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Mathematics > Logic

arXiv:2210.02216 (math)
[Submitted on 5 Oct 2022]

Title:Correspondence Theory for Modal Fairtlough-Mendler Semantics of Intuitionistic Modal Logic

Authors:Zhiguang Zhao
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Abstract:We study the correspondence theory of intuitionistic modal logic in modal Fairtlough-Mendler semantics (modal FM semantics) \cite{FaMe97}, which is the intuitionistic modal version of possibility semantics \cite{Ho16}. We identify the fragment of inductive formulas \cite{GorankoV06} in this language and give the algorithm $\mathsf{ALBA}$ \cite{CoPa12} in this semantic setting. There are two major features in the paper: one is that in the expanded modal language, the nominal variables, which are interpreted as atoms in perfect Boolean algebras, complete join-prime elements in perfect distributive lattices and complete join-irreducible elements in perfect lattices, are interpreted as the refined regular open closures of singletons in the present setting, similar to the possibility semantics for classical normal modal logic \cite{Zh21d}; the other feature is that we do not use conominals or diamond, which restricts the fragment of inductive formulas significantly. We prove the soundness of the $\mathsf{ALBA}$ with respect to modal FM frames and show that the $\mathsf{ALBA}$ succeeds on inductive formulas, similar to existing settings like \cite{CoPa12,Zh21d,Zh22a}.
Subjects: Logic (math.LO); Logic in Computer Science (cs.LO)
Cite as: arXiv:2210.02216 [math.LO]
  (or arXiv:2210.02216v1 [math.LO] for this version)
  https://doi.org/10.48550/arXiv.2210.02216

Submission history

From: Zhiguang Zhao [view email]
[v1] Wed, 5 Oct 2022 12:57:48 UTC (22 KB)
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