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Mathematics > Logic

arXiv:2405.09162 (math)
[Submitted on 15 May 2024 (v1), last revised 21 Nov 2024 (this version, v2)]

Title:Complete and Terminating Tableau Calculus for Undirected Graph

Authors:Yuki Nishimura, Tsubasa Takagi
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Abstract:Hybrid logic is a modal logic with additional operators specifying nominals and is highly expressive. For example, there is no formula corresponding to the irreflexivity of Kripke frames in basic modal logic, but there is in hybrid logic. Irreflexivity is significant in that irreflexive and symmetric Kripke frames can be regarded as undirected graphs reviewed from a graph theoretic point of view. Thus, the study of the hybrid logic with axioms corresponding to irreflexivity and symmetry can help to elucidate the logical properties of undirected graphs. In this paper, we formulate the tableau method of the hybrid logic for undirected graphs. Our main result is to show the completeness theorem and the termination property of the tableau method, which leads us to prove the decidability.
Comments: 19 pages, 6 figures, accepted as the conference 'AWPL 2024' post-proceeding
Subjects: Logic (math.LO); Logic in Computer Science (cs.LO)
Cite as: arXiv:2405.09162 [math.LO]
  (or arXiv:2405.09162v2 [math.LO] for this version)
  https://doi.org/10.48550/arXiv.2405.09162

Submission history

From: Yuki Nishimura [view email]
[v1] Wed, 15 May 2024 07:48:24 UTC (34 KB)
[v2] Thu, 21 Nov 2024 06:31:59 UTC (509 KB)
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