preference in some detail. Next, I study the foundational issue of entanglement between preference and beliefs, and relate the resulting richer logics to belief revision theory and decision theory.

A Logic for Extensive Games with Short Sight

To characterize the structures and reason about strategies of extensivegames,much work has been done to provide the logical systems for such games. These logic systems focus on various perspectives of extensive games: Harrenstein et al., 2003 concentrated on describing equilibrium concepts and strategic reasoning. van Benthem, 2002 used dynamic logic to describe games as well as strategies.