The Experts below are selected from a list of 4044 Experts worldwide ranked by ideXlab platform
Vasilyi Shangin - One of the best experts on this subject based on the ideXlab platform.
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Automating Natural Deduction for temporal logic
2020Co-Authors: Alexander Bolotov, Oleg Grigoriev, Vasilyi ShanginAbstract:We present our recent work on the construction of Natural Deduction calculi for temporal logic. We analyse propositional linear-time temporal logic (PLTL) and Computation Tree Logic (CTL) and corresponding proof searching algorithms. The automation of the Natural Deduction calculi for these temporal logics opens the new prospect to apply our techniques as an automatic reasoning tool in the areas, where the linear-time or branching-time setting is required.
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Natural Deduction in a Paracomplete Setting
2020Co-Authors: Alexander Bolotov, Vasilyi ShanginAbstract:In this paper we present the automated proof search technique in Natural Deduction paracomplete logic. Here, for some statements we do not have evidence to conclude if they are true or false, as it happens in the classical framework. As a consequence, for example, formulae of the type p_:p, are not valid. In this paper we formulate the Natural Deduction system for paracompletelogic PComp, explain its main concepts, define proof searching techniques and the searching algorithm providing examples proofs.
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IICAI - Automated first order Natural Deduction
2020Co-Authors: Alexander Bolotov, Vyacheslav Bocharov, Alexander Gorchakov, Vasilyi ShanginAbstract:We present a proof-searching algorithm for the classical first order Natural Deduction calculus and prove its correctness. For any given task (if this task is indeed solvable), a searching algorithm terminates, either finding a corresponding Natural Deduction proof or giving a set of constraints, from which a counter-example can be extracted. Proofs of the properties which characterize correctness of the searching algorithm are given. Based on a fully automatic goal-directed searching procedure, our technique can be efficiently applied as an automatic reasoning tool in a deliberative decision making framework across various AI applications.
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Natural three-valued logics characterized by Natural Deduction
Logique Et Analyse, 2018Co-Authors: Yaroslav Petrukhin, Vasilyi ShanginAbstract:In this paper, we combine the concept of Natural Deduction and the concept of three-valued Natural logic. In particular, we use a semantic definition of the concept of Natural logic presented by N. Tomova. By using the correspondence analysis given by B. Kooi and A. Tamminga, we present a syntactical counterpart of the semantic definition in question, i.e. in this paper, three-valued Natural logics are characterised by Natural Deduction systems.
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On the Complexity of the Natural Deduction Proof Search Algorithm
2017Co-Authors: Alexander Bolotov, Vasilyi Shangin, D. KozhemiachenkoAbstract:We present our first account of the complexity of Natural Deduction proof search algorithms. Though we target the complexity for Natural Deduction for temporal logic, here we only tackle classical case, comparing the classical part of the proof search for temporal logic with the classical analytical tableau.
Alexander Bolotov - One of the best experts on this subject based on the ideXlab platform.
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Automating Natural Deduction for temporal logic
2020Co-Authors: Alexander Bolotov, Oleg Grigoriev, Vasilyi ShanginAbstract:We present our recent work on the construction of Natural Deduction calculi for temporal logic. We analyse propositional linear-time temporal logic (PLTL) and Computation Tree Logic (CTL) and corresponding proof searching algorithms. The automation of the Natural Deduction calculi for these temporal logics opens the new prospect to apply our techniques as an automatic reasoning tool in the areas, where the linear-time or branching-time setting is required.
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Natural Deduction in a Paracomplete Setting
2020Co-Authors: Alexander Bolotov, Vasilyi ShanginAbstract:In this paper we present the automated proof search technique in Natural Deduction paracomplete logic. Here, for some statements we do not have evidence to conclude if they are true or false, as it happens in the classical framework. As a consequence, for example, formulae of the type p_:p, are not valid. In this paper we formulate the Natural Deduction system for paracompletelogic PComp, explain its main concepts, define proof searching techniques and the searching algorithm providing examples proofs.
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IICAI - Automated first order Natural Deduction
2020Co-Authors: Alexander Bolotov, Vyacheslav Bocharov, Alexander Gorchakov, Vasilyi ShanginAbstract:We present a proof-searching algorithm for the classical first order Natural Deduction calculus and prove its correctness. For any given task (if this task is indeed solvable), a searching algorithm terminates, either finding a corresponding Natural Deduction proof or giving a set of constraints, from which a counter-example can be extracted. Proofs of the properties which characterize correctness of the searching algorithm are given. Based on a fully automatic goal-directed searching procedure, our technique can be efficiently applied as an automatic reasoning tool in a deliberative decision making framework across various AI applications.
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Natural Deduction calculus for quantified propositional linear-time temporal logic (QPTL)
2020Co-Authors: Alexander Bolotov, Oleg GrigorievAbstract:We present a Natural Deduction calculus for the quantified propositional linear-time temporal logic (QPTL) and prove its correctness. The system extends previous Natural Deduction constructions for the propositional linear-time temporal logic. These developments extend the applicability of the Natural Deduction to more sophisticated specifications due to the expressive power of QPTL and, on the hand, supply QPTL itself with an elegant reasoning tool.
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On the Complexity of the Natural Deduction Proof Search Algorithm
2017Co-Authors: Alexander Bolotov, Vasilyi Shangin, D. KozhemiachenkoAbstract:We present our first account of the complexity of Natural Deduction proof search algorithms. Though we target the complexity for Natural Deduction for temporal logic, here we only tackle classical case, comparing the classical part of the proof search for temporal logic with the classical analytical tableau.
Carsten Schurmann - One of the best experts on this subject based on the ideXlab platform.
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focused Natural Deduction
International Conference on Logic Programming, 2010Co-Authors: Taus Brocknannestad, Carsten SchurmannAbstract:Natural Deduction for intuitionistic linear logic is known to be full of non-deterministic choices. In order to control these choices, we combine ideas from intercalation and focusing to arrive at the calculus of focused Natural Deduction. The calculus is shown to be sound and complete with respect to first-order intuitionistic linear Natural Deduction and the backward linear focusing calculus.
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LPAR (Yogyakarta) - Focused Natural Deduction
Logic for Programming Artificial Intelligence and Reasoning, 2010Co-Authors: Taus Brock-nannestad, Carsten SchurmannAbstract:Natural Deduction for intuitionistic linear logic is known to be full of non-deterministic choices. In order to control these choices, we combine ideas from intercalation and focusing to arrive at the calculus of focused Natural Deduction. The calculus is shown to be sound and complete with respect to first-order intuitionistic linear Natural Deduction and the backward linear focusing calculus.
Oleg Grigoriev - One of the best experts on this subject based on the ideXlab platform.
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Automating Natural Deduction for temporal logic
2020Co-Authors: Alexander Bolotov, Oleg Grigoriev, Vasilyi ShanginAbstract:We present our recent work on the construction of Natural Deduction calculi for temporal logic. We analyse propositional linear-time temporal logic (PLTL) and Computation Tree Logic (CTL) and corresponding proof searching algorithms. The automation of the Natural Deduction calculi for these temporal logics opens the new prospect to apply our techniques as an automatic reasoning tool in the areas, where the linear-time or branching-time setting is required.
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Natural Deduction calculus for quantified propositional linear-time temporal logic (QPTL)
2020Co-Authors: Alexander Bolotov, Oleg GrigorievAbstract:We present a Natural Deduction calculus for the quantified propositional linear-time temporal logic (QPTL) and prove its correctness. The system extends previous Natural Deduction constructions for the propositional linear-time temporal logic. These developments extend the applicability of the Natural Deduction to more sophisticated specifications due to the expressive power of QPTL and, on the hand, supply QPTL itself with an elegant reasoning tool.
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Natural Deduction calculus for computation tree logic
IEEE John Vincent Atanasoff 2006 International Symposium on Modern Computing (JVA'06), 2006Co-Authors: Alexander Bolotov, Oleg Grigoriev, Vasilyi ShanginAbstract:The authors present a Natural Deduction calculus for the computation tree logic, CTL, defined with the full set of classical and temporal logic operators. The system extends the Natural Deduction construction of the linear-time temporal logic. This opens the prospect to apply our technique as an automatic reasoning tool in a deliberative decision making framework across various applications in AI and computer science, where the branching-time setting is required
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Natural Deduction calculus for linear time temporal logic
European Conference on Logics in Artificial Intelligence, 2006Co-Authors: Alexander Bolotov, Oleg Grigoriev, Artie Basukoski, Vasilyi ShanginAbstract:We present a Natural Deduction calculus for the propositional linear-time temporal logic and prove its correctness. The system extends the Natural Deduction construction of the classical propositional logic. This will open the prospect to apply our technique as an automatic reasoning tool in a deliberative decision making framework across various AI applications.
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JELIA - Natural Deduction calculus for linear-time temporal logic
Logics in Artificial Intelligence, 2006Co-Authors: Alexander Bolotov, Oleg Grigoriev, Artie Basukoski, Vasilyi ShanginAbstract:We present a Natural Deduction calculus for the propositional linear-time temporal logic and prove its correctness. The system extends the Natural Deduction construction of the classical propositional logic. This will open the prospect to apply our technique as an automatic reasoning tool in a deliberative decision making framework across various AI applications.
Torben Braüner - One of the best experts on this subject based on the ideXlab platform.
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Labelled Versus Internalized Natural Deduction
Applied Logic Series, 2010Co-Authors: Torben BraünerAbstract:In this chapter we compare the hybrid-logical Natural Deduction system given in Section 2.2 to a labelled Natural Deduction system for modal logic. The chapter is structured as follows. In the first section of the chapter we describe the labelled Natural Deduction system under consideration and in the second section we define a translation from this system to the hybrid-logical Natural Deduction system given in Section 2.2. In the third section we compare reductions in the two systems. The material in this chapter is taken from Brauner(2007).
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Comparison to Seligman’s Natural Deduction System
Applied Logic Series, 2010Co-Authors: Torben BraünerAbstract:In this chapter we compare and contrast the Natural Deduction system given in Section 2.2 to a modified version of a hybrid-logical Natural Deduction system given by Jerry Seligman. The chapter is structured as follows. In the first section of the chapter we describe the Natural Deduction systems under consideration, in particular, we define our version of Seligman’s system. In the second and third sections, we give translations of derivations backwards and forwards between the systems, and in the fourth section we devise a set of reduction rules for our version of Seligman’s system by translation of the reduction rules for the system given in Section 2.2. In the final section we discuss the results.
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Natural Deduction for first order hybrid logic
Journal of Logic Language and Information, 2005Co-Authors: Torben BraünerAbstract:This is a companion paper to Brauner (2004b, Journal of Logic and Computation 14, 329--353) where a Natural Deduction system for propositional hybrid logic is given. In the present paper we generalize the system to the first-order case. Our Natural Deduction system for first-order hybrid logic can be extended with additional inference rules corresponding to conditions on the accessibility relations and the quantifier domains expressed by so-called geometric theories. We prove soundness and completeness and we prove a normalisation theorem. Moreover, we give an axiom system first-order hybrid logic.
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Natural Deduction for hybrid logic
Journal of Logic and Computation, 2004Co-Authors: Torben BraünerAbstract:In this paper we give a Natural Deduction formulation of hybrid logic. Our Natural Deduction system can be extended with additional inference rules corresponding to conditions on the accessibility relations expressed by so-called geometric theories. Thus, we give Natural Deduction systems in a uniform way for a wide class of hybrid logics which appears to be impossible in the context of ordinary modal logic. We prove soundness and completeness and we prove a normalization theorem. We finally prove a result which says that normal derivations in the Natural Deduction system correspond to derivations in a cut-free Gentzen system.
