The Experts below are selected from a list of 117 Experts worldwide ranked by ideXlab platform
Jakub Kozik - One of the best experts on this subject based on the ideXlab platform.
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In the full Propositional logic, 5/8 of classical tautologies are intuitionistically valid
Annals of Pure and Applied Logic, 2012Co-Authors: Antoine Genitrini, Jakub KozikAbstract:Abstract We present a quantitative comparison of classical and intuitionistic logics, based on the notion of density, within the framework of several Propositional languages. In the most general case–the language of the “full Propositional System”–we prove that the fraction of intuitionistic tautologies among classical tautologies of size n tends to 5 / 8 when n goes to infinity. We apply two approaches, one with a bounded number of variables, and another, in which formulae are considered “up to the names of variables”. In both cases, we obtain the same results. Our results for both approaches are derived in a unified way based on structural properties of formulae. As a by-product of these considerations, we present a characterization of the structures of almost all random tautologies.
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quantitative comparison of intuitionistic and classical logics full Propositional System
Foundations of Computer Science, 2009Co-Authors: Antoine Genitrini, Jakub KozikAbstract:We address the problem of quantitative comparison of classical and intuitionistic logics within the language of the full Propositional System. We apply two different approaches, to estimate the asymptotic fraction of intuitionistic tautologies among classical tautologies, obtaining the same results for both. Our results justify informal statements such as "about 5/8 of classical tautologies are intuitionistic".
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LFCS - Quantitative Comparison of Intuitionistic and Classical Logics - Full Propositional System
Logical Foundations of Computer Science, 2008Co-Authors: Antoine Genitrini, Jakub KozikAbstract:We address the problem of quantitative comparison of classical and intuitionistic logics within the language of the full Propositional System. We apply two different approaches, to estimate the asymptotic fraction of intuitionistic tautologies among classical tautologies, obtaining the same results for both. Our results justify informal statements such as "about 5/8 of classical tautologies are intuitionistic".
Antoine Genitrini - One of the best experts on this subject based on the ideXlab platform.
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In the full Propositional logic, 5/8 of classical tautologies are intuitionistically valid
Annals of Pure and Applied Logic, 2012Co-Authors: Antoine Genitrini, Jakub KozikAbstract:Abstract We present a quantitative comparison of classical and intuitionistic logics, based on the notion of density, within the framework of several Propositional languages. In the most general case–the language of the “full Propositional System”–we prove that the fraction of intuitionistic tautologies among classical tautologies of size n tends to 5 / 8 when n goes to infinity. We apply two approaches, one with a bounded number of variables, and another, in which formulae are considered “up to the names of variables”. In both cases, we obtain the same results. Our results for both approaches are derived in a unified way based on structural properties of formulae. As a by-product of these considerations, we present a characterization of the structures of almost all random tautologies.
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quantitative comparison of intuitionistic and classical logics full Propositional System
Foundations of Computer Science, 2009Co-Authors: Antoine Genitrini, Jakub KozikAbstract:We address the problem of quantitative comparison of classical and intuitionistic logics within the language of the full Propositional System. We apply two different approaches, to estimate the asymptotic fraction of intuitionistic tautologies among classical tautologies, obtaining the same results for both. Our results justify informal statements such as "about 5/8 of classical tautologies are intuitionistic".
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LFCS - Quantitative Comparison of Intuitionistic and Classical Logics - Full Propositional System
Logical Foundations of Computer Science, 2008Co-Authors: Antoine Genitrini, Jakub KozikAbstract:We address the problem of quantitative comparison of classical and intuitionistic logics within the language of the full Propositional System. We apply two different approaches, to estimate the asymptotic fraction of intuitionistic tautologies among classical tautologies, obtaining the same results for both. Our results justify informal statements such as "about 5/8 of classical tautologies are intuitionistic".
Antonino Rotolo - One of the best experts on this subject based on the ideXlab platform.
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labelled tableaux for nonmonotonic reasoning cumulative consequence relations
Journal of Logic and Computation, 2002Co-Authors: Alberto Artosi, Guido Governatori, Antonino RotoloAbstract:In this paper we present a labelled proof method for computing nonmonotonic consequence relations in a conditional logic setting. The method exploits the strong connection between these deductive relations and conditional logics, and it is based on the usual possible world semantics devised for the latter. The label formalism KEM, introduced to account for the semantics of normal modal logics, is easily adapted to the semantics of conditional logic by simply indexing labels with formulas. The basic inference rules are provided by the Propositional System KE+ - a tableau-like analytic proof System devised to be used both as a refutation method and a direct method of proof - that is the classical core of KEM which is thus enlarged with suitable elimination rules for the conditional connective. The resulting algorithmic framework is able to compute cumulative consequence relations in so far as they can be expressed as conditional implications.
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a labelled tableau calculus for nonmonotonic cumulative consequence relations
Theorem Proving with Analytic Tableaux and Related Methods, 2000Co-Authors: Alberto Artosi, Guido Governatori, Antonino RotoloAbstract:In this paper we present a labelled proof method for computing nonmonotonic consequence relations in a conditional logic setting. The method is based on the usual possible world semantics for conditional logic. The label formalism KEM, introduced to account for the semantics of normal modal logics, is easily adapted to the semantics of conditional logic by simply indexing labels with formulas. The inference rules are provided by the Propositional System KE + —a tableau-like analytic proof System devised to be used both as a refutation and a direct method of proof— enlarged with suitable elimination rules for the conditional connective. The resulting algorithmic framework is able to compute cumulative consequence relations in so far as they can be expressed as conditional implications.
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TABLEAUX - A Labelled Tableau Calculus for Nonmonotonic (Cumulative) Consequence Relations
Lecture Notes in Computer Science, 2000Co-Authors: Alberto Artosi, Guido Governatori, Antonino RotoloAbstract:In this paper we present a labelled proof method for computing nonmonotonic consequence relations in a conditional logic setting. The method is based on the usual possible world semantics for conditional logic. The label formalism KEM, introduced to account for the semantics of normal modal logics, is easily adapted to the semantics of conditional logic by simply indexing labels with formulas. The inference rules are provided by the Propositional System KE + —a tableau-like analytic proof System devised to be used both as a refutation and a direct method of proof— enlarged with suitable elimination rules for the conditional connective. The resulting algorithmic framework is able to compute cumulative consequence relations in so far as they can be expressed as conditional implications.
Alberto Artosi - One of the best experts on this subject based on the ideXlab platform.
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labelled tableaux for nonmonotonic reasoning cumulative consequence relations
Journal of Logic and Computation, 2002Co-Authors: Alberto Artosi, Guido Governatori, Antonino RotoloAbstract:In this paper we present a labelled proof method for computing nonmonotonic consequence relations in a conditional logic setting. The method exploits the strong connection between these deductive relations and conditional logics, and it is based on the usual possible world semantics devised for the latter. The label formalism KEM, introduced to account for the semantics of normal modal logics, is easily adapted to the semantics of conditional logic by simply indexing labels with formulas. The basic inference rules are provided by the Propositional System KE+ - a tableau-like analytic proof System devised to be used both as a refutation method and a direct method of proof - that is the classical core of KEM which is thus enlarged with suitable elimination rules for the conditional connective. The resulting algorithmic framework is able to compute cumulative consequence relations in so far as they can be expressed as conditional implications.
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a labelled tableau calculus for nonmonotonic cumulative consequence relations
Theorem Proving with Analytic Tableaux and Related Methods, 2000Co-Authors: Alberto Artosi, Guido Governatori, Antonino RotoloAbstract:In this paper we present a labelled proof method for computing nonmonotonic consequence relations in a conditional logic setting. The method is based on the usual possible world semantics for conditional logic. The label formalism KEM, introduced to account for the semantics of normal modal logics, is easily adapted to the semantics of conditional logic by simply indexing labels with formulas. The inference rules are provided by the Propositional System KE + —a tableau-like analytic proof System devised to be used both as a refutation and a direct method of proof— enlarged with suitable elimination rules for the conditional connective. The resulting algorithmic framework is able to compute cumulative consequence relations in so far as they can be expressed as conditional implications.
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A tableau methodology for deontic conditional logics
arXiv: Logic in Computer Science, 2000Co-Authors: Alberto Artosi, Guido GovernatoriAbstract:In this paper we present a theorem proving methodology for a restricted but significant fragment of the conditional language made up of (boolean combinations of) conditional statements with unnested antecedents. The method is based on the possible world semantics for conditional logics. The KEM label formalism, designed to account for the semantics of normal modal logics, is easily adapted to the semantics of conditional logics by simply indexing labels with formulas. The inference rules are provided by the Propositional System KE+ - a tableau-like analytic proof System devised to be used both as a refutation and a direct method of proof - enlarged with suitable elimination rules for the conditional connective. The theorem proving methodology we are going to present can be viewed as a first step towards developing an appropriate algorithmic framework for several conditional logics for (defeasible) conditional obligation.
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TABLEAUX - A Labelled Tableau Calculus for Nonmonotonic (Cumulative) Consequence Relations
Lecture Notes in Computer Science, 2000Co-Authors: Alberto Artosi, Guido Governatori, Antonino RotoloAbstract:In this paper we present a labelled proof method for computing nonmonotonic consequence relations in a conditional logic setting. The method is based on the usual possible world semantics for conditional logic. The label formalism KEM, introduced to account for the semantics of normal modal logics, is easily adapted to the semantics of conditional logic by simply indexing labels with formulas. The inference rules are provided by the Propositional System KE + —a tableau-like analytic proof System devised to be used both as a refutation and a direct method of proof— enlarged with suitable elimination rules for the conditional connective. The resulting algorithmic framework is able to compute cumulative consequence relations in so far as they can be expressed as conditional implications.
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A tableaux methodology for deontic conditional logics
1998Co-Authors: Alberto Artosi, Guido GovernatoriAbstract:In this paper we present a theorem proving methodology for a restricted but significant fragment of the conditional language made up of (boolean combinations of) conditional statements with unnested antecedents. The method is based on the possible world semantics for conditional logics. The KEM label formalism, designed to account for the semantics of normal modal logics, is easily adapted to the semantics of conditional logics by simply indexing labels with formulas. The inference rules are provided by the Propositional System $KE^{+}$ --- a tableau-like analytic proof System devised to be used both as a refutation and a direct method of proof --- enlarged with suitable elimination rules for the conditional connective. The theorem proving methodology we are going to present can be viewed as a first step towards developing an appropriate algorithmic framework for several conditional logics for (defeasible) conditional obligation.
Guido Governatori - One of the best experts on this subject based on the ideXlab platform.
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labelled tableaux for nonmonotonic reasoning cumulative consequence relations
Journal of Logic and Computation, 2002Co-Authors: Alberto Artosi, Guido Governatori, Antonino RotoloAbstract:In this paper we present a labelled proof method for computing nonmonotonic consequence relations in a conditional logic setting. The method exploits the strong connection between these deductive relations and conditional logics, and it is based on the usual possible world semantics devised for the latter. The label formalism KEM, introduced to account for the semantics of normal modal logics, is easily adapted to the semantics of conditional logic by simply indexing labels with formulas. The basic inference rules are provided by the Propositional System KE+ - a tableau-like analytic proof System devised to be used both as a refutation method and a direct method of proof - that is the classical core of KEM which is thus enlarged with suitable elimination rules for the conditional connective. The resulting algorithmic framework is able to compute cumulative consequence relations in so far as they can be expressed as conditional implications.
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a labelled tableau calculus for nonmonotonic cumulative consequence relations
Theorem Proving with Analytic Tableaux and Related Methods, 2000Co-Authors: Alberto Artosi, Guido Governatori, Antonino RotoloAbstract:In this paper we present a labelled proof method for computing nonmonotonic consequence relations in a conditional logic setting. The method is based on the usual possible world semantics for conditional logic. The label formalism KEM, introduced to account for the semantics of normal modal logics, is easily adapted to the semantics of conditional logic by simply indexing labels with formulas. The inference rules are provided by the Propositional System KE + —a tableau-like analytic proof System devised to be used both as a refutation and a direct method of proof— enlarged with suitable elimination rules for the conditional connective. The resulting algorithmic framework is able to compute cumulative consequence relations in so far as they can be expressed as conditional implications.
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A tableau methodology for deontic conditional logics
arXiv: Logic in Computer Science, 2000Co-Authors: Alberto Artosi, Guido GovernatoriAbstract:In this paper we present a theorem proving methodology for a restricted but significant fragment of the conditional language made up of (boolean combinations of) conditional statements with unnested antecedents. The method is based on the possible world semantics for conditional logics. The KEM label formalism, designed to account for the semantics of normal modal logics, is easily adapted to the semantics of conditional logics by simply indexing labels with formulas. The inference rules are provided by the Propositional System KE+ - a tableau-like analytic proof System devised to be used both as a refutation and a direct method of proof - enlarged with suitable elimination rules for the conditional connective. The theorem proving methodology we are going to present can be viewed as a first step towards developing an appropriate algorithmic framework for several conditional logics for (defeasible) conditional obligation.
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TABLEAUX - A Labelled Tableau Calculus for Nonmonotonic (Cumulative) Consequence Relations
Lecture Notes in Computer Science, 2000Co-Authors: Alberto Artosi, Guido Governatori, Antonino RotoloAbstract:In this paper we present a labelled proof method for computing nonmonotonic consequence relations in a conditional logic setting. The method is based on the usual possible world semantics for conditional logic. The label formalism KEM, introduced to account for the semantics of normal modal logics, is easily adapted to the semantics of conditional logic by simply indexing labels with formulas. The inference rules are provided by the Propositional System KE + —a tableau-like analytic proof System devised to be used both as a refutation and a direct method of proof— enlarged with suitable elimination rules for the conditional connective. The resulting algorithmic framework is able to compute cumulative consequence relations in so far as they can be expressed as conditional implications.
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A tableaux methodology for deontic conditional logics
1998Co-Authors: Alberto Artosi, Guido GovernatoriAbstract:In this paper we present a theorem proving methodology for a restricted but significant fragment of the conditional language made up of (boolean combinations of) conditional statements with unnested antecedents. The method is based on the possible world semantics for conditional logics. The KEM label formalism, designed to account for the semantics of normal modal logics, is easily adapted to the semantics of conditional logics by simply indexing labels with formulas. The inference rules are provided by the Propositional System $KE^{+}$ --- a tableau-like analytic proof System devised to be used both as a refutation and a direct method of proof --- enlarged with suitable elimination rules for the conditional connective. The theorem proving methodology we are going to present can be viewed as a first step towards developing an appropriate algorithmic framework for several conditional logics for (defeasible) conditional obligation.
