Tableaux for Public Announcement Logic

Balbiani, Philippe; Ditmarsch, Hans van; Herzig, Andreas; Lima, Tiago de

doi:10.1093/logcom/exn060

Cited by 34 publications

(31 citation statements)

References 8 publications

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“…In our case the argument is essentially the same (see also [3]): we only keep in memory the information concerning the current node and its path to the root node, in order to be able to backtrack. We moreover restrict the applicability of the (hear) rule to the atomic propositions h a for which a occurs in the input formula.…”

Section: Proposition 15mentioning

confidence: 99%

Announcements to Attentive Agents

Bolander

Ditmarsch

Herzig

et al. 2015

J of Log Lang and Inf

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In public announcement logic it is assumed that all agents pay attention to the announcement. Weaker observational conditions can be modelled in action model logic. In this work, we propose a version of public announcement logic wherein it is encoded in the states of the epistemic model which agents pay attention to the announcement. This logic is called attention-based announcement logic. We give an axiomatization of the logic and prove that complexity of satisfiability is the same as that of public announcement logic, and therefore lower than that of action model logic. An attention-based announcement can also be described as an action model. We extend our logic by integrating attention change. Finally, we add the notion of common belief to the language, we exploit this to formalize the concept of joint attention, that has been widely discussed in the philosophical and cognitive science literature, and we provide a corresponding axiomatization. This axiomatization also employs the auxiliary notion of attention-based relativized common belief.

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Section: Proposition 15mentioning

confidence: 99%

Announcements to Attentive Agents

Bolander

Ditmarsch

Herzig

et al. 2015

J of Log Lang and Inf

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“…Intriguing results on this are presented by Sadzik in [21]. 7 Here again, the observation that for some given model M of information there is an infinite informative sequence ψ 1 , ψ 2 , . .…”

mentioning

confidence: 77%

“…A tableau calculus for dynamic consequence seems an interesting challenge, where, possibly, the reported calculi for public announcement logic such as [7] may provide inspiration. Recalling the dynamic consequence pattern Σ |= given background conditions and a desirable goal, which sequence of announcements will always realize that goal?…”

mentioning

confidence: 99%

Dynamic Consequence and Public Announcement

Franco

Ditmarsch

Nepomuceno

2013

The Review of Symbolic Logic

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In [25] van Benthem proposes a dynamic consequence relation defined aswhere the latter denotes consequence in public announcement logic, a dynamic epistemic logic. In this paper we investigate the structural properties of a conditional dynamic consequence relation |= d Γ extending van Benthem's proposal. It takes into account a set of background conditions Γ, inspired by [18] wherein Makinson calls this reasoning 'modulo' a set Γ. In the presence of common knowledge, conditional dynamic consequence is definable from (unconditional) dynamic consequence. An open question is whether dynamic consequence is compact. We further investigate a dynamic consequence relation for soft instead of hard announcements. Surprisingly, it shares many properties with (hard) dynamic consequence. Dynamic consequence relations provide a novel perspective on reasoning about protocols in multi-agent systems.

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“…It is clear persistence will not (and should not) hold for action modalities, but at any given model persistence will hold. To extend the tableaux system we should instead take sequences of CSSs, together with a history of actions following similar approaches in the proof theory of Public Announcement Logic [3].…”

Section: Extension To Resources and Actions: Examplesmentioning

confidence: 99%

Intuitionistic Layered Graph Logic

Docherty

Pym

2016

Automated Reasoning

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Abstract. Models of complex systems are widely used in the physical and social sciences, and the concept of layering, typically building upon graph-theoretic structure, is a common feature. We describe an intuitionistic substructural logic that gives an account of layering. As in bunched systems, the logic includes the usual intuitionistic connectives, together with a non-commutative, non-associative conjunction (used to capture layering) and its associated implications. We give soundness and completeness theorems for labelled tableaux and Hilbert-type systems with respect to a Kripke semantics on graphs. To demonstrate the utility of the logic, we show how to represent a range of systems and security examples, illuminating the relationship between services/policies and the infrastructures/architectures to which they are applied.

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Tableaux for Public Announcement Logic

Cited by 34 publications

References 8 publications

Announcements to Attentive Agents

Announcements to Attentive Agents

Dynamic Consequence and Public Announcement

Intuitionistic Layered Graph Logic

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