Many-valued hybrid logic

Jens Ulrik Hansen*, Thomas Bolander, Torben Braüner

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review

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Abstract

In this article we define a family of many-valued semantics for hybrid logic, where each semantics is based on a finite Heyting algebra of truth-values. We provide sound and complete tableau systems for these semantics. Moreover, we show how the tableau systems can be made terminating and thereby give rise to decision procedures for the logics in question. Our many-valued hybrid logics turn out to be ‘intermediate’ logics between intuitionistic hybrid logic and classical hybrid logic in a specific sense explained in the article. Our results show that many-valued hybrid logic is indeed a natural enterprise.

Original languageEnglish
JournalJournal of Logic and Computation
Volume28
Issue number5
Pages (from-to)883-908
ISSN0955-792X
DOIs
Publication statusPublished - 2018

Keywords

  • Modal logic
  • Hybrid logic
  • Many-valued logic
  • Intuitionistic hybrid logic
  • Tableau systems

Cite this

Hansen, Jens Ulrik ; Bolander, Thomas ; Braüner, Torben. / Many-valued hybrid logic. In: Journal of Logic and Computation. 2018 ; Vol. 28, No. 5. pp. 883-908.
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Many-valued hybrid logic. / Hansen, Jens Ulrik; Bolander, Thomas; Braüner, Torben.

In: Journal of Logic and Computation, Vol. 28, No. 5, 2018, p. 883-908.

Research output: Contribution to journalJournal articleResearchpeer-review

TY - JOUR

T1 - Many-valued hybrid logic

AU - Hansen, Jens Ulrik

AU - Bolander, Thomas

AU - Braüner, Torben

PY - 2018

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N2 - In this article we define a family of many-valued semantics for hybrid logic, where each semantics is based on a finite Heyting algebra of truth-values. We provide sound and complete tableau systems for these semantics. Moreover, we show how the tableau systems can be made terminating and thereby give rise to decision procedures for the logics in question. Our many-valued hybrid logics turn out to be ‘intermediate’ logics between intuitionistic hybrid logic and classical hybrid logic in a specific sense explained in the article. Our results show that many-valued hybrid logic is indeed a natural enterprise.

AB - In this article we define a family of many-valued semantics for hybrid logic, where each semantics is based on a finite Heyting algebra of truth-values. We provide sound and complete tableau systems for these semantics. Moreover, we show how the tableau systems can be made terminating and thereby give rise to decision procedures for the logics in question. Our many-valued hybrid logics turn out to be ‘intermediate’ logics between intuitionistic hybrid logic and classical hybrid logic in a specific sense explained in the article. Our results show that many-valued hybrid logic is indeed a natural enterprise.

KW - Modal logic

KW - Hybrid logic

KW - Many-valued logic

KW - Intuitionistic hybrid logic

KW - Tableau systems

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DO - 10.1093/logcom/exv040

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