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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 ...
Dynamic Epistemic Logic
 Logic, Language, and Information 2, Stanford University, CSLI Publication
, 1997
"... This paper is the result of combining two traditions in formal logic: epistemic logic and dynamic semantics. Dynamic semantics is a branch of formal semantics that is concerned with ..."
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Cited by 36 (1 self)
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This paper is the result of combining two traditions in formal logic: epistemic logic and dynamic semantics. Dynamic semantics is a branch of formal semantics that is concerned with
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.
Dynamic Bits And Pieces
, 1997
"... Arrow Logic remains PSPACEcomplete. Further arrow axioms can easily lead to 36 undecidability. (In private correspondence, Marx has also announced EXPTIME complexity for the original Guarded Fragment, via a reduction to CRS over 'locally cube' models.) Marx and Venema 1996 is a systematic stateo ..."
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Cited by 26 (3 self)
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Arrow Logic remains PSPACEcomplete. Further arrow axioms can easily lead to 36 undecidability. (In private correspondence, Marx has also announced EXPTIME complexity for the original Guarded Fragment, via a reduction to CRS over 'locally cube' models.) Marx and Venema 1996 is a systematic stateoftheart presentation of manydimensional modal logic, including bridges with algebraic logic, as well as many key techniques for dynamic logic, broadly conceived. Ter Meulen 1995 proposes a concise framework for temporal representation in natural language that may be viewed as an alternative dynamification of temporal logic, using an extra, intermediate level of representation. Successive formulas algorithmically generate successive 'dynamic aspect trees', for which there is a notion of 'succesful embedding' into standard temporal models. Valid inference can then be defined as verification of the conclusion by any succesful embedding for the DAT of the premise sequence. This alternative d...
Descriptions of game actions
 JOURNAL OF LOGIC, LANGUAGE AND INFORMATION
, 2002
"... To describe simultaneous knowledge updates for different subgroups we propose an epistemic language with dynamic operators for actions. The language is interpreted on equivalence states (S5 states). The actions are interpreted as state transformers. Two crucial action constructors are learning and ..."
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Cited by 14 (10 self)
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To describe simultaneous knowledge updates for different subgroups we propose an epistemic language with dynamic operators for actions. The language is interpreted on equivalence states (S5 states). The actions are interpreted as state transformers. Two crucial action constructors are learning and local choice. Learning is the dynamic equivalent of common knowledge. Local choice aids in constraining the interpretation of an action to a functional interpretation (state transformer). Bisimilarity is preserved under execution of actions. The language is applied to describe various actions in card games.
Dynamic Logic Reasoning about Actions and Agents
 LogicBased Artificial Intelligence
, 1999
"... Dynamic logic is a logic to reason about the dynamics of (natural or artificial) systems in general, ranging from the effects of actions of human agents to the behaviour of artificial agents and software systems. Therefore it is to be expected that in AI it can be fruitfully employed both to rep ..."
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Cited by 13 (0 self)
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Dynamic logic is a logic to reason about the dynamics of (natural or artificial) systems in general, ranging from the effects of actions of human agents to the behaviour of artificial agents and software systems. Therefore it is to be expected that in AI it can be fruitfully employed both to represent knowledge about the dynamics of the domain at hand as well as to describe / specify (the dynamic behaviour of) AI systems themselves. A typical example of the former is the description of the effects of actions (of humans, for example) in the commonsense world, while the specification of a particular reasoning system would be of the latter type. In this paper a number of examples are given to illustrate the usefulness (and wide scope!) of dynamic logic for AI. 1 Introduction Originally, dynamic logic has been proposed in computer science as a logic for reasoning about programs in order to verify their correctness. Later it was realised that dynamic logic could also be fruitful...
Evolution of Collective Commitment during Teamwork
, 2003
"... In this paper we aim to describe dynamic aspects of social and collective attitudes in teams of agents involved in Cooperative Problem Solving (CPS). Particular attention is given to the strongest motivational attitude, collective commitment, and its evolution during team action. First, building ..."
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Cited by 13 (3 self)
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In this paper we aim to describe dynamic aspects of social and collective attitudes in teams of agents involved in Cooperative Problem Solving (CPS). Particular attention is given to the strongest motivational attitude, collective commitment, and its evolution during team action. First, building on our previous work, a logical framework is sketched in which a number of relevant social and collective attitudes is formalized, leading to the planbased definition of collective commitments.
Dynamic Odds & Ends
 Ethics
, 1998
"... Modal logic becomes action logic by adding programs as in propositional dynamic logic or the µ calculus. Modal languages can be seen as decidable fragments of firstorder logic that admit a natural bisimulation, and hence enjoy a good model theory. Recently, much stronger 'guarded fragments' of f ..."
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Cited by 13 (2 self)
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Modal logic becomes action logic by adding programs as in propositional dynamic logic or the µ calculus. Modal languages can be seen as decidable fragments of firstorder logic that admit a natural bisimulation, and hence enjoy a good model theory. Recently, much stronger 'guarded fragments' of firstorder logic have been identified that enjoy the same pleasant features. The latter can serve as richer action languages as well. We will develop the logic of guarded fragments as a form of process theory. ln particular, moving from sequential to parallel process operations correlates with moving to firstorder fragments that are close to, or perhaps just over the decidableundecidable fence. 1 The modal dynamics of actions We will start by reviewing the basics. Standard polymodal logic is a decidable fragment of the firstorder logic of process graphs (labeled transition systems, Kripke models). It can be characterized semantically as consisting, up to logical equivalence, of those firs...
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),