Modeling and Automating Public Announcement Logic with Relativized Common Knowledge as a Fragment of HOL in LogiKEy

• URL: http://arxiv.org/abs/2111.01654v2
• Date: Wed, 3 Nov 2021 07:07:55 GMT
• Title: Modeling and Automating Public Announcement Logic with Relativized Common Knowledge as a Fragment of HOL in LogiKEy
• Authors: Christoph Benzm\"uller and Sebastian Reiche
• Abstract summary: This article presents a semantical embedding for public announcement logic with relativized common knowledge. It enables the first-time automation of this logic with off-the-shelf theorem provers for classical higher-order logic. The work constitutes an important addition to the pluralist LogiKEy knowledge engineering methodology.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: A shallow semantical embedding for public announcement logic with relativized common knowledge is presented. This embedding enables the first-time automation of this logic with off-the-shelf theorem provers for classical higher-order logic. It is demonstrated (i) how meta-theoretical studies can be automated this way, and (ii) how non-trivial reasoning in the target logic (public announcement logic), required e.g. to obtain a convincing encoding and automation of the wise men puzzle, can be realized. Key to the presented semantical embedding is that evaluation domains are modeled explicitly and treated as an additional parameter in the encodings of the constituents of the embedded target logic; in previous related works, e.g. on the embedding of normal modal logics, evaluation domains were implicitly shared between meta-logic and target logic. The work presented in this article constitutes an important addition to the pluralist LogiKEy knowledge engineering methodology, which enables experimentation with logics and their combinations, with general and domain knowledge, and with concrete use cases -- all at the same time.

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