An efficient approach to nominal equalities in hybrid logic tableaux (2010)

by S Cerrito, M Cialdea Mayer
Venue:Journal of Applied Non-classical Logics
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Nominal substitution at work with the global and converse modalities

by Serenella Cerrito, Marta Cialdea Mayer, Lab Ibisc - Advances in Modal Logic , 2010
"... This is a draft version of a paper appeared on the Proceedings of AIMAL 2010. It should not be cited, quoted or reproduced. This paper represents a continuation of a previous work, where a practical approach to the treatment of nominal equalities in tableaux for basic Hybrid Logic ..."
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This is a draft version of a paper appeared on the Proceedings of AIMAL 2010. It should not be cited, quoted or reproduced. This paper represents a continuation of a previous work, where a practical approach to the treatment of nominal equalities in tableaux for basic Hybrid Logic
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Herod and Pilate: two Tableau Provers for Basic Hybrid Logic

by Serenella Cerrito, Marta Cialdea Mayer, Lab Ibisc, Université D’evry Val D’essonne
"... IJCAR 2010. It should not be cited, quoted or reproduced. This work presents two provers for basic hybrid logic HL(@), which havebeenimplementedwiththeaimofcomparingtheinternalisedtableau calculi independently proposed, respectively, by Bolander and Blackburn [3] and Cerrito and Cialdea Mayer [5]. E ..."
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IJCAR 2010. It should not be cited, quoted or reproduced. This work presents two provers for basic hybrid logic HL(@), which havebeenimplementedwiththeaimofcomparingtheinternalisedtableau calculi independently proposed, respectively, by Bolander and Blackburn [3] and Cerrito and Cialdea Mayer [5]. Experimental results are reported, evaluating, from the practical point of view, the different treatment of nominal equalities of the two calculi. 1 A Brief Presentation of the Calculi P and H The treatment of nominal equalities in proof systems for hybrid logics may easily induce many redundancies. In fact, when processing a statement of the form
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A Proof Procedure for Hybrid Logic with Binders, Transitivity and Relation Hierarchies

by Marta Cialdea Mayer, Università Di Roma Tre
"... Abstract. A tableau calculus constituting a decision procedure for hybrid logic with the converse modalities, the global ones and a restricted use of the binder has been defined in a previous paper. This work shows how to extend such a calculus to multi-modal logic equipped with two features largely ..."
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Abstract. A tableau calculus constituting a decision procedure for hybrid logic with the converse modalities, the global ones and a restricted use of the binder has been defined in a previous paper. This work shows how to extend such a calculus to multi-modal logic equipped with two features largely used in description logics, i.e. transitivity and relation inclusion assertions. An implementation of the proof procedure is also briefly presented, along with the results of some preliminary experiments. 1
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A Goal-Directed Decision Procedure for Hybrid PDL

by Mark Kaminski, Gert Smolka , 2013
"... We present the first goal-directed decision procedure for hybrid PDL. The procedure is based on a modular approach that scales from basic modal logic with eventualities to hybrid PDL. The approach is designed so that nominals and eventualities are treated orthogonally. To deal with the com-plex prog ..."
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We present the first goal-directed decision procedure for hybrid PDL. The procedure is based on a modular approach that scales from basic modal logic with eventualities to hybrid PDL. The approach is designed so that nominals and eventualities are treated orthogonally. To deal with the com-plex programs of PDL, the approach employs a novel disjunctive program decomposition. In arguing the correctness of our approach, we employ the novel notion of support generalizing the standard notion of Hintikka sets. 1
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Tableaux with Substitution for Hybrid Logic with the Global

by Converse Modalities, Serenella Cerrito, Marta Cialdea Mayer , 2009
"... This work provides the full proofs of the properties of the tableaux calculus for hybrid logic with the global and converse modalities presented in [3], which focuses on the HL(@) fragment of the calculus. While such a fragment terminates without loop checks, when the converse and global modalities ..."
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This work provides the full proofs of the properties of the tableaux calculus for hybrid logic with the global and converse modalities presented in [3], which focuses on the HL(@) fragment of the calculus. While such a fragment terminates without loop checks, when the converse and global modalities are added to the language, and the corresponding rules to the system, termination is achieved by means of a loop checking mechanism. The peculiarity of the system is the treatment of nominal equalities by means of a substitution rule. The main advantage of such a rule, compared with other approaches, is its efficiency, that has been experimentally verified for the HL(@) fragment. Such an advantage should persist in the extended calculus. In this work we give the detailed termination and completeness proofs for the entire calculus. Although the main guidelines are the same as the corresponding proofs for
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