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Katsuhiko Sano - One of the best experts on this subject based on the ideXlab platform.
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strong completeness and the finite model property for bi intuitionistic stable tense logics
Electronic Proceedings in Theoretical Computer Science, 2017Co-Authors: Katsuhiko Sano, John G StellAbstract:Bi-Intuitionistic Stable Tense Logics (BIST Logics) are tense logics with a Kripke Semantics where worlds in a frame are equipped with a pre-order as well as with an accessibility relation which is ‘stable’ with respect to this pre-order. BIST logics are extensions of a logic, BiSKt, which arose in the semantic context of hypergraphs, since a special case of the pre-order can represent the incidence structure of a hypergraph. In this paper we provide, for the first time, a Hilbert-style axiomatisation of BISKt and prove the strong completeness of BiSKt. We go on to prove strong completeness of a class of BIST logics obtained by extending BiSKt by formulas of a certain form. Moreover we show that the finite model property and the decidability hold for a class of BIST logics.
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cut free labelled sequent calculus for dynamic logic of relation changers
2017Co-Authors: Ryo Hatano, Katsuhiko Sano, Satoshi TojoAbstract:Dynamic epistemic logic (\(\mathbf {DEL}\)) is known as a large family of logics that extend standard epistemic logic with dynamic operators. Such dynamic operators can be regarded as epistemic actions over Kripke Semantics (or its variant). Therefore, \(\mathbf {DEL}\) is often used to model changes of agents’ knowledge, belief or preference over Kripke Semantics in terms of dynamic operators in many literatures. As a variant of \(\mathbf {DEL}\), (van Benthem and Liu, J Appl Non-Classical Logics 17(2):157–18 2007; Liu, Reasoning about preference dynamics, Springer Science & Business Media, Berlin 2011) proposed dynamic logic of relation changers (\(\mathbf {DLRC}\)). They provided a general framework to capture many dynamic operators in terms of relation changing operation written in programs of propositional dynamic logic, and they also provided a sound and complete Hilbert-style axiomatization for \(\mathbf {DLRC}\). While \(\mathbf {DLRC}\) can cover many dynamic operators in a uniform manner, proof theory for \(\mathbf {DLRC}\) is not well-studied except the Hilbert-style axiomatization. Therefore, we propose a cut-free labelled sequent calculus for \(\mathbf {DLRC}\). We show that our sequent calculus is equipollent with the Hilbert-style axiomatization.
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a cut free labelled sequent calculus for dynamic epistemic logic
Foundations of Computer Science, 2016Co-Authors: Shoshin Nomura, Hiroakira Ono, Katsuhiko SanoAbstract:Dynamic Epistemic Logic is a logic that is aimed at formally expressing how a person’s knowledge changes. We provide a cut-free labelled sequent calculus (\(\mathbf {GDEL}\)) on the background of existing studies of Hilbert-style axiomatization \(\mathbf {HDEL}\) by Baltag et al. (1989) and labelled calculi for Public Announcement Logic by Maffezioli et al. (2011) and Nomura et al. (2015). We first show that the cut rule is admissible in \(\mathbf {GDEL}\). Then we show \(\mathbf {GDEL}\) is sound and complete for Kripke Semantics. Lastly, we touch briefly on our on-going work of an automated theorem prover of \(\mathbf {GDEL}\).
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revising a labelled sequent calculus for public announcement logic
2016Co-Authors: Shoshin Nomura, Katsuhiko Sano, Satoshi TojoAbstract:We first show that a labelled sequent calculus \(\mathbf {G3PAL}\) for Public Announcement Logic (PAL) by Maffezioli and Negri (2011) has been lacking rules for deriving an axiom of Hilbert-style axiomatization of PAL. Then, we provide our revised calculus \(\mathbf {GPAL}\) to show that all the formulas provable in Hilbert-style axiomatization of PAL are also provable in \(\mathbf {GPAL}\) together with the cut rule. We also establish that our calculus enjoys cut elimination theorem. Moreover, we show the soundness of our calculus for Kripke Semantics with the notion of surviveness of possible worlds in a restricted domain. Finally, we provide a direct proof of the semantic completeness of \(\mathbf {GPAL}\) for the link-cutting Semantics of PAL.
