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Communication Dans Un Congrès Année : 2007

What can we achieve by arbitrary announcements? A dynamic take on Fitch's knowability

Résumé

This paper presents the logics Normal Coalition Logic NCL and its conformant version of Normal Coalition Logic CNCL. NCL is a multi-agent version of Chellas' STIT logic, extended with a next time operator (X). We show NCL subsumes coalition logic and give a complete axiomatization. Conformant NCL extends NCL with a standard S5 knowledge operator. This enables us to express that agents see to something under uncertainty about the present state or uncertainty about which action is being taken. In accordance with established terminology in the planning community, we call this version of NCL the `Conformant NCL'. The Conformant NCL enables us to express that agents are able to perform a uniform strategy. Public announcement logic is an extension of multi-agent epistemic logic with dynamic operators to model the informational consequences of announcements to the entire group of agents. We propose an extension of public announcement logic with a dynamic modal operator that expresses what is true after any announcement: ϕ expresses that ϕ is true after an arbitrary announcement ψ. As this includes the trivial announcement >, one might as well say that ϕ expresses what remains true after any announcement: it therefore corresponds to truth persistence after (definable) relativisation. The dual operation ϕ expresses that there is an announcement after which ϕ. This gives a perspective on Fitch’s knowability issues: for which formulas ϕ does it hold that ϕ → Kϕ? We give various semantic results, and we show completeness for a Hilbert-style axiomatisation of this logic
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hal-03516650 , version 1 (10-01-2022)

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Philippe Balbiani, Alexandru Baltag, Hans Van Ditmarsch, Andreas Herzig, Tomohiro Hoshi, et al.. What can we achieve by arbitrary announcements? A dynamic take on Fitch's knowability. Theoretical Aspects of Rationality and Knowledge (TARK 2007), Jun 2007, Bruxelles, Belgium. pp.42-51, ⟨10.1145/1324249.1324259⟩. ⟨hal-03516650⟩
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