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Renate A Schmidt - One of the best experts on this subject based on the ideXlab platform.
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rule refinement for Semantic Tableau calculi
Theorem Proving with Analytic Tableaux and Related Methods, 2017Co-Authors: Dmitry Tishkovsky, Renate A SchmidtAbstract:This paper investigates refinement techniques for Semantic Tableau calculi. The focus is on techniques to reduce branching in inference rules and thus allow more effective ways of carrying out deductions. We introduce an easy to apply, general principle of atomic rule refinement, which depends on a purely syntactic condition that can be easily verified. The refinement has a wide scope, for example, it is immediately applicable to inference rules associated with frame conditions of modal logics, or declarations of role properties in description logics, and it allows for routine development of hyperTableau-like calculi for logics with disjunction and negation. The techniques are illustrated on Humberstone’s modal logic \({{\mathrm{K}_m}(\lnot )}\) with modal operators defined with respect to both accessibility and inaccessibility, for which two refined calculi are given.
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TableauX - Rule Refinement for Semantic Tableau Calculi
Lecture Notes in Computer Science, 2017Co-Authors: Dmitry Tishkovsky, Renate A SchmidtAbstract:This paper investigates refinement techniques for Semantic Tableau calculi. The focus is on techniques to reduce branching in inference rules and thus allow more effective ways of carrying out deductions. We introduce an easy to apply, general principle of atomic rule refinement, which depends on a purely syntactic condition that can be easily verified. The refinement has a wide scope, for example, it is immediately applicable to inference rules associated with frame conditions of modal logics, or declarations of role properties in description logics, and it allows for routine development of hyperTableau-like calculi for logics with disjunction and negation. The techniques are illustrated on Humberstone’s modal logic \({{\mathrm{K}_m}(\lnot )}\) with modal operators defined with respect to both accessibility and inaccessibility, for which two refined calculi are given.
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TableauX - Modal Tableau Systems with Blocking and Congruence Closure
Lecture Notes in Computer Science, 2015Co-Authors: Renate A Schmidt, Uwe WaldmannAbstract:Our interest in this paper are Semantic Tableau approaches closely related to bottom-up model generation methods. Using equality-based blocking techniques these can be used to decide logics representable in first-order logic that have the finite model property. Many common modal and description logics have these properties and can therefore be decided in this way. This paper integrates congruence closure, which is probably the most powerful and efficient way to realise reasoning with ground equations, into a modal Tableau system with equality-based blocking. The system is described for an extension of modal logici?źK characterised by frames in which the accessibility relation is transitive and every world has a distinct immediate predecessor. We show the system is sound and complete, and discuss how various forms of blocking such as ancestor blocking can be realised in this setting. Though the investigation is focussed on a particular modal logic, the modal logic was chosen to show the most salient ideas and techniques for the results to be generalised to other Tableau calculi and other logics.
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modal Tableau systems with blocking and congruence closure
Theorem Proving with Analytic Tableaux and Related Methods, 2015Co-Authors: Renate A Schmidt, Uwe WaldmannAbstract:Our interest in this paper are Semantic Tableau approaches closely related to bottom-up model generation methods. Using equality-based blocking techniques these can be used to decide logics representable in first-order logic that have the finite model property. Many common modal and description logics have these properties and can therefore be decided in this way. This paper integrates congruence closure, which is probably the most powerful and efficient way to realise reasoning with ground equations, into a modal Tableau system with equality-based blocking. The system is described for an extension of modal logici?źK characterised by frames in which the accessibility relation is transitive and every world has a distinct immediate predecessor. We show the system is sound and complete, and discuss how various forms of blocking such as ancestor blocking can be realised in this setting. Though the investigation is focussed on a particular modal logic, the modal logic was chosen to show the most salient ideas and techniques for the results to be generalised to other Tableau calculi and other logics.
Anthony Hunter - One of the best experts on this subject based on the ideXlab platform.
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a Semantic Tableau version of first order quasi classical logic
European Conference on Symbolic and Quantitative Approaches to Reasoning and Uncertainty, 2001Co-Authors: Anthony HunterAbstract:Quasi-classical logic (QC logic) allows the derivation of non-trivial classical inferences from inconsistent information. A paraconsistent, or non-trivializable, logic is, by necessity, a compromise, or weakening, of classical logic. The compromises on QC logic seem to be more appropriate than other paraconsistent logics for applications in computing. In particular, the connectives behave in a "classical manner" at the object level so that important proof rules such as modus tollens, modus ponens, and disjunctive syllogism hold. Here we develop QC logic by presenting a Semantic Tableau version for first-order QC logic.
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ECSQARU - A Semantic Tableau Version of First-Order Quasi-Classical Logic
Lecture Notes in Computer Science, 2001Co-Authors: Anthony HunterAbstract:Quasi-classical logic (QC logic) allows the derivation of non-trivial classical inferences from inconsistent information. A paraconsistent, or non-trivializable, logic is, by necessity, a compromise, or weakening, of classical logic. The compromises on QC logic seem to be more appropriate than other paraconsistent logics for applications in computing. In particular, the connectives behave in a "classical manner" at the object level so that important proof rules such as modus tollens, modus ponens, and disjunctive syllogism hold. Here we develop QC logic by presenting a Semantic Tableau version for first-order QC logic.
Uwe Waldmann - One of the best experts on this subject based on the ideXlab platform.
