This work is part of the on-going trend (see Aueher, 2003; van Benthem, 2004; van Ditmarseh, 2005; Baltag and Sadrzadeh, 2006; Baltag and Smets, 2006a,b,e, 2007a,b, 2008) towards ineorporating belief revision meehanisms within the Dynamie-Epistemie Logie (DEL) approach to information update. As sueh, this paper ean be eonsidered a sequel to our recent work (Baltag and Smets, 2008), and it is based on a revised and improved version of our older unpublished paper (Baltag and Smets, 2006e), presented at the 2006 ESSLLI Workshop on “Rationality and Knowledge”.

We assume the general distinetion, made by van Ditmarseh (2005), Baltag and Smets...

In this commentary on ‘The Logic of Conditional Doxastic Actions’ I am in the delightful position of having the last word in an argument with Alexandru Baltag. This position is very hard to obtain. But because in this volume my commentary follows the chapter by Alexandru Baltag and Sonja Smets, any further elaborations and involutions will be out of re ach to the readers of the volume. lam going to use this rare advantage to the limit.

Having said that, I sent a preliminary version of these comments to Alexandru and Sonja for comments, and immediately received in response an...

Since the foundational work of Alchourrón, Gärdenfors and Makinson (1985), the theory of belief revision has been a very active area of research. Recently several authors have been attempting to re-cast belief revision within a modal framework. Pioneering work in this new area was done by Segerberg (1995, 1999) in the context of dynarnic doxastic logic, Board (2002) in the context of multi-agent doxastic logic and van Benthem (2004) in the context of dynarnic epistemic logic. Much progress has been made both in dynarnic episternic logic (see, for example, Baltag and Smets, 2006; van Ditmarseh, 2005; van Ditmarsch and Labuschagne,...

Bonanno’s paper offers a rational reconstruction of Alchourrón Gärdenfors Makinson style belief revision (AGM belief revision) (Alchourrón et al., 1985; see also Gärdenfors, 1988 and Gärdenfors and Rott, 1995), in a framework where modalitiesBfor single agent belief andIfor being informed are mixed with a next time operator 0 and its inverse O-¹.

Both the AGM framework and Bonanno’s reconstruction of it do not explicitly represent the triggers that cause belief change in the first place. / φ expresses that the agent is informed that φ, but the communicative action that causes this change in information state...

The modeling of information in strategie settings has been the centerpieee of economie theory for almost four decades now. Models of signaling, bargaining, auctions, contracts, mechanism design and more, are grounded in the premise that the decision makers posses private information relevant for outcomes, that their behavior is conditioned on their information, that they form beliefs about the information held by others and that they revise these beliefs based on observed actions. In addition, these fields of research add the possibility of communication between decision makers. However, formal theoretical economics modeling tends to overlook thecontent, or meaning of the...

A persuasion situation involves an agent(the speakerswho attempts to persuade another agent(the listeneT)to take a certain action. Whether or not the listener should accept the speaker's suggestion depends on information possessed by the speaker. In such a situation, the speaker often presents hard evidence to support his position, but is restricted as to how many pieces of evidence he can present. This restrietion may be due either to time constraints or to limitations on the listener’s capability to process information. Our purpose in this paper is to shed light on the rules that determine which of...

Jacob Glazer and Ariel Rubinstein profter an exciting new approach to analyze persuasion. Perhaps even without being aware of it, and at least not acknowledged in the bibliography, their paper addresses questions that argumentation theorists, logicians, and cognitive and social psychologists have been interested in since Aristotle’sRhetoric. Traditionally, argumentation was thought of as an activity involving knowiedge, beliefs, opinions, and it was contrasted with bargaining, negotiation and other strategie activities involving coereion, threats, deception, and what have you. More recently, however, several theorists have argued that strict boundaries are conceptually indefensible and undesirable methodologically, separating as they do researchers...

Infinite games in which two or more players take turns to move a token through a directed graph, tracing out an infinite path, have numerous applications in computer science. The fundamental mathematical questions on such games concern the existence of optimal strategies for the players, the complexity and structural properties of such strategies, and their realisation by efficient algorithms. Which games are determined, in the sense that from each position, one of the players has a winning strategy? How to compute winning positions and optimal strategies? How much knowledge on the past of a play is necessary to determine an...

