A guide to completeness and complexity for modal logics of knowledge and belief

Halpern, Joseph Y.; Moses, Yoram

doi:10.1016/0004-3702(92)90049-4

Cited by 630 publications

(480 citation statements)

References 25 publications

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“…In particular, the accessibility relations of S5 nmodels are equivalence relations, those of S4 n -models are re exive and transitive, and KD45 n -models are serial, transitive, and Euclidean (cf. [2], [9], [12]. )…”

Section: Zusammenfassungmentioning

confidence: 99%

Reasoning about rational, but not logically omniscient, agents

Duc

1997

Journal of Logic and Computation

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Section: Zusammenfassungmentioning

confidence: 99%

Reasoning about rational, but not logically omniscient, agents

Duc

1997

Journal of Logic and Computation

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“…The role of common knowledge has been studied in the fields of distributed computing and artificial intelligence [11,7,12]. This line of work suggests that knowledge is an important abstraction for distributed systems and for the design and analysis of distributed protocols, in particular for achieving consistent simultaneous actions.…”

Section: Related Workmentioning

confidence: 99%

Common Knowledge and State-Dependent Equilibria

Dalkıran

Hoffman

Paturi

et al. 2012

Algorithmic Game Theory

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Abstract. Many puzzling social behaviors, such as avoiding eye contact, using innuendos, and insignificant events that trigger revolutions, seem to relate to common knowledge and coordination, but the exact relationship has yet to be formalized. Herein, we present such a formalization. We state necessary and sufficient conditions for what we call state-dependent equilibria -equilibria where players play different strategies in different states of the world. In particular, if everybody behaves a certain way (e.g. does not revolt) in the usual state of the world, then in order for players to be able to behave a different way (e.g. revolt) in another state of the world, it is both necessary and sufficient for it to be common p-believed that it is not the usual state of the world, where common p-belief is a relaxation of common knowledge introduced by Monderer and Samet [16]. Our framework applies to many player r-coordination games -a generalization of coordination games that we introduce -and common (r, p)-beliefs -a generalization of common p-beliefs that we introduce. We then apply these theorems to two particular signaling structures to obtain novel results.

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“…Most well-known modal logics considered in the literature (both normal and non-normal) fit Definition 6.9: these include standard unary unimodal systems like K, T, K4, S4, S5 and so on [34], tense systems like K t and other temporal logics [35], the propositional dynamic logic PDL [36], common knowledge systems [37], and computational tree logic CTL [38]. 28 Modal logics with so-called graded modalities [40][41][42] (which correspond to qualified number restrictions in Description Logics [43]) are examples of classical modal logics that are not normal [17].…”

Section: Equational Theories Induced By Modal Logicsmentioning

confidence: 99%

“…Therefore it is enough to show the validity of As a final remark observe that if we replace in the example the logic R by the logic E, the execution of the procedure is the same but the final test is negative. To get a falsifying model for the modal propositional formula in the final test, it is sufficient to observe that any Boolean algebra in which the operator c is interpreted as the Boolean complement is a model of E. 37 …”

Section: Examplesmentioning

confidence: 99%

A New Combination Procedure for the Word Problem That Generalizes Fusion Decidability Results in Modal Logics

Baader

Ghilardi

Tinelli

2004

Automated Reasoning

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Previous results for combining decision procedures for the word problem in the nondisjoint case do not apply to equational theories induced by modal logics-which are not disjoint for sharing the theory of Boolean algebras. Conversely, decidability results for the fusion of modal logics are strongly tailored towards the special theories at hand, and thus do not generalize to other types of equational theories.In this paper, we present a new approach for combining decision procedures for the word problem in the non-disjoint case that applies to equational theories induced by modal logics, but is not restricted to them. The known fusion decidability results for modal logics are instances of our approach. However, even for equational theories induced by modal logics our results are more general since they are not restricted to so-called normal modal logics.

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A guide to completeness and complexity for modal logics of knowledge and belief

Cited by 630 publications

References 25 publications

Reasoning about rational, but not logically omniscient, agents

Reasoning about rational, but not logically omniscient, agents

Common Knowledge and State-Dependent Equilibria

A New Combination Procedure for the Word Problem That Generalizes Fusion Decidability Results in Modal Logics

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