No Finite Model Property for Logics of Quantified Announcements

Ditmarsch, Hans van; French, Tim; Galimullin, Rustam

doi:10.4204/eptcs.335.12

Cited by 4 publications

(2 citation statements)

References 18 publications

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“…This is significant since given BAPAL has a finitary axiomatisation [17], a finite model property would have implied decidability [6]. A similar lack of finite model property for other logics with quantification over announcements is given in [18].…”

Section: Introductionmentioning

confidence: 94%

“…One of the procedures must halt, and if ¬ϕ is provable, ϕ is not satisfiable, and if ϕ has a model, ϕ is satisfiable (see [6] for a more formal treatment.) The recent paper [18] applies a similar approach to show that group announcement logic [1] and coalition announcement logic [2,11] also lack the finite model property, although the constructions given there are more complex than the ones we require for BAPAL.…”

Section: Bapal Does Not Have the Finite Model Propertymentioning

confidence: 99%

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Satisfiability of Quantified Boolean Announcements

Ditmarsch¹,

French²,

Galimullin³

2022

Preprint

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Dynamic epistemic logics consider formal representations of agents' knowledge, and how the knowledge of agents changes in response to informative events, such as public announcements. Quantifying over informative events allows us to ask whether it is possible to achieve some state of knowledge, and has important applications in synthesising secure communication protocols. However, quantifying over quite simple informative events, public announcements, is not computable: such an arbitrary public announcement logic, APAL, has an undecidable satisfiability problem. Here we consider even simpler informative events called Boolean announcements, where announcements are restricted to be a Boolean combination of atomic propositions. The logic is called Boolean arbitrary public announcement logic, BAPAL. A companion paper provides a complete finitary axiomatization, and related expressivity results, for BAPAL. In this work the satisfiability problem for BAPAL is shown to decidable, and also that BAPAL does not have the finite model property.

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Section: Introductionmentioning

confidence: 94%

Section: Bapal Does Not Have the Finite Model Propertymentioning

confidence: 99%

Satisfiability of Quantified Boolean Announcements

Ditmarsch¹,

French²,

Galimullin³

2022

Preprint

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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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Verification and Strategy Synthesis for Coalition Announcement Logic

Alechina

Ditmarsch

Galimullin

et al. 2021

J of Log Lang and Inf

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Coalition announcement logic (CAL) is one of the family of the logics of quantified announcements. It allows us to reason about what a coalition of agents can achieve by making announcements in the setting where the anti-coalition may have an announcement of their own to preclude the former from reaching its epistemic goals. In this paper, we describe a PSPACE-complete model checking algorithm for CAL that produces winning strategies for coalitions. The algorithm is implemented in a proof-of-concept model checker.

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No Finite Model Property for Logics of Quantified Announcements

Cited by 4 publications

References 18 publications

Satisfiability of Quantified Boolean Announcements

Satisfiability of Quantified Boolean Announcements

Quantifying over information change with common knowledge

Verification and Strategy Synthesis for Coalition Announcement Logic

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