Knowledge Games and Coalitional Abilities

Ågotnes, Thomas; Ditmarsch, Hans van

doi:10.1007/978-3-319-06025-5_16

Cited by 4 publications

(7 citation statements)

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“…To the best of our knowledge, there is no complete axiomatization for Coalition Announcement Logic (CAL) introduced in [2], though an extension of it (subsuming both GAL and CAL) was completely axiomatized in [22] using infinitary rules. But no recursive axiomatization is known for GAL, CAL, or any of their extensions [2][3][4]33]. In contrast, in this paper we showed that the memory-enhanced version of CAL is embeddable in the (recursively axiomatized) GALM.…”

Section: Discussionmentioning

confidence: 75%

“…To the best of our knowledge, there are no known recursive axiomatizations for GAL, CAL etc. 23 In fact, the same state of affair applies to any logic that contains coalition announcement operators [2][3][4]33].…”

Section: Coalition Modality a Related Operator Is The Coalition Annou...mentioning

confidence: 99%

“…It is therefore not guaranteed that the validities of these logics are recursively enumerable. 2 The seminal paper on APAL [6] proved completeness using an infinitary rule, and then went on to claim that in theorem-proving 3 this rule can be replaced by the following finitary rule: from ψ → [θ][p]ϕ, infer ψ → [θ] ϕ, as long as the propositional variable p is "fresh". A similar method is adopted in the completeness proof of GAL in [1] and it was claimed that the infinitary rule used in the completeness proof could be replaced by the finitary rule 'from χ → [θ][ i∈G K i p i ]ψ infer χ → [θ][G]ψ', where p i 's are "fresh" and [G] is the group announcement operator, quantifying over updates with formulas of the form i∈G K i ϕ i .…”

Section: Introductionmentioning

confidence: 99%

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Arbitrary Public Announcement Logic with Memory

2022

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We introduce Arbitrary Public Announcement Logic with Memory (APALM), obtained by adding to the models a ‘memory’ of the initial states, representing the information before any communication took place (“the prior”), and adding to the syntax operators that can access this memory. We show that APALM is recursively axiomatizable (in contrast to the original Arbitrary Public Announcement Logic, for which the corresponding question is still open). We present a complete recursive axiomatization, that includes a natural finitary rule, and study this logic’s expressivity and the appropriate notion of bisimulation. We then examine Group Announcement Logic with Memory (GALM), the extension of APALM obtained by adding to its syntax group announcement operators, and provide a complete finitary axiomatization (again in contrast to the original Group Announcement Logic, for which the only known axiomatization is infinitary). We also show that, in the memory-enhanced context, there is a natural reduction of the so-called coalition announcement modality to group announcements (in contrast to the memory-free case, where this natural translation was shown to be invalid).

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Section: Discussionmentioning

confidence: 75%

Section: Coalition Modality a Related Operator Is The Coalition Annou...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Arbitrary Public Announcement Logic with Memory

2022

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“…To the best of our knowledge, there is no complete axiomatisation of CAL [3,11,4,5] or any other logic with coalition announcement operators. In this paper, we consider Coalition and Relativised Group Announcement Logic (CoRGAL), a combination of an extension of GAL and CAL, which includes operators for both group and coalition announcements.…”

mentioning

confidence: 99%

“…Note that following[8,7,2,3,5,9,11,4] we restrict formulas which agents in a group or coalition can announce to formulas of L EL . This allows us to avoid circularity in the definition.…”

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confidence: 99%

Coalition and Group Announcement Logic

Galimullin

Alechina

2017

Electron. Proc. Theor. Comput. Sci.

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Dynamic epistemic logics which model abilities of agents to make various announcements and influence each other's knowledge have been studied extensively in recent years. Two notable examples of such logics are Group Announcement Logic and Coalition Announcement Logic. They allow us to reason about what groups of agents can achieve through joint announcements in non-competitive and competitive environments. In this paper, we consider a combination of these logics -- Coalition and Group Announcement Logic and provide its complete axiomatisation. Moreover, we partially answer the question of how group and coalition announcement operators interact, and settle some other open problems.Comment: In Proceedings TARK 2017, arXiv:1707.0825

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Temporal Aspects of the Dynamics of Knowledge

Goranko

Pacuit

2014

Outstanding Contributions to Logic

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Knowledge Games and Coalitional Abilities

Cited by 4 publications

References 60 publications

Arbitrary Public Announcement Logic with Memory

Arbitrary Public Announcement Logic with Memory

Coalition and Group Announcement Logic

Temporal Aspects of the Dynamics of Knowledge

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