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121
Concurrent Dynamic Epistemic Logic
, 2003
"... When giving an nalysis of knowledge in multiagent systems, one needs a framework in which higherorder information and its dynamics can both be represented. A recent tradition stoxting in origina work by Plaza treats all of knowledge, higherorder knowledge, and its dynamics on the sae foot. Our ..."
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Cited by 111 (21 self)
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When giving an nalysis of knowledge in multiagent systems, one needs a framework in which higherorder information and its dynamics can both be represented. A recent tradition stoxting in origina work by Plaza treats all of knowledge, higherorder knowledge, and its dynamics on the sae foot. Our work is in that tradition. It also fits in approaches that not only dynaize the epistemics, but also epistemize the dynamics: the ac tions that (groups of) agents perform oxe epistemic actions. Different agents may have different information about which action is taking place, including higherorder information. We demonstrate that such information changes require subtle descriptions. Our contribution is to provide a complete axiomatization for n action language of vn Ditmoxsch, where an action is interpreted as a relation between epistemic states (pointed models) and sets of epistemic states. The applicability of the framework is found in every context where multiagent strategic decision making is at stake, and aready demonstrated in gaelike scenoxios such as Cluedo and coxd games.
A Logic for Suspicious Players: Epistemic Actions and BeliefUpdates in Games
, 2000
"... In this paper, we introduce a notion of "epistemic action" to describe changes in the information states of the players in a game. For this, we use ideas that we have developed in our previous papers [BMS], [BMS2] and [B], enriching them to cover, not just purely epistemic actions, but also factc ..."
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Cited by 46 (2 self)
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In this paper, we introduce a notion of "epistemic action" to describe changes in the information states of the players in a game. For this, we use ideas that we have developed in our previous papers [BMS], [BMS2] and [B], enriching them to cover, not just purely epistemic actions, but also factchanging actions ("real moves", e.g. choosing a card, exchanging cards etc.) and nondeterministic actions and strategies (conditional actions having knowledge tests as conditions). We consider natural operations with epistemic actions and we use them to describe significant aspects of the interaction between beliefs and actions in a game. For this, we use a logic that combines in a specific way a multiagent epistemic logic with a dynamic logic of "epistemic actions". We give (without proof) a complete and decidable proof system for this logic. As an application, we analyze a specific example of a dialogue game (a version of the Muddy Children Puzzle, in which some of the children can ...
Expressivity and completeness for public update logic via reduction axioms
 Journal of Applied NonClassical Logics
"... ABSTRACT. In this paper, we present several extensions of epistemic logic with update operators modelling public information change. Next to the wellknown public announcement operators, we also study public substitution operators. We prove many of the results regarding expressivity and completeness ..."
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Cited by 30 (6 self)
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ABSTRACT. In this paper, we present several extensions of epistemic logic with update operators modelling public information change. Next to the wellknown public announcement operators, we also study public substitution operators. We prove many of the results regarding expressivity and completeness using socalled reduction axioms. We develop a general method for using reduction axioms and apply it to the logics at hand.
Epistemic actions as resources
 Journal of Logic and Computation
, 2007
"... We provide algebraic semantics together with a sound and complete sequent calculus for information update due to epistemic actions. This semantics is flexible enough to accommodate incomplete as well as wrong information e.g. deceit. We give a purely algebraic treatment of the muddy children puzzle, ..."
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Cited by 19 (13 self)
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We provide algebraic semantics together with a sound and complete sequent calculus for information update due to epistemic actions. This semantics is flexible enough to accommodate incomplete as well as wrong information e.g. deceit. We give a purely algebraic treatment of the muddy children puzzle, which moreover extends to situations where the children are allowed to lie and cheat. Epistemic actions, that is, information exchanges between agents A, B,... ∈ A, are modeled as elements of a quantale, hence conceiving them as resources. Indeed, quantales are to locales what monoidal closed categories are to Cartesian closed categories, respectively providing semantics for Intuitionistic Logic, and for noncommutative Intuitionistic Linear Logic, including Lambek calculus. The quantale (Q, � , •) acts on an underlying Qright module (M, � ) of epistemic propositions and facts. The epistemic content is encoded by appearance maps, one pair f M A: M → M and f Q A: Q → Q of (lax) morphisms for each agent A ∈ A. By adjunction, they give rise to epistemic modalities [12], capturing the agents ’ knowledge on propositions and actions. The module action is epistemic update and gives rise to dynamic modalities [20] — cf. weakest preconditions. This model subsumes the crucial fragment of Baltag, Moss and Solecki’s [6] dynamic epistemic logic, abstracting it in a constructive fashion while introducing resourcesensitive structure on the epistemic actions. Keywords: Multiagent communication, knowledge update, resourcesensitivity, quantale, Galois adjoints, dynamic epistemic logic, sequent calculus, Lambek calculus, Linear Logic.
