Logics with Group Announcements and Distributed Knowledge: Completeness and Expressive Power

Ågotnes, Thomas; Alechina, Natasha; Galimullin, Rustam

doi:10.1007/s10849-022-09355-0

Cited by 5 publications

(4 citation statements)

References 25 publications

(36 reference statements)

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“…Completeness of the whole system can be shown by combining and adapting techniques from [40] (to deal with distributed knowledge) and [7] (to tackle quantifiers). The reader interested in details is referred to [1], where the authors presented a relatively similar completeness proof for a system with distributed knowledge and quantification over public announcements. ).…”

Section: Language Semantics and Basic Resultsmentioning

confidence: 99%

“…For showing that a form of model equivalence implies invariance for a language, one usually uses induction on the language's formulas. 1 For P-bisimilarity and L, see [29].…”

Section: Pmentioning

confidence: 99%

“…and suppose ( , ) ⇄ ( ′ , ′ ). For Item (1), proceed by structural induction on . The cases for atoms, Boolean operators and D G are as in Theorem 2.7.…”

Section: A Appendix Proof Of Theorem 211mentioning

confidence: 99%

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(Arbitrary) Partial Communication

Galimullin¹,

Velázquez–Quesada²

2023

Preprint

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Communication within groups of agents has been lately the focus of research in dynamic epistemic logic (DEL). This paper studies a recently introduced form of partial (more precisely, topic-based) communication. This type of communication allows for modelling scenarios of multi-agent collaboration and negotiation, and it is particularly well-suited for situations in which sharing all information is not feasible/advisable. After presenting results on invariance and complexity of model checking, the paper compares partial communication to public announcements, probably the most well-known type of communication in DEL. It is shown that the settings are, update-wise, incomparable: there are scenarios in which the effect of a public announcement cannot be replicated by partial communication, and vice versa. Then, the paper shifts its attention to strategic topic-based communication. It does so by extending the language with a modality that quantifies over the topics the agents can 'talk about'. For this new framework, it provides a complete axiomatisation, showing also that the new language's model checking problem is PSPACE-complete. The paper closes showing that, in terms of expressivity, this new language of arbitrary partial communication is incomparable to that of arbitrary public announcements. CCS CONCEPTS• Theory of computation → Modal and temporal logics.

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Section: Language Semantics and Basic Resultsmentioning

confidence: 99%

“…For showing that a form of model equivalence implies invariance for a language, one usually uses induction on the language's formulas. 1 For P-bisimilarity and L, see [29].…”

Section: Pmentioning

confidence: 99%

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(Arbitrary) Partial Communication

Galimullin¹,

Velázquez–Quesada²

2023

Preprint

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“…Apart from that, we also plan to extend our framework and allow quantification over queries in the spirit of logics of quantified announcements, e.g. APAL [15], GAL [3], CAL [5,37], and their versions with group knowledge [2,4]. Another important direction for future work is to consider more complicated communicative actions (e.g.…”

Section: Discussion and Future Workmentioning

confidence: 99%

Dynamic Epistemic Logic for Budget-Constrained Agents

Dolgorukov

Gladyshev²

2023

Lecture Notes in Computer Science

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Logics for resource-bounded agents have been getting more and more attention in recent years since they provide us with more realistic tools for modelling and reasoning about multi-agent systems. While many existing approaches are based on the idea of agents as imperfect reasoners, who must spend their resources to perform logical inference, this is not the only way to introduce resource constraints into logical settings. In this paper we study agents as perfect reasoners, who may purchase a new piece of information from a trustworthy source. For this purpose we propose dynamic epistemic logic for semi-public queries for resource-bounded agents. In this logic (groups of) agents can perform a query (ask a question) about whether some formula is true and receive a correct answer. These queries are called semi-public, because the very fact of the query is public, while the answer is private. We also assume that every query has a cost and every agent has a budget constraint. Finally, our framework allows us to reason about group queries, in which agents may share resources to obtain a new piece of information together. We demonstrate that our logic is complete, decidable and has an efficient model checking procedure.

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Quantifying over information change with common knowledge

Ågotnes

Galimullin

2023

Auton Agent Multi-Agent Syst

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Public announcement logic (PAL) extends multi-agent epistemic logic with dynamic operators modelling the effects of public communication. Allowing quantification over public announcements lets us reason about the existence of an announcement that reaches a certain epistemic goal. Two notable examples of logics of quantified announcements are arbitrary public announcement logic (APAL) and group announcement logic (GAL). While the notion of common knowledge plays an important role in PAL, and in particular in characterisations of epistemic states that an agent or a group of agents might make come about by performing public announcements, extensions of APAL and GAL with common knowledge still haven’t been studied in detail. That is what we do in this paper. In particular, we consider both conservative extensions, where the semantics of the quantifiers is not changed, as well as extensions where the scope of quantification also includes common knowledge formulas. We compare the expressivity of these extensions relative to each other and other connected logics, and provide sound and complete axiomatisations. Finally, we show how the completeness results can be used for other logics with quantification over information change.

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Logics with Group Announcements and Distributed Knowledge: Completeness and Expressive Power

Cited by 5 publications

References 25 publications

(Arbitrary) Partial Communication

(Arbitrary) Partial Communication

Dynamic Epistemic Logic for Budget-Constrained Agents

Quantifying over information change with common knowledge

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