Mathematical Foundations for Joining Only Knowing and Common Knowledge

Onderzoeksoutput: Conference paper

Samenvatting

Common knowledge and only knowing capture two intuitive and natural notions that have proven to be useful in a variety of settings, for example to reason about coordination or agreement between agents, or to analyse the knowledge of knowledge-based agents. While these two epistemic operators have been extensively studied in isolation, the approaches made to encode their complex interplay failed to capture some essential properties of only knowing. We propose a novel solution by defining a notion of μ-biworld for countable ordinals μ, which approximates not only the worlds that an agent deems possible, but also those deemed impossible. This approach allows us to define a multi-agent epistemic logic with common knowledge and only knowing operators, and a three-valued model semantics for it. Moreover, we show that we only really need biworlds of depth at most ω²+1. Based on this observation, we define a Kripke semantics on a canonical Kripke structure and show that this semantics coincides with the model semantics. Finally, we discuss issues arising when combining negative introspection or truthfulness with only knowing and show how positive introspection can be integrated into our logic.
Originele taal-2English
TitelProceedings of the 20th International Conference on Principles of Knowledge Representation and Reasoning
RedacteurenPierre Marquis, Tran Cao Son, Gabriele Kern-Isberner
Uitgeverijijcai.org
Pagina's167-177
Aantal pagina's11
ISBN van elektronische versie978-1-956792-02-7
DOI's
StatusPublished - sep 2023
Evenement20th International Conference on Principles of Knowledge Representation and Reasoning - , Greece
Duur: 2 sep 20239 sep 2023
Congresnummer: 20

Publicatie series

NaamProceedings of the International Conference on Knowledge Representation and Reasoning
ISSN van geprinte versie2334-1025
ISSN van elektronische versie2334-1033

Conference

Conference20th International Conference on Principles of Knowledge Representation and Reasoning
Verkorte titelKR 2023
Land/RegioGreece
Periode2/09/239/09/23

Bibliografische nota

Publisher Copyright:
© 2023 Proceedings of the International Conference on Knowledge Representation and Reasoning. All rights reserved

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