Hybrid Logic as Extension of Modal and Temporal Logics

Abstract Developed by Arthur Prior, Temporal Logic allows to represent temporal information on a logical system using modal (temporal) operators such as P, F, H or G, whose intuitive meaning is “it was sometime in the Past...”, “it will be sometime in the Future...&...

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Autor principal:	Álvarez Domínguez,Daniel
Lenguaje:	English
Publicado:	Universidad de Valparaíso. Facultad de Humanidades .Instituto de Filosofía. 2019
Materias:	Arthur Prior First-Order Correspondence Language Temporal Representation Nominals Translations
Acceso en línea:	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-42422019000100034
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spelling	oai:scielo:S0719-424220190001000342019-08-28Hybrid Logic as Extension of Modal and Temporal LogicsÁlvarez Domínguez,Daniel Arthur Prior First-Order Correspondence Language Temporal Representation Nominals Translations Abstract Developed by Arthur Prior, Temporal Logic allows to represent temporal information on a logical system using modal (temporal) operators such as P, F, H or G, whose intuitive meaning is “it was sometime in the Past...”, “it will be sometime in the Future...”, “it Has always been in the past...” and “it will always Going to be in the future...” respectively. Valuation of formulae built from these operators are carried out on Kripke semantics, so Modal Logic and Temporal Logic are consequently related. In fact, Temporal Logic is an extension of Modal one. Even when both logics mechanisms are able to formalize modal-temporal information with some accuracy, they suffer from a lack of expressiveness which Hybrid Logic can solve. Indeed, one of the problems of Modal Logic consists in its incapacity of naming specific points inside a model. As Temporal Logic is based on it, it cannot make such a thing neither. But First-Order Logic does can by means of constants and equality relation. Hybrid Logic, which results from combining Modal Logic and First-Order Logic, may solve this shortcoming. The main aim of this paper is to explain how Hybrid Logic emanates from Modal and Temporal ones in order to show what it adds to both logics with regard to information representation, why it is more expressive than them and what relation it maintains with the First-Order Correspondence Language.info:eu-repo/semantics/openAccessUniversidad de Valparaíso. Facultad de Humanidades .Instituto de Filosofía. Revista de humanidades de Valparaíso n.13 20192019-08-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-42422019000100034en10.22370/rhv2019iss13pp34-67
institution	Scielo Chile
collection	Scielo Chile
language	English
topic	Arthur Prior First-Order Correspondence Language Temporal Representation Nominals Translations
spellingShingle	Arthur Prior First-Order Correspondence Language Temporal Representation Nominals Translations Álvarez Domínguez,Daniel Hybrid Logic as Extension of Modal and Temporal Logics
description	Abstract Developed by Arthur Prior, Temporal Logic allows to represent temporal information on a logical system using modal (temporal) operators such as P, F, H or G, whose intuitive meaning is “it was sometime in the Past...”, “it will be sometime in the Future...”, “it Has always been in the past...” and “it will always Going to be in the future...” respectively. Valuation of formulae built from these operators are carried out on Kripke semantics, so Modal Logic and Temporal Logic are consequently related. In fact, Temporal Logic is an extension of Modal one. Even when both logics mechanisms are able to formalize modal-temporal information with some accuracy, they suffer from a lack of expressiveness which Hybrid Logic can solve. Indeed, one of the problems of Modal Logic consists in its incapacity of naming specific points inside a model. As Temporal Logic is based on it, it cannot make such a thing neither. But First-Order Logic does can by means of constants and equality relation. Hybrid Logic, which results from combining Modal Logic and First-Order Logic, may solve this shortcoming. The main aim of this paper is to explain how Hybrid Logic emanates from Modal and Temporal ones in order to show what it adds to both logics with regard to information representation, why it is more expressive than them and what relation it maintains with the First-Order Correspondence Language.
author	Álvarez Domínguez,Daniel
author_facet	Álvarez Domínguez,Daniel
author_sort	Álvarez Domínguez,Daniel
title	Hybrid Logic as Extension of Modal and Temporal Logics
title_short	Hybrid Logic as Extension of Modal and Temporal Logics
title_full	Hybrid Logic as Extension of Modal and Temporal Logics
title_fullStr	Hybrid Logic as Extension of Modal and Temporal Logics
title_full_unstemmed	Hybrid Logic as Extension of Modal and Temporal Logics
title_sort	hybrid logic as extension of modal and temporal logics
publisher	Universidad de Valparaíso. Facultad de Humanidades .Instituto de Filosofía.
publishDate	2019
url	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-42422019000100034
work_keys_str_mv	AT alvarezdominguezdaniel hybridlogicasextensionofmodalandtemporallogics
_version_	1714207185938939904

Hybrid Logic as Extension of Modal and Temporal Logics

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