The Experts below are selected from a list of 315 Experts worldwide ranked by ideXlab platform
Larisa Maksimova - One of the best experts on this subject based on the ideXlab platform.
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Interpolation and the projective Beth Property in well-composed logics
Algebra and Logic, 2012Co-Authors: Larisa MaksimovaAbstract:We study the Interpolation and Beth definability problems in propositional extensions of minimal logic J. Previously, all J-logics with the weak Interpolation Property (WIP) were described, and it was proved that WIP is decidable over J. In this paper, we deal with so-called well-composed J-logics, i.e., J-logics satisfying an axiom (⊥ → A) ∨ (A → ⊥). Representation theorems are proved for well-composed logics possessing Craig’s Interpolation Property (CIP) and the restricted Interpolation Property (IPR). As a consequence, we show that only finitely many well-composed logics share these properties and that IPR is equivalent to the projective Beth Property (PBP) on the class of well-composed J-logics.
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Advances in Modal Logic - Interpolation and Beth Definability over the Minimal Logic.
2012Co-Authors: Larisa MaksimovaAbstract:Extensions of the Johansson minimal logic J are investigated. It is proved that the weak Interpolation Property WIP is decidable over J. Well-composed logics with the Graig Interpolation Property CIP, restricted Interpolation Property IPR and projective Beth Property PBP are fully described. It is proved that there are only finitely many well-composed logics with CIP, IPR or PBP; for any well-composed logic PBP is equivalent to IPR, and all the properties CIP, IPR and PBP are decidable on the class of well-composed logics..
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Interpolation and Definability over the Logic Gl
Studia Logica, 2011Co-Authors: Larisa MaksimovaAbstract:In a previous paper [21] all extensions of Johansson's minimal logic J with the weak Interpolation Property WIP were described. It was proved that WIP is decidable over J. It turned out that the weak Interpolation problem in extensions of J is reducible to the same problem over a logic Gl, which arises from J by adding tertium non datur. In this paper we consider extensions of the logic Gl. We prove that only finitely many logics over Gl have the Craig Interpolation Property CIP, the restricted Interpolation Property IPR or the projective Beth Property PBP. The full list of Gl-logics with the mentioned properties is found, and their description is given. We note that IPR and PBP are equivalent over Gl. It is proved that CIP, IPR and PBP are decidable over the logic Gl.
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Restricted Interpolation Property in superintuitionistic logics
Algebra and Logic, 2009Co-Authors: Larisa MaksimovaAbstract:The restricted Interpolation Property IPR in modal and superintuitionistic logics is investigated. It is proved that in superintuitionistic logics of finite slices and in finite-slice extensions of the Grzegorczyk logic, the Property IPR is equivalent to the projective Beth Property PB2.
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ALGEBRAIC APPROACH TO NON-CLASSICAL LOGICS
2008Co-Authors: Larisa MaksimovaAbstract:Study of non-classical logics in Novosibirsk started in 60-th due to initiative and by supervision of A.I.Maltsev. His interest to this area was stimulated by the existence of an adequate algebraic semantics for the most known non-classical logics. In the present paper inter-connections of syntactic properties of non-classical logics and categorial properties of appropriate classes of algebras are investigated. We consider such fundamental properties as the Interpolation Property, the Beth denability Property, joint consistency Property and their variants. In the case of modal, superintuitionistic and related logics the mentioned properties of logics proved to be equivalent to appropriate variants of the amalgamation Property or epimorphism surjectivity [1, 3]. It allows to solve, for instance, Interpolation problem for some important classes of logical calculi and, at the same time, amalgamation problem for varieties. In particular, the following problems are decidable: Craig’s Interpolation Property and deductive Interpolation Property for superintuitionistic and positive calculi and for modal calculi over the modal S4 logic, amalgamation and super-amalgamation properties for subvarieties of Heyting algebras, implicative lattices and closure algebras, projective Beth Property and restricted Interpolation Property over the intuitionistic logic and over the Grzegorczyk logic, strong epimorphisms surjectivity for subvarieties of Heyting algebras, implicative lattices and of Grzegorczyk algebras, weak Interpolation Property over the modal K4 logic [2], weak amalgamation Property for varieties of transitive modal algebras.
L. L. Maksimova - One of the best experts on this subject based on the ideXlab platform.
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Extensions of the Minimal Logic and the Interpolation Problem
Siberian Mathematical Journal, 2018Co-Authors: L. L. Maksimova, V. F. YunAbstract:Under study is the Interpolation problem over Johansson’s minimal logic J. We give a detailed exposition of the current state of this difficult problem, establish Craig’s Interpolation Property for several extensions of J, prove the absence of CIP in some families of extensions of J, and survey the results on Interpolation over J. Also, the relationship is discussed between the Interpolation properties and the recognizability of logics.
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Interpolation OVER THE MINIMAL LOGIC AND ODINTSOV INTERVALS
Siberian Mathematical Journal, 2015Co-Authors: L. L. Maksimova, V. F. YunAbstract:We study Craig’s Interpolation Property in the extensions of Johansson’s minimal logic. We consider the Odintsov classification of J-logics according to their intuitionistic and negative companions which subdivides all logics into intervals. We prove that the lower endpoint of an interval has Craig Interpolation Property if and only if both its companions do so. We also establish the recognizability of the lower and upper endpoints which have Craig Interpolation Property, and find their semantic characterization.