The tree of knowledge in action: Towards a common perspective
 In G. Governatori, I. Hodkinson, & Y. Venema (Eds.), Proceedings of advances in modal logic
, 2006
"... abstract. We survey a number of decidablity and undecidablity results concerning epistemic temporal logic. The goal is to provide a general picture which will facilitate the ‘sharing of ideas ’ from a number of different areas concerned with modeling agents in interactive social situations. ..."
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Cited by 17 (7 self)
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abstract. We survey a number of decidablity and undecidablity results concerning epistemic temporal logic. The goal is to provide a general picture which will facilitate the ‘sharing of ideas ’ from a number of different areas concerned with modeling agents in interactive social situations.
Dynamic Update with Probabilities
, 2008
"... Current dynamicepistemic logics model different types of information change in multiagent scenarios. We propose a way to generalize these logics to a probabilistic setting, obtaining a calculus for multiagent update with different slots for probability, and a matching dynamic logic of information ..."
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Cited by 15 (2 self)
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Current dynamicepistemic logics model different types of information change in multiagent scenarios. We propose a way to generalize these logics to a probabilistic setting, obtaining a calculus for multiagent update with different slots for probability, and a matching dynamic logic of information change that has a probabilistic character itself. We present a general completeness result that not only holds for the particular logical system set out in this paper, but for a larger class of dynamic probabilistic logics as well. Finally, we discuss how our basic update rule can be parameterized for different ‘update policies’.
The secret of My Success
 SYNTHESE
, 2004
"... In an information state where various agents have both factual knowledge and knowledge about each other, announcements can be made that change the state of information. Such informative announcements can have the curious property that they become false because they are announced. The most typical ex ..."
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Cited by 14 (6 self)
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In an information state where various agents have both factual knowledge and knowledge about each other, announcements can be made that change the state of information. Such informative announcements can have the curious property that they become false because they are announced. The most typical example of that is `fact p is true and you don't know that', after which you know that p,which entails the negation of the announcement formula. The announcement of such a formula in a given information state is called an unsuccessful update. A successful formula is a formula that always becomes common knowledge after being announced. Analysis of information systems and `philosophical puzzles' reveals a growing number of dynamic phenomena that can be described or explained by unsuccessful updates. This increases our understanding of such philosophical problems. We also investigate the syntactic characterization of the successful formulas.
Keep ‘Hoping’ for Rationality: A solution to the Backward Induction Paradox
, 2009
"... Aumann has proved that common knowledge of substantive rationality implies the backward induction solution in games of perfect information. Stalnaker has proved that it does not. (Halpern, 2001) The jury is still out concerning the epistemic conditions for backward induction, the “oldest idea in gam ..."
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Cited by 12 (0 self)
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Aumann has proved that common knowledge of substantive rationality implies the backward induction solution in games of perfect information. Stalnaker has proved that it does not. (Halpern, 2001) The jury is still out concerning the epistemic conditions for backward induction, the “oldest idea in game theory ” (Aumann, 1995, p. 635). Aumann (1995) and Stalnaker (1996) take conflicting positions in the debate: the former claims that common “knowledge ” of “rationality ” in a game of perfect information entails the backwardinduction solution; the latter that it does not. 1 Of course there is nothing wrong with any of their relevant formal proofs, but rather, as pointed out by Halpern (2001), there are differences between their interpretations of the notions of knowledge, belief, strategy and rationality. Moreover, as pointed out by Binmore (1987; 1996),