One traditional view in philosophy and linguistics is that without rules of usage common to the speaker and the listener, communication would be impossible. According to it, every linguistic expression has a meaning which is determined by the rules for its correct use. This obviously brings language and games together, for it is in the latter that rules are explicitly given. Here are two examples of language games which iliustrate in a very simple and ideal way how a communication language could emerge out oflanguage games. They are due to the Finnish logician Erik Stenius who thought that they...

What do games have to do with natural language? On the traditional view of linguists and logicians,syntaxis about grammatical code,semanticsis about mathematical relationships between syntactic code and structures in reality, while the rest of language use is the bustling but unsystematic world ofpmgmatics. In particular, on this view, meaning does not involve agency of any kind: it is a ‘O-agent notion’. But starting from the 1970s, another view emerged placing actions of language users at centre stage, making meaning the ‘information change’, or more general ‘context change potential’ of linguistic expressions. Speakers or writers change...

Fifty years ago, during the “Summer Institute of Symbolic Logic” at Cornell University in 1957, Alonzo Church (1957) considered a problem which is both simply stated and fundamental.

Imagine a scenario in which an infinite bit stream α is to be transformed, bit by bit, into an infinite stream13, as indicated in the following figure.

The task is to construct a finite-state proeed ure for this transformation when we are given a “specification” of the relation between α and13. This specification is usually presented as a formula of a logical system. In short words: We have to fill...

Is it possible that in the future currency exchange rates depend only on government decisions? It is perhaps possible, but it is certainly not necessary. In (Väänänen, 2007) we outlined the basics of the logic of dependence. In this paper we take it upon ourselves to start a study of the logic of “possible dependence” .

Eydependeneewe mean dependence as it occurs in the foliowing contexts: Dependence of

a move of a player in a game on previous moves

an attribute of a database on other attributes

an event in history on other events

a variabie of an...

Dependence is one of these subtie concepts with so many connotations and usages, that any analysis of its meaning is predestined to fall short of some of its aspects. In the first paragraph of the bookDependenee Logic, Väänänen (2007), states:

‘Dependence is a common phenomenon, wherever one looks: ecological systems, astronomy, human history, stock markets. With global warming, the dependence of life on earth on the actions of mankind has become a burning issue. But what is the logic of dependence?’

The book promises a systematic study of the concept, and to show that there is a mathematical theory...

Economists and game theorists use concepts of knowiedge, belief, and rationality to characterize solution concepts. In this work we present an epistemic characterization of the red uction process introduced by Pearce (1984). To do this, we use a syntactic environment in a way that correlates a language to every extensive-form game.

A natural starting point is Aumann’s work on backward induction (Aumann, 1995). This work uses the usual knowledge partition setup for anaIyzing interactive rationality in generic perfect information (PI) games.

Let r be a PI game and let Ω be a set of states of the world such that...

Boolean games (Harrenstein et al., 2001; Harrenstein, 2004; Dunne and van der Hoek, 2004; Bonzon et al., 2006b) are a logical setting for representing strategie games in a succinct way, taking advantage of the expressive power and conciseness of propositional logic. Informally, a Boolean game consists of a set of players, each of whom controls a set of propositional variables and has a specific goal expressed by a propositional formula ¹. Thus, a player in a Boolean game has a dichotomous preferenee relation: either her goal is satisfied or it is not. This restrietion may appeal’ at first glance unreasonable....

Often we express more with the use of our words than what those words mean literal!y. For example, if you were to say that this observation is not particularly new, I would clearly get the hint and understand that you meant to say that it is more than just not particularly new, indeed a werking standard in linguistic pragmatics. Suchconoersationol implicaiureswere first studied by Grice (1989) and stil! concern the community in various ways. In particular, recent years saw an increasing interest in game-theoretic models of conversational implicature calculation, and this study belongs to this line of research....

Markov decision processes model situations where a controller wishes to control optimally a system, taking her decisions in a sequential way and facing stochastic behaviour of the system. Step aftel’ step, the Markov decision process goes through a sequence of statessa, sl, ... from a set of states S. At each step, the controller chooses an actionaΕ A, which causes the process to change from state s to new statetwith fixed probabilityp(tls, a). The probability that the decision process stops is 0, i.e.,\Sigma _{t\in \mathrm{S}} \: p(t|s,\: a) = 1and the time horizon is not bounded hence the decision...