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 Resolution Gaintzarain Ibarmia, José Hermo Huguet, Montserrat Lucio Carrasco, Francisca Navarro, Marisa Orejas, Fernando propositional linear-time temporal logic resolution invariant-free clausal normal form 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 This work has been partially supported by the Spanish Project TIN2007-66523 and the Basque Project LoRea GIU07/35 Springer http://hdl.handle.net/10810/64604
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
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
topic propositional linear-time temporal logic
resolution
invariant-free
clausal normal form
topic_facet 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
format article
url http://hdl.handle.net/10810/64604
eu_rights_str_mv openAccess
publisher Springer
institution Universidad del País Vasco
collection Addi. Archivo Digital para la Docencia y la Investigación
reponame_str Addi. Archivo Digital para la Docencia y la Investigación
instname_str Universidad del País Vasco
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publishDateSort 2011
author_browse Gaintzarain Ibarmia, José
Hermo Huguet, Montserrat
Lucio Carrasco, Francisca
Navarro, Marisa
Orejas, Fernando
publisherStr Springer
score 6,9303427

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