Many-Valued Hybrid Logic

Research output: Contribution to journalJournal articleResearchpeer-review

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.
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.
LanguageEnglish
JournalJournal of Logic and Computation
Volume28
Issue number5
Pages883-908
ISSN0955-792X
DOIs
StatePublished - 2018

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
@article{10771db8763a4f5a8489d34a20d28c4c,
title = "Many-Valued Hybrid Logic",
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.",
author = "Hansen, {Jens Ulrik} and Thomas Bolander and Torben Bra{\"u}ner",
year = "2018",
doi = "10.1093/logcom/exv040",
language = "English",
volume = "28",
pages = "883--908",
journal = "Journal of Logic and Computation",
issn = "0955-792X",
publisher = "Oxford University Press",
number = "5",

}

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

Y1 - 2018

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.

U2 - 10.1093/logcom/exv040

DO - 10.1093/logcom/exv040

M3 - Journal article

VL - 28

SP - 883

EP - 908

JO - Journal of Logic and Computation

T2 - Journal of Logic and Computation

JF - Journal of Logic and Computation

SN - 0955-792X

IS - 5

ER -