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Relevant Epistemic Logic with Public Announcements and Common Knowledge

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Logic and Argumentation (CLAR 2021)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 13040))

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Abstract

Building on our previous work in non-classical dynamic epistemic logic, we add common knowledge operators to a version of public announcement logic based on the relevant logic \(\mathsf {R}\). We prove a completeness result with respect to a relational semantics, and we show that an alternative semantics based on information states is dual to the relational one. We add a question-forming inquisitive disjunction operator to the language and prove a completeness result with respect to the information semantics. It is argued that relevant public announcements are particularly suitable for modelling public argumentation.

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Notes

  1. 1.

    We note that while “announcement” seem to us to best express the notion we have in mind, we have hesitated because of its technical connotations. Another term that may be used is “reception” – upon an announcement agents receive a piece of information, but nothing is implied about the nature of the information nor about what the agents make of it.

  2. 2.

    Note that this notation is somewhat misleading as \(E^{*}(A)\) does not denote the reflexive transitive closure of E(A).

  3. 3.

    This reading is related to a number of interpretations of R popular in the relevant logic literature. For instance, Dunn and Restall point out that “perhaps the best reading [of Rstu] is to say that the combination of the pieces of information s and t (not necessarily the union) is a piece of information in u” [8, p. 67]. Restall adds that “a body of information warrants \(\varphi \rightarrow \psi \) if and only if whenever you update that information with new information which warrants \(\varphi \), the resulting (perhaps new) body of information warrants \(\psi \)” [17, p. 362] (notation adjusted).

  4. 4.

    In [6] issues were introduced in the context of standard inquisitive epistemic logic based on classical logic. In [16] issues were introduced in the semantics of substructural inquisitive epistemic logic.

  5. 5.

    The inquisitive analogue of \(B_a\) is a standard modality in inquisitive epistemic logic usually denoted as \(E_a\) (see [6]). The inquisitive analogue of \(C_A\) was introduced semantically in [5] in the context of standard inquisitive epistemic logic without an axiomatic characterization.

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Acknowledgement

This work is supported by the Czech Science Foundation grant number GJ18-19162Y. We thank three anonymous reviewers for their valuable comments.

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Authors and Affiliations

  1. Institute of Computer Science, Czech Academy of Sciences, Prague, Czech Republic

    Vít Punčochář & Igor Sedlár

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  1. Vít Punčochář
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  2. Igor Sedlár
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Correspondence to Igor Sedlár .

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Editors and Affiliations

  1. Department of Information Engineering, University of Brescia, Brescia, Italy

    Pietro Baroni

  2. Department of Mathematics and Computer Science, Freie Universität Berlin, Berlin, Germany

    Christoph Benzmüller

  3. Department of Philosophy (Zhuhai), Sun Yat-sen University, Zhuhai, China

    Yὶ N. Wáng

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Punčochář, V., Sedlár, I. (2021). Relevant Epistemic Logic with Public Announcements and Common Knowledge. In: Baroni, P., Benzmüller, C., Wáng, Y.N. (eds) Logic and Argumentation. CLAR 2021. Lecture Notes in Computer Science(), vol 13040. Springer, Cham. https://doi.org/10.1007/978-3-030-89391-0_19

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  • DOI: https://doi.org/10.1007/978-3-030-89391-0_19

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