PP-2019-14: Arbitrary Public Announcement Logic with Memory

PP-2019-14: Baltag, Alexandru and Özgün, Aybüke and Vargas, Ana Lucia (2019) Arbitrary Public Announcement Logic with Memory. [Pre-print] (Submitted)

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Abstract

We introduce Arbitrary Public Announcement Logic with Memory (APALM), obtained by adding to the models a 'memory' of the initial states, representing the information before any communication took place ("the prior"), and adding to the syntax operators that can access this memory. We show that APALM is recursively axiomatizable (in contrast to the original Arbitrary Public Announcement Logic, for which the corresponding question is still open). We present a complete recursive axiomatization, that includes a natural finitary rule, and study this logic's expressivity and the appropriate notion of bisimulation. We then examine Group Announcement Logic with Memory (GALM), the extension of APALM obtained by adding to its syntax group announcement operators, and provide a complete finitary axiomatization (again in contrast to the original Group Announcement Logic, for which the only known axiomatization is infinitary). We also show that, in the memory-enhanced context, there is a `natural' reduction of the so-called coalition announcement modality to group announcements (in contrast to the memory-free case, where this natural translation was shown to be invalid).

Item Type: Pre-print
Report Nr: PP-2019-14
Series Name: Prepublication (PP) Series
Year: 2019
Uncontrolled Keywords: dynamic epistemic logic, arbitrary public announcement logic, group announcement logic, modal logic, subset space semantics, epistemology
Subjects: Logic
Philosophy
Depositing User: Dr Aybüke Özgün
Date Deposited: 08 Apr 2021 14:41
Last Modified: 08 Apr 2021 14:41
URI: https://eprints.illc.uva.nl/id/eprint/1787

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