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The Lyndon Property and uniform Interpolation over the Grzegorczyk logic
Siberian Mathematical Journal, 2014Co-Authors: L. L. MaksimovaAbstract:We consider versions of the Interpolation Property stronger than the Craig Interpolation Property and prove the Lyndon Interpolation Property for the Grzegorczyk logic and some of its extensions. We also establish the Lyndon Interpolation Property for most extensions of the intuitionistic logic with Craig Interpolation Property. For all modal logics over the Grzegorczyk logic as well as for all superintuitionistic logics, the uniform Interpolation Property is equivalent to Craig’s Property.
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The projective Beth Property in well-composed logics
Algebra and Logic, 2013Co-Authors: L. L. MaksimovaAbstract:The Interpolation and Beth definability problems are proved decidable in well-composed logics, i.e., in extensions of Johansson’s minimal logic J satisfying an axiom (⊥ → A) ∨ (A → ⊥). In previous studies, all J-logics with the weak Interpolation Property (WIP) were described and WIP was proved decidable over J. Also it was shown that only finitely many well-composed logics possess Craig’s Interpolation Property (CIP) and the restricted Interpolation Property (IPR), and moreover, IPR is equivalent to the projective Beth Property (PBP) on the class of logics in question. These results are applied to prove decidability of IPR and PBP in well-composed logics. The decidability of CIP in such logics was stated earlier. Thus all basic versions of the Interpolation and Beth properties are decidable on the class of well-composed logics.
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The decidability of craig’s Interpolation Property in well-composed J-logics
Siberian Mathematical Journal, 2012Co-Authors: L. L. MaksimovaAbstract:Under study are the extensions of Johansson’s minimal logic J. We find sufficient conditions for the finite approximability of J-logics in dependence on the form of their axioms. Using these conditions, we prove the decidability of Craig’s Interpolation Property (CIP) in well-composed J-logics. Previously all J-logics with weak Interpolation Property (WIP) were described and the decidability of WIP over J was proved. Also we establish the decidability of the problem of amalgamability of well-composed varieties of J-algebras.
Wang Jia-yin - One of the best experts on this subject based on the ideXlab platform.
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Sufficient and necessary conditions for fuzzy systems possessing Interpolation Property
Control theory & applications, 2006Co-Authors: Hou Jian, Li Hongxing, Wang Jia-yinAbstract:Fuzzy system is universally approximating when it possesses Interpolation Property.Approximation ability of fuzzy system can be studied by its Interpolation Property.In this paper,we discussed respectively the Interpolation properties of two types of fuzzy systems generated by inference rules of combination of "intersection" and "union".First,fuzzy systems adopting "singleton" fuzzification,compositional rule of inference (CRI) algorithm and "barycenter method" defuzzification are studied,and it is pointed out that Interpolation properties of these fuzzy systems depend on the expressions or values of implication operator when its second variable take 0 and 1.Based on it,the sufficient and necessary conditions for fuzzy systems possessing Interpolation properties are proposed.Furthermore,some commonly applied fuzzy implication operators that satisfy the sufficient and necessary conditions are given.
Frank Wolter - One of the best experts on this subject based on the ideXlab platform.
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A Note on the Interpolation Property in Tense Logic
Journal of Philosophical Logic, 1997Co-Authors: Frank WolterAbstract:It is proved that all bimodal tense logics which contain the logic of the weak orderings and have unbounded depth do not have the Interpolation Property.
Taishi Kurahashi - One of the best experts on this subject based on the ideXlab platform.
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The fixed point and the Craig Interpolation properties for sublogics of $\mathbf{IL}$
arXiv: Logic, 2020Co-Authors: Sohei Iwata, Taishi Kurahashi, Yuya OkawaAbstract:We study the fixed point Property and the Craig Interpolation Property for sublogics of the interpretability logic $\mathbf{IL}$. We provide a complete description of these sublogics concerning the uniqueness of fixed points, the fixed point Property and the Craig Interpolation Property.
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Uniform Lyndon Interpolation Property in propositional modal logics
Archive for Mathematical Logic, 2020Co-Authors: Taishi KurahashiAbstract:We introduce and investigate the notion of uniform Lyndon Interpolation Property (ULIP) which is a strengthening of both uniform Interpolation Property and Lyndon Interpolation Property. We prove several propositional modal logics including $$\mathbf{K}$$, $$\mathbf{KB}$$, $$\mathbf{GL}$$ and $$\mathbf{Grz}$$ enjoy ULIP. Our proofs are modifications of Visser’s proofs of uniform Interpolation Property using layered bisimulations (Visser, in: Hajek (ed) Godel’96, logical foundations of mathematics, computer science and physics—Kurt Godel’s legacy, Springer, Berlin, 1996). Also we give a new upper bound on the complexity of uniform interpolants for $$\mathbf{GL}$$ and $$\mathbf{Grz}$$.
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Uniform Lyndon Interpolation Property in propositional modal logics.
arXiv: Logic, 2018Co-Authors: Taishi KurahashiAbstract:We introduce and investigate the notion of uniform Lyndon Interpolation Property (ULIP) which is a strengthening of both uniform Interpolation Property and Lyndon Interpolation Property. We prove several propositional modal logics including ${\bf K}$, ${\bf KB}$, ${\bf GL}$ and ${\bf Grz}$ enjoy ULIP. Our proofs are modifications of Visser's proofs of uniform Interpolation Property using layered bisimulations. Also we give a new upper bound on the complexity of uniform interpolants for ${\bf GL}$ and ${\bf Grz}$.