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a labelled sequent calculus for intuitionistic public announcement logic
International Conference on Logic Programming, 2015Co-Authors: Shoshin Nomura, Katsuhiko Sano, Satoshi TojoAbstract:Intuitionistic Public Announcement Logic IntPAL proposed by Ma et al. 2014 aims at formalizing changes of an agent's knowledge in a constructive manner. IntPAL can be regarded as an intuitionistic generalization of Public Announcement Logic PAL whose modal basis is the intuitionistic modal logic IK by Fischer Servi 1984 and Simpson 1994. We also refer to IK for the basis of this paper. Meanwhile, Nomura et al. 2015 provided a cut-free labelled sequent calculus based on the study of Maffezioli et al. 2010. In this paper, we introduce a labelled sequent calculus for IntPAL we call it $$\mathbf {GIntPAL}$$ as both an intuitionistic variant of $$\mathbf {GPAL}$$ and a public announcement extension of Simpson's labelled calculus, and show that all theorems of the Hilbert axiomatization of IntPAL are also derivable in $$\mathbf {GIntPAL}$$ with the cut rule. Then we prove the admissibility of the cut rule in $$\mathbf {GIntPAL}$$ and also the soundness result for birelational Kripke Semantics. Finally, we derive the semantic completeness of $$\mathbf {GIntPAL}$$ as a corollary of these theorems.
Shoshin Nomura - One of the best experts on this subject based on the ideXlab platform.
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a cut free labelled sequent calculus for dynamic epistemic logic
Foundations of Computer Science, 2016Co-Authors: Shoshin Nomura, Hiroakira Ono, Katsuhiko SanoAbstract:Dynamic Epistemic Logic is a logic that is aimed at formally expressing how a person’s knowledge changes. We provide a cut-free labelled sequent calculus (\(\mathbf {GDEL}\)) on the background of existing studies of Hilbert-style axiomatization \(\mathbf {HDEL}\) by Baltag et al. (1989) and labelled calculi for Public Announcement Logic by Maffezioli et al. (2011) and Nomura et al. (2015). We first show that the cut rule is admissible in \(\mathbf {GDEL}\). Then we show \(\mathbf {GDEL}\) is sound and complete for Kripke Semantics. Lastly, we touch briefly on our on-going work of an automated theorem prover of \(\mathbf {GDEL}\).
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revising a labelled sequent calculus for public announcement logic
2016Co-Authors: Shoshin Nomura, Katsuhiko Sano, Satoshi TojoAbstract:We first show that a labelled sequent calculus \(\mathbf {G3PAL}\) for Public Announcement Logic (PAL) by Maffezioli and Negri (2011) has been lacking rules for deriving an axiom of Hilbert-style axiomatization of PAL. Then, we provide our revised calculus \(\mathbf {GPAL}\) to show that all the formulas provable in Hilbert-style axiomatization of PAL are also provable in \(\mathbf {GPAL}\) together with the cut rule. We also establish that our calculus enjoys cut elimination theorem. Moreover, we show the soundness of our calculus for Kripke Semantics with the notion of surviveness of possible worlds in a restricted domain. Finally, we provide a direct proof of the semantic completeness of \(\mathbf {GPAL}\) for the link-cutting Semantics of PAL.
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a labelled sequent calculus for intuitionistic public announcement logic
International Conference on Logic Programming, 2015Co-Authors: Shoshin Nomura, Katsuhiko Sano, Satoshi TojoAbstract:Intuitionistic Public Announcement Logic IntPAL proposed by Ma et al. 2014 aims at formalizing changes of an agent's knowledge in a constructive manner. IntPAL can be regarded as an intuitionistic generalization of Public Announcement Logic PAL whose modal basis is the intuitionistic modal logic IK by Fischer Servi 1984 and Simpson 1994. We also refer to IK for the basis of this paper. Meanwhile, Nomura et al. 2015 provided a cut-free labelled sequent calculus based on the study of Maffezioli et al. 2010. In this paper, we introduce a labelled sequent calculus for IntPAL we call it $$\mathbf {GIntPAL}$$ as both an intuitionistic variant of $$\mathbf {GPAL}$$ and a public announcement extension of Simpson's labelled calculus, and show that all theorems of the Hilbert axiomatization of IntPAL are also derivable in $$\mathbf {GIntPAL}$$ with the cut rule. Then we prove the admissibility of the cut rule in $$\mathbf {GIntPAL}$$ and also the soundness result for birelational Kripke Semantics. Finally, we derive the semantic completeness of $$\mathbf {GIntPAL}$$ as a corollary of these theorems.
Satoshi Tojo - One of the best experts on this subject based on the ideXlab platform.
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cut free labelled sequent calculus for dynamic logic of relation changers
2017Co-Authors: Ryo Hatano, Katsuhiko Sano, Satoshi TojoAbstract:Dynamic epistemic logic (\(\mathbf {DEL}\)) is known as a large family of logics that extend standard epistemic logic with dynamic operators. Such dynamic operators can be regarded as epistemic actions over Kripke Semantics (or its variant). Therefore, \(\mathbf {DEL}\) is often used to model changes of agents’ knowledge, belief or preference over Kripke Semantics in terms of dynamic operators in many literatures. As a variant of \(\mathbf {DEL}\), (van Benthem and Liu, J Appl Non-Classical Logics 17(2):157–18 2007; Liu, Reasoning about preference dynamics, Springer Science & Business Media, Berlin 2011) proposed dynamic logic of relation changers (\(\mathbf {DLRC}\)). They provided a general framework to capture many dynamic operators in terms of relation changing operation written in programs of propositional dynamic logic, and they also provided a sound and complete Hilbert-style axiomatization for \(\mathbf {DLRC}\). While \(\mathbf {DLRC}\) can cover many dynamic operators in a uniform manner, proof theory for \(\mathbf {DLRC}\) is not well-studied except the Hilbert-style axiomatization. Therefore, we propose a cut-free labelled sequent calculus for \(\mathbf {DLRC}\). We show that our sequent calculus is equipollent with the Hilbert-style axiomatization.
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revising a labelled sequent calculus for public announcement logic
2016Co-Authors: Shoshin Nomura, Katsuhiko Sano, Satoshi TojoAbstract:We first show that a labelled sequent calculus \(\mathbf {G3PAL}\) for Public Announcement Logic (PAL) by Maffezioli and Negri (2011) has been lacking rules for deriving an axiom of Hilbert-style axiomatization of PAL. Then, we provide our revised calculus \(\mathbf {GPAL}\) to show that all the formulas provable in Hilbert-style axiomatization of PAL are also provable in \(\mathbf {GPAL}\) together with the cut rule. We also establish that our calculus enjoys cut elimination theorem. Moreover, we show the soundness of our calculus for Kripke Semantics with the notion of surviveness of possible worlds in a restricted domain. Finally, we provide a direct proof of the semantic completeness of \(\mathbf {GPAL}\) for the link-cutting Semantics of PAL.
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a labelled sequent calculus for intuitionistic public announcement logic
International Conference on Logic Programming, 2015Co-Authors: Shoshin Nomura, Katsuhiko Sano, Satoshi TojoAbstract:Intuitionistic Public Announcement Logic IntPAL proposed by Ma et al. 2014 aims at formalizing changes of an agent's knowledge in a constructive manner. IntPAL can be regarded as an intuitionistic generalization of Public Announcement Logic PAL whose modal basis is the intuitionistic modal logic IK by Fischer Servi 1984 and Simpson 1994. We also refer to IK for the basis of this paper. Meanwhile, Nomura et al. 2015 provided a cut-free labelled sequent calculus based on the study of Maffezioli et al. 2010. In this paper, we introduce a labelled sequent calculus for IntPAL we call it $$\mathbf {GIntPAL}$$ as both an intuitionistic variant of $$\mathbf {GPAL}$$ and a public announcement extension of Simpson's labelled calculus, and show that all theorems of the Hilbert axiomatization of IntPAL are also derivable in $$\mathbf {GIntPAL}$$ with the cut rule. Then we prove the admissibility of the cut rule in $$\mathbf {GIntPAL}$$ and also the soundness result for birelational Kripke Semantics. Finally, we derive the semantic completeness of $$\mathbf {GIntPAL}$$ as a corollary of these theorems.
Norihiro Kamide - One of the best experts on this subject based on the ideXlab platform.
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finite model property for modal ideal paraconsistent four valued logic
International Symposium on Multiple-Valued Logic, 2019Co-Authors: Norihiro Kamide, Yoni ZoharAbstract:A modal extension M4CC of Arieli, Avron, and Zamansky's ideal paraconsistent four-valued logic 4CC is introduced as a Gentzen-type sequent calculus. The completeness theorem with respect to a Kripke Semantics for M4CC is proved. The finite model property for M4CC is shown by modifying the completeness proof. The decidability of M4CC is obtained as a corollary.
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Conceptual modeling in full computation-tree logic with sequence modal operator
International Journal of Intelligent Systems, 2011Co-Authors: Ken Kaneiwa, Norihiro KamideAbstract:In this paper, we propose a method for modeling concepts in full computation-tree logic with sequence modal operators. An extended full computation-tree logic, CTLS*, is introduced as a Kripke Semantics with a sequence modal operator. This logic can appropriately represent hierarchical tree structures in cases where sequence modal operators in CTLS* are applied to tree structures. We prove a theorem for embedding CTLS* into CTL*. The validity, satisfiability, and model-checking problems of CTLS* are shown to be decidable. An illustrative example of biological taxonomy is presented using CTLS* formulas. © 2011 Wiley Periodicals, Inc. (This paper is an extended version of Kamide and Kaneiwa.)
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extended full computation tree logic with sequence modal operator representing hierarchical tree structures
Australasian Joint Conference on Artificial Intelligence, 2009Co-Authors: Norihiro Kamide, Ken KaneiwaAbstract:An extended full computation-tree logic, CTLS*, is introduced as a Kripke Semantics with a sequence modal operator. This logic can appropriately represent hierarchical tree structures where sequence modal operators in CTLS* are applied to tree structures. An embedding theorem of CTLS* into CTL* is proved. The validity, satisfiability and model-checking problems of CTLS* are shown to be decidable. An illustrative example of biological taxonomy is presented using CTLS* formulas.
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Phase Semantics and Petri Net Interpretation for Resource-Sensitive Strong Negation
Journal of Logic Language and Information, 2006Co-Authors: Norihiro KamideAbstract:Wansing’s extended intuitionistic linear logic with strong negation, called WILL, is regarded as a resource-conscious refinment of Nelson’s constructive logics with strong negation. In this paper, (1) the completeness theorem with respect to phase Semantics is proved for WILL using a method that simultaneously derives the cut-elimination theorem, (2) a simple correspondence between the class of Petri nets with inhibitor arcs and a fragment of WILL is obtained using a Kripke Semantics, (3) a cut-free sequent calculus for WILL, called twist calculus, is presented, (4) a strongly normalizable typed λ-calculus is obtained for a fragment of WILL, and (5) new applications of WILL in medical diagnosis and electric circuit theory are proposed. Strong negation in WILL is found to be expressible as a resource-conscious refutability, and is shown to correspond to inhibitor arcs in Petri net theory.
David J Pym - One of the best experts on this subject based on the ideXlab platform.
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intuitionistic layered graph logic
International Joint Conference on Automated Reasoning, 2016Co-Authors: Simon Docherty, David J PymAbstract:Models of complex systems are widely used in the physical and social sciences, and the concept of layering, typically building upon graph-theoretic structure, is a common feature. We describe an intuitionistic substructural logic that gives an account of layering. As in bunched systems, the logic includes the usual intuitionistic connectives, together with a non-commutative, non-associative conjunction used to capture layering and its associated implications. We give soundness and completeness theorems for labelled tableaux and Hilbert-type systems with respect to a Kripke Semantics on graphs. To demonstrate the utility of the logic, we show how to represent a range of systems and security examples, illuminating the relationship between services/policies and the infrastructures/architectures to which they are applied.
