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Some constructive variants of S4 with the finite model property

Abstract : The logics CS4 and IS4 are intuitionistic variants of the modal logic S4. Whether the finite model property holds for each of these logics has been a long-standing open problem. In this paper we introduce two logics closely related to IS4: GS4, obtained by adding the Gödel-Dummett axiom to IS4, and S4I, obtained by reversing the roles of the modal and intuitionistic relations. We then prove that CS4, GS4, and S4I all enjoy the finite model property.
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Conference papers
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https://hal.archives-ouvertes.fr/hal-03248058
Contributor : Philippe Balbiani <>
Submitted on : Thursday, June 3, 2021 - 12:45:45 PM
Last modification on : Wednesday, June 9, 2021 - 10:00:27 AM

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2104.15053.pdf
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  • HAL Id : hal-03248058, version 1
  • ARXIV : 2104.15053

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Philippe Balbiani, Martín Diéguez, David Fernández Duque. Some constructive variants of S4 with the finite model property. 36th IEEE Annual Symposium on Logic in Computer Science (LICS 2021), Jun 2021, Rome (on line), Italy. ⟨hal-03248058⟩

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