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Michael Zakharyaschev [47]M. Zakharyaschev [12]M. V. Zakharyaschev [1]
  1. (1 other version)Many-Dimensional Modal Logics: Theory and Applications.D. M. Gabbay, A. Kurucz, F. Wolter & M. Zakharyaschev - 2005 - Studia Logica 81 (1):147-150.
     
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  2. Canonical formulas for k4. part I: Basic results.Michael Zakharyaschev - 1992 - Journal of Symbolic Logic 57 (4):1377-1402.
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  3.  26
    Kripke completeness of strictly positive modal logics over meet-semilattices with operators.Stanislav Kikot, Agi Kurucz, Yoshihito Tanaka, Frank Wolter & Michael Zakharyaschev - 2019 - Journal of Symbolic Logic 84 (2):533-588.
    Our concern is the completeness problem for spi-logics, that is, sets of implications between strictly positive formulas built from propositional variables, conjunction and modal diamond operators. Originated in logic, algebra and computer science, spi-logics have two natural semantics: meet-semilattices with monotone operators providing Birkhoff-style calculi and first-order relational structures (aka Kripke frames) often used as the intended structures in applications. Here we lay foundations for a completeness theory that aims to answer the question whether the two semantics define the same (...)
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  4.  75
    (1 other version)Decidable fragments of first-order temporal logics.Ian Hodkinson, Frank Wolter & Michael Zakharyaschev - 2000 - Annals of Pure and Applied Logic 106 (1-3):85-134.
    In this paper, we introduce a new fragment of the first-order temporal language, called the monodic fragment, in which all formulas beginning with a temporal operator have at most one free variable. We show that the satisfiability problem for monodic formulas in various linear time structures can be reduced to the satisfiability problem for a certain fragment of classical first-order logic. This reduction is then used to single out a number of decidable fragments of first-order temporal logics and of two-sorted (...)
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  5.  32
    Canonical formulas for k4. part II: Cofinal subframe logics.Michael Zakharyaschev - 1996 - Journal of Symbolic Logic 61 (2):421-449.
    Related Works: Part I: Michael Zakharyaschev. Canonical Formulas for $K4$. Part I: Basic Results. J. Symbolic Logic, Volume 57, Issue 4 , 1377--1402. Project Euclid: euclid.jsl/1183744119 Part III: Michael Zakharyaschev. Canonical Formulas for K4. Part III: The Finite Model Property. J. Symbolic Logic, Volume 62, Issue 3 , 950--975. Project Euclid: euclid.jsl/1183745306.
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  6.  14
    The price of query rewriting in ontology-based data access.Georg Gottlob, Stanislav Kikot, Roman Kontchakov, Vladimir Podolskii, Thomas Schwentick & Michael Zakharyaschev - 2014 - Artificial Intelligence 213 (C):42-59.
  7.  49
    Speaking about transitive frames in propositional languages.Yasuhito Suzuki, Frank Wolter & Michael Zakharyaschev - 1998 - Journal of Logic, Language and Information 7 (3):317-339.
    This paper is a comparative study of the propositional intuitionistic (non-modal) and classical modal languages interpreted in the standard way on transitive frames. It shows that, when talking about these frames rather than conventional quasi-orders, the intuitionistic language displays some unusual features: its expressive power becomes weaker than that of the modal language, the induced consequence relation does not have a deduction theorem and is not protoalgebraic. Nevertheless, the paper develops a manageable model theory for this consequence and its extensions (...)
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  8. The undecidability of the disjunction property of propositional logics and other related problems.Alexander Chagrov & Michael Zakharyaschev - 1993 - Journal of Symbolic Logic 58 (3):967-1002.
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  9.  52
    Products of 'transitive' modal logics.David Gabelaia, Agi Kurucz, Frank Wolter & Michael Zakharyaschev - 2005 - Journal of Symbolic Logic 70 (3):993-1021.
    We solve a major open problem concerning algorithmic properties of products of ‘transitive’ modal logics by showing that products and commutators of such standard logics as K4, S4, S4.1, K4.3, GL, or Grz are undecidable and do not have the finite model property. More generally, we prove that no Kripke complete extension of the commutator [K4,K4] with product frames of arbitrary finite or infinite depth (with respect to both accessibility relations) can be decidable. In particular, if.
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  10.  32
    Non-primitive recursive decidability of products of modal logics with expanding domains.David Gabelaia, Agi Kurucz, Frank Wolter & Michael Zakharyaschev - 2006 - Annals of Pure and Applied Logic 142 (1):245-268.
    We show that—unlike products of ‘transitive’ modal logics which are usually undecidable—their ‘expanding domain’ relativisations can be decidable, though not in primitive recursive time. In particular, we prove the decidability and the finite expanding product model property of bimodal logics interpreted in two-dimensional structures where one component—call it the ‘flow of time’—is • a finite linear order or a finite transitive tree and the other is composed of structures like • transitive trees/partial orders/quasi-orders/linear orders or only finite such structures expanding (...)
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  11.  35
    Axiomatizing the monodic fragment of first-order temporal logic.Frank Wolter & Michael Zakharyaