Logics for Dynamics of Information and Preferences
Working sessions

This talk gives an introduction of the logical framework of bargaining. The Nash’s cooperative bargaining theory is reviewed from AI and MAS perspectives. By representing bargainers’ demands, beliefs and threats in logical statements and bargainers’ preferences over their negotiation terms in numerical form, an n-person bargaining situation is modelled as a tuple of bargainers’ belief states. A solution to the n-person bargaining problem is proposed based on the maxmin rule over the degrees of bargainers' satisfaction. The solution is uniquely characterized by four axioms: collective rationality, scale invariance, symmetry and mutually comparable monotonicity in conjunction with three other fundamental assumptions: individual rationality, consistency and comprehensiveness. The relationships of these axioms and assumptions, and their links to belief revision postulates and game theory axioms are discussed. The framework would help us to identify the rationality of bargaining agents and would initiate a new methodology of bargaining analysis.

 

 

Public announcement logic (PAL) is an extension of multi-agent epistemic logic that describes how agents' epistemic states change when pieces of information are conveyed publicly. The extension is given by the operator [A], where the intended reading of [A]p is ``after the announcement that A, p is true.''
This logic has been developed in two directions. One direction, studied by P.Balbiani, A. Baltag, H. van Ditmarsch, A. Herzig, T. Hoshi, and T. de Lima in TARK 2007. extends PAL with the operator [] that generalizes the operator [A] of PAL, where []p reads as ``after an arbitrary announcement, p is true.''
The other direction, investigated by J. van Benthem, J. Gerbrandy, and E. Pacuit in Tark 2007, gives a semantic setting to model various restrictions on the set of ``permissible'' sequences of announcements, while PAL is based on the assumption that an announcement can be made whenever what is to be announced is true.
The purpose of my talk will be to merge these two kinds of developments. I will talk about the extension of public announcement logic with the generalized public announcement operator within the framework that models the restricted set of permissible sequences of public announcements.

 

A well-known problem in the economic theory of choice is how a preference order among options can be derived on the assumption that the notion of choice is primitive. Assuming a choice function that selects elements from each finite set of options Arrow (1959) already showed how we can generate an ordering relation by putting constraints on how this function should behave on different sets of options. Arrow proposed that rational agents can be modeled by such choice functions. Arrow's standard model of rationality has been criticized in economics and gave rise to approaches of bounded rationality. Two standard assumptions of rationality will be given up in this paper. First, the idea that agents are utility optimizers (Simon). Second, the idea that the relation of `indifference' gives rise to an equivalence relation (Luce). To account for the latter, Luce (1956) introduced semi-orders. Extending some ideas of Van Benthem (1983), we will propose to derive semi-orders (and so-called interval orders) based on the idea that agents are utility satisficers rather than utility optimizers.

 

I will present some new developments in the so-called "token semantics" for modal logic that Paul Egre and I have been developing as a tool to solve a variety of epistemic puzzles. The main idea of token semantics is to parametrize the evaluation of modal formulas with respect to a fixed number of tokens: every move along the accessibility relation has a price and when all tokens have been spent, one has to backtrack in order to get tokens back. Token semantics is thus a family of semantics TS(n) where n, the number of tokens available to start with, is a fixed parameter determining how deep into the model a formula can go.

Some of you might have already heard Paul Egre talking about some of the (nice) applications we have in mind for the semantics. To avoid repetition and to echo some recent developments, I will rather focus in this talk on model-theoretic aspects:

a) Token semantics as a new twist on correspondence theory:
- token semantics makes some modal axioms (e.g. 4 and 5 for TS(1) ) valid even though the accessibility relation does not have the properties which standardly correspond to those axioms: in this sense, token semantics "makes more models available".
- extensions of standard correspondence results (e.g. by taking token semantics over the class of reflexive frames and adding T to the axioms) are shown to be non trivial. As an example, I will show how one can get from a logic of belief to a logic of knowledge and explain what the general issue is.

b) Completeness proofs for token semantics
We have completeness results for the single and multi agent versions of token semantics. The proofs involve some kind of reduction to completeness proofs for standard Kripke semantics. I will state the results and introduce some of the tools used in the proofs that might be considered to have a general interest: a notion of bisimulation for our logics and a special way of unwinding models.

 

As mentioned by van Benthem, “actual planning and problem solving often involves an entanglement of two logical processes: inference and update” [van Benthem, 2007]. Standard epistemic logics allows to express how updates (public announcements) modify the knowledge of agents, but there is no framework combining it with the more fine-grained inference steps.

Based on the work of Mark Jago [Jago, 2006a, Jago, 2006b], we present a logical language that allows us to express these two different ways of getting new information. Through public announcements, the agent discard situations that are not consistent with the announced fact; through inference steps, the agent make explicit information that was only implicit before. Moreover, we can express combinations of both: formulas like
K(I(p -> q)) -> [p!]<p -> q> K(I q)
(“if the agent knows p -> q then, after p is announced, she can perform an inference step with p -> q after which she will know that q is the case”), expressing the intertwine of the two logical process, have meaning in our language.

[Jago, 2006a] Jago, M. (2006a). Logics for Resource-Bounded Agents. PhD thesis, University of Nottingham.

[Jago, 2006b] Jago, M. (2006b). Rule-based and resource-bounded: A new look at epistemic logic. In Agotnes, T. and Alechina, N., editors, Proceedings of the Workshop on Logics for Resource-Bounded Agents, (ESSLLI 2006).

[van Benthem, 2007] van Benthem, J. (2007). Tell it like it is:
Information flow in logic. Unpublished manuscript.

 

I will use standard tools of modal logic with nominals to formalize lexicographic preference aggregation (or something like that). I will either present a completeness proof or show how to introduce dynamic actions, viz. agent promotion or demotion in (sub)groups. (or something like that).

 

Paolo Turrini (Computer Science)
A Deontic Logic for Socially Optimal Norms
To understand the dynamics of norms, and in particular, the reason why a norm emerges or is useful for a society, one has to understand in what sense norms are related to the social preferences and abilities of coalitions of agents. We investigate this relation by defining an operator for social rational choice, and by considering situations where what is rational for sub-groups may conflict with what is rational for the whole group. We assume that the presence of reachable outcomes that are optimal for the whole group gives rise to a social norm saying that sub-groups should not pursue their own best interest if that conflicts with what is best for the group. We do not study or represent norms explicitly. Instead, we define a semantics for deontic operators for permission, prohibition and obligation to perform collective action, in terms of the implicit social norms resulting from the social preferences and collective abilities of agents. Finally, we discuss how preferences themselves, in turn, might be affected by social norms. In particular, agents may internalize norms such that they actually become preferences. One question we address is whether this internalization process should be seen as a process of norm change or not. We will argue that our concepts are broadly applicable, especially in game-theoretical and social science domains. (work with Jan Broersen, Rosja Mastop, John-Jules Meyer)

Rosja Mastop (Philosophy)
On granting choices. Deontic logic as founded on Update
semantics
In the 1990s von Wright offered an interesting view on the nature of deontic logic. Norm systems can, and often are, inconsistent. Yet, the concept of `norm consistency' does not express a logical necessity of consistent norms, but rather the personal consistency of the norm-giver (or norm-accepter). Permission must be understood as a self-imposed constraint of the norm-giver on possible commands. In this presentation I will propose a formal explication of von Wright's view. The basic idea will be to develop an update semantics on top of Pauly's Coalition Logic.

Patrick Girard (Stanford)

Jan Broersen (Computer science)
Doing Things (Un)knowingly: Explorations in Epistemic STIT Theory
Coalition Logic, Alternating Time Temporal Logic and STIT theory have in common that action is viewed as enforcing the actual world to be among the elements of a set of possible worlds satisfying the effect of the action. We show how in this setting we can suitably introduce epistemic indistinguishability relations between action-state pairs. This enables one to characterize uniformity of strategies as a standard commutativity axiom. The resulting logic raises many conceptual points on the nature of action and knowledge. One of the issues I will discuss is the difference between doing something knowingly and doing something unknowingly. (work with Andreas Herzig, Nicolas Troquard, John Horty)

Thomas Müller (Philosophy)
Doing several things at once -- A challenge for a spatial
extension of STIT
STIT theory is based on branching time structures that disregard the spatial environment of agents. Even though there is room for multiple independent agents in the framework, that may appear as a merely formal add-on. Rather than postulating independent agents labeled by different abstract indexes, it would be nicer to derive agents' independence from their spatio-temporal relations. There are other reasons besides this that also speak in favor of a spatial extension of STIT. Nuel Belnap has proposed such an extension, which is based not on branching time, but on branching space-times structures. In his tentative listing of postulates for such a STIT extension, agents are represented by point-thin world lines in space-time. In my paper, I will present reasons for favoring a (literally) broader basis for agents in space-time. My argument is based on an exploration of the rich phenomenology of "doing several things at once". My claim is that at least some familiar cases of doing several things at once can only be understood if one presupposes spatially extended agents.