Invariant-Free Clausal Temporal Resolution

Resolution is a well-known proof method for classical logics that is well suited for mechanization. The most fruitful approach in the literature on temporal logic, which was started with the seminal paper of M. Fisher, deals with Propositional Linear-time Temporal Logic (PLTL) and requires generatin...

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Autores: Gaintzarain Ibarmia, José, Hermo Huguet, Montserrat, Lucio Carrasco, Francisca, Navarro, Marisa, Orejas, Fernando
Tipo de recurso: artículo
Fecha de publicación:2011
País:España
Institución:Universidad del País Vasco
Repositorio:Addi. Archivo Digital para la Docencia y la Investigación
OAI Identifier:oai:addi.ehu.eus:10810/64604
Acceso en línea:http://hdl.handle.net/10810/64604
Access Level:acceso abierto
Palabra clave:propositional linear-time temporal logic
resolution
invariant-free
clausal normal form
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spelling Invariant-Free Clausal Temporal ResolutionGaintzarain Ibarmia, JoséHermo Huguet, MontserratLucio Carrasco, FranciscaNavarro, MarisaOrejas, Fernandopropositional linear-time temporal logicresolutioninvariant-freeclausal normal formResolution is a well-known proof method for classical logics that is well suited for mechanization. The most fruitful approach in the literature on temporal logic, which was started with the seminal paper of M. Fisher, deals with Propositional Linear-time Temporal Logic (PLTL) and requires generating invariants for performing resolution on eventualities. The methods and techniques developed in that approach have also been successfully adapted to obtain a clausal resolution method for Computation Tree Logic (CTL), but invariant handling seems to be a handicap for further extension to more general branching temporal logics. In this paper, we present a new approach to applying resolution to PLTL. The main novelty of our approach is that we do not generate invariants for performing resolution on eventualities. Hence, we say that the approach presented in this paper is invariant-free. Our method is based on the dual methods of tableaux and sequents for PLTL that we presented in a previous paper. Our resolution method involves translation into a clausal normal form that is a direct extension of classical CNF. We first show that any PLTL-formula can be transformed into this clausal normal form. Then, we present our temporal resolution method, called trs-resolution, that extends classical propositional resolution. Finally, we prove that trs-resolution is sound and complete. In fact, it finishes for any input formula deciding its satisfiability, hence it gives rise to a new decision procedure for PLTLThis work has been partially supported by the Spanish Project TIN2007-66523 and the Basque Project LoRea GIU07/35Springer202420242011info:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10810/64604reponame:Addi. Archivo Digital para la Docencia y la Investigacióninstname:Universidad del País VascoIngléshttps://link.springer.com/article/10.1007/s10817-011-9241-2info:eu-repo/semantics/openAccess© 2011, Springer Science Business Media B.V.oai:addi.ehu.eus:10810/646042026-06-18T09:23:17Z
dc.title.none.fl_str_mv Invariant-Free Clausal Temporal Resolution
title Invariant-Free Clausal Temporal Resolution
spellingShingle Invariant-Free Clausal Temporal Resolution
Gaintzarain Ibarmia, José
propositional linear-time temporal logic
resolution
invariant-free
clausal normal form
title_short Invariant-Free Clausal Temporal Resolution
title_full Invariant-Free Clausal Temporal Resolution
title_fullStr Invariant-Free Clausal Temporal Resolution
title_full_unstemmed Invariant-Free Clausal Temporal Resolution
title_sort Invariant-Free Clausal Temporal Resolution
dc.creator.none.fl_str_mv Gaintzarain Ibarmia, José
Hermo Huguet, Montserrat
Lucio Carrasco, Francisca
Navarro, Marisa
Orejas, Fernando
author Gaintzarain Ibarmia, José
author_facet Gaintzarain Ibarmia, José
Hermo Huguet, Montserrat
Lucio Carrasco, Francisca
Navarro, Marisa
Orejas, Fernando
author_role author
author2 Hermo Huguet, Montserrat
Lucio Carrasco, Francisca
Navarro, Marisa
Orejas, Fernando
author2_role author
author
author
author
dc.subject.none.fl_str_mv propositional linear-time temporal logic
resolution
invariant-free
clausal normal form
topic propositional linear-time temporal logic
resolution
invariant-free
clausal normal form
description Resolution is a well-known proof method for classical logics that is well suited for mechanization. The most fruitful approach in the literature on temporal logic, which was started with the seminal paper of M. Fisher, deals with Propositional Linear-time Temporal Logic (PLTL) and requires generating invariants for performing resolution on eventualities. The methods and techniques developed in that approach have also been successfully adapted to obtain a clausal resolution method for Computation Tree Logic (CTL), but invariant handling seems to be a handicap for further extension to more general branching temporal logics. In this paper, we present a new approach to applying resolution to PLTL. The main novelty of our approach is that we do not generate invariants for performing resolution on eventualities. Hence, we say that the approach presented in this paper is invariant-free. Our method is based on the dual methods of tableaux and sequents for PLTL that we presented in a previous paper. Our resolution method involves translation into a clausal normal form that is a direct extension of classical CNF. We first show that any PLTL-formula can be transformed into this clausal normal form. Then, we present our temporal resolution method, called trs-resolution, that extends classical propositional resolution. Finally, we prove that trs-resolution is sound and complete. In fact, it finishes for any input formula deciding its satisfiability, hence it gives rise to a new decision procedure for PLTL
publishDate 2011
dc.date.none.fl_str_mv 2011
2024
2024
dc.type.none.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv http://hdl.handle.net/10810/64604
url http://hdl.handle.net/10810/64604
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv https://link.springer.com/article/10.1007/s10817-011-9241-2
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
© 2011, Springer Science Business Media B.V.
eu_rights_str_mv openAccess
rights_invalid_str_mv © 2011, Springer Science Business Media B.V.
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Springer
publisher.none.fl_str_mv Springer
dc.source.none.fl_str_mv reponame:Addi. Archivo Digital para la Docencia y la Investigación
instname:Universidad del País Vasco
instname_str Universidad del País Vasco
reponame_str Addi. Archivo Digital para la Docencia y la Investigación
collection Addi. Archivo Digital para la Docencia y la Investigación
repository.name.fl_str_mv
repository.mail.fl_str_mv
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