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Toward a Theory of Play: A Logical Perspective on Games and Interaction
, 2010
"... The combination of logic and game theory provides a finegrained perspective on information and interaction dynamics, a Theory of Play. In this paper we lay down the main components of such a theory, drawing on recent advances in the logical dynamics of actions, preferences, and information. We then ..."
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The combination of logic and game theory provides a finegrained perspective on information and interaction dynamics, a Theory of Play. In this paper we lay down the main components of such a theory, drawing on recent advances in the logical dynamics of actions, preferences, and information. We then show how this finegrained perspective has already shed new light on the longterm dynamics of information exchange, as well as on the muchdiscussed question of extensive game rationality.
A Uniform Logic of Information Dynamics
"... Unlike standard modal logics, many dynamic epistemic logics are not closed under uniform substitution. A distinction therefore arises between the logic and its substitution core, the set of formulas all of whose substitution instances are valid. The classic example of a nonuniform dynamic epistemic ..."
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Unlike standard modal logics, many dynamic epistemic logics are not closed under uniform substitution. A distinction therefore arises between the logic and its substitution core, the set of formulas all of whose substitution instances are valid. The classic example of a nonuniform dynamic epistemic logic is Public Announcement Logic (PAL), and a wellknown open problem is to axiomatize the substitution core of PAL. In this paper we solve this problem for PAL over the class of all relational models with infinitely many agents, PALKω, as well as standard extensions thereof, e.g., PALTω, PALS4ω, and PALS5ω. We introduce a new Uniform Public Announcement Logic (UPAL), prove completeness of a deductive system with respect to UPAL semantics, and show that this system axiomatizes the substitution core of PAL.
doi:10.1111/j.17552567.2011.01119.x Everything is Knowable – How to Get to Know Whether a Proposition is Truetheo_1119 1..22
, 2012
"... Abstract: Fitch showed that not every true proposition can be known in due time; in other words, that not every proposition is knowable. Moore showed that certain propositions cannot be consistently believed. A more recent dynamic phrasing of Mooresentences is that not all propositions are known af ..."
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Abstract: Fitch showed that not every true proposition can be known in due time; in other words, that not every proposition is knowable. Moore showed that certain propositions cannot be consistently believed. A more recent dynamic phrasing of Mooresentences is that not all propositions are known after their announcement, i.e., not every proposition is successful. Fitch’s and Moore’s results are related, as they equally apply to standard notions of knowledge and belief (S 5 and KD45, respectively). If we interpret ‘successful ’ as ‘known after its announcement ’ and ‘knowable ’ as ‘known after some announcement’, successful implies knowable. Knowable does not imply successful: there is a proposition j that is not known after its announcement but there is another announcement after which j is known. We show that all propositions are knowable in the more general sense that for each proposition, it can become known or its negation can become known. We can get to know whether it is true: �(Kj ⁄ K¬j). This result comes at a price. We cannot get to know whether the proposition was true. This restricts the philosophical relevance of interpreting ‘knowable ’ as ‘known after an announcement’. Keywords: modal logic, knowability, Fitch’s paradox, dynamic epistemics, public announcements 1. Successful – the Historical Record
Moorean Phenomena in Epistemic Logic
, 2010
"... ◮ Under what conditions does a true piece of information remain true when it is received by an agent? ..."
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◮ Under what conditions does a true piece of information remain true when it is received by an agent?
Dynamic consequence and public announcement
, 2013
"... In [25] van Benthem proposes a dynamic consequence relation defined as ψ1,..., ψn =d ϕ iff =pa [ψ1]...[ψn]ϕ, where the latter denotes consequence in public announcement logic, a dynamic epistemic logic. In this paper we investigate the structural properties of a conditional dynamic consequence re ..."
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In [25] van Benthem proposes a dynamic consequence relation defined as ψ1,..., ψn =d ϕ iff =pa [ψ1]...[ψn]ϕ, where the latter denotes consequence in public announcement logic, a dynamic epistemic logic. In this paper we investigate the structural properties of a conditional dynamic consequence relation =dΓ extending van Benthem’s proposal. It takes into account a set of background conditions Γ, inspired by [18] wherein Makinson calls this reasoning ‘modulo ’ a set Γ. In the presence of common knowledge, conditional dynamic consequence is definable from (unconditional) dynamic consequence. An open question is whether dynamic consequence is compact. We further investigate a dynamic consequence relation for soft instead of hard announcements. Surprisingly, it shares many properties with (hard) dynamic consequence. Dynamic consequence relations provide a novel perspective on reasoning about protocols in multiagent systems. 1 Introduction and
Characterizing Successful Formulas: the Multiagent Case
"... Abstract. Characterization of successful formulas in Public Announcement Logic (PAL) is a well known open problem in Dynamic Epistemic Logic. Recently, Holliday and ICard have given a complete characterization for the single agent case in [6]. However, the problem for the multiagent case is open. T ..."
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Abstract. Characterization of successful formulas in Public Announcement Logic (PAL) is a well known open problem in Dynamic Epistemic Logic. Recently, Holliday and ICard have given a complete characterization for the single agent case in [6]. However, the problem for the multiagent case is open. This paper gives a partial solution to the problem, characterizing the subclass of the language consisting of unary operators, and discusses methods to give a complete solution. 1