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TableauX - Modal Tableau Systems with Blocking and Congruence Closure
Lecture Notes in Computer Science, 2015Co-Authors: Renate A Schmidt, Uwe WaldmannAbstract:Our interest in this paper are Semantic Tableau approaches closely related to bottom-up model generation methods. Using equality-based blocking techniques these can be used to decide logics representable in first-order logic that have the finite model property. Many common modal and description logics have these properties and can therefore be decided in this way. This paper integrates congruence closure, which is probably the most powerful and efficient way to realise reasoning with ground equations, into a modal Tableau system with equality-based blocking. The system is described for an extension of modal logici?źK characterised by frames in which the accessibility relation is transitive and every world has a distinct immediate predecessor. We show the system is sound and complete, and discuss how various forms of blocking such as ancestor blocking can be realised in this setting. Though the investigation is focussed on a particular modal logic, the modal logic was chosen to show the most salient ideas and techniques for the results to be generalised to other Tableau calculi and other logics.
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modal Tableau systems with blocking and congruence closure
Theorem Proving with Analytic Tableaux and Related Methods, 2015Co-Authors: Renate A Schmidt, Uwe WaldmannAbstract:Our interest in this paper are Semantic Tableau approaches closely related to bottom-up model generation methods. Using equality-based blocking techniques these can be used to decide logics representable in first-order logic that have the finite model property. Many common modal and description logics have these properties and can therefore be decided in this way. This paper integrates congruence closure, which is probably the most powerful and efficient way to realise reasoning with ground equations, into a modal Tableau system with equality-based blocking. The system is described for an extension of modal logici?źK characterised by frames in which the accessibility relation is transitive and every world has a distinct immediate predecessor. We show the system is sound and complete, and discuss how various forms of blocking such as ancestor blocking can be realised in this setting. Though the investigation is focussed on a particular modal logic, the modal logic was chosen to show the most salient ideas and techniques for the results to be generalised to other Tableau calculi and other logics.
Jinzhao Wu - One of the best experts on this subject based on the ideXlab platform.
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CSE (2) - Quasi-classical Semantics and Tableau Calculus of Description Logics for Paraconsistent Reasoning in the Semantic Web
2009 International Conference on Computational Science and Engineering, 2009Co-Authors: Jinzhao WuAbstract:The knowledge and data in the Semantic Web are large-scale, dispersive, multi-authored and therefore usually inconsistent. It is reasonable to develop practical reasoning techniques for inconsistent ontologies.We propose a new type of paraconsistent description logics based on quasi-classical logic (QCL), called quasi-classical description logics (QCDLs). Furthermore, we present a Semantic Tableau calculus for QCDLs and define a sound, complete and decidable consequence relation based on the calculus. These enable the paraconsistent reasoning in the Semantic Web. We also give a comparison with other key paraconsistent description logics and show that QCDLs possess more expressive and stronger Semantics and other advantages.
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Quasi-classical Semantics and Tableau Calculus of Description Logics for Paraconsistent Reasoning in the Semantic Web
2009 International Conference on Computational Science and Engineering, 2009Co-Authors: Jinzhao WuAbstract:The knowledge and data in the Semantic Web are large-scale, dispersive, multi-authored and therefore usually inconsistent. It is reasonable to develop practical reasoning techniques for inconsistent ontologies. We propose a new type of paraconsistent description logics based on quasi-classical logic (QCL), called quasi-classical description logics (QCDLs). Furthermore, we present a Semantic Tableau calculus for QCDLs and define a sound, complete and decidable consequence relation based on the calculus. These enable the paraconsistent reasoning in the Semantic Web. We also give a comparison with other key paraconsistent description logics and show that QCDLs possess more expressive and stronger Semantics and other advantages.
Dmitry Tishkovsky - One of the best experts on this subject based on the ideXlab platform.
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rule refinement for Semantic Tableau calculi
Theorem Proving with Analytic Tableaux and Related Methods, 2017Co-Authors: Dmitry Tishkovsky, Renate A SchmidtAbstract:This paper investigates refinement techniques for Semantic Tableau calculi. The focus is on techniques to reduce branching in inference rules and thus allow more effective ways of carrying out deductions. We introduce an easy to apply, general principle of atomic rule refinement, which depends on a purely syntactic condition that can be easily verified. The refinement has a wide scope, for example, it is immediately applicable to inference rules associated with frame conditions of modal logics, or declarations of role properties in description logics, and it allows for routine development of hyperTableau-like calculi for logics with disjunction and negation. The techniques are illustrated on Humberstone’s modal logic \({{\mathrm{K}_m}(\lnot )}\) with modal operators defined with respect to both accessibility and inaccessibility, for which two refined calculi are given.
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TableauX - Rule Refinement for Semantic Tableau Calculi
Lecture Notes in Computer Science, 2017Co-Authors: Dmitry Tishkovsky, Renate A SchmidtAbstract:This paper investigates refinement techniques for Semantic Tableau calculi. The focus is on techniques to reduce branching in inference rules and thus allow more effective ways of carrying out deductions. We introduce an easy to apply, general principle of atomic rule refinement, which depends on a purely syntactic condition that can be easily verified. The refinement has a wide scope, for example, it is immediately applicable to inference rules associated with frame conditions of modal logics, or declarations of role properties in description logics, and it allows for routine development of hyperTableau-like calculi for logics with disjunction and negation. The techniques are illustrated on Humberstone’s modal logic \({{\mathrm{K}_m}(\lnot )}\) with modal operators defined with respect to both accessibility and inaccessibility, for which two refined calculi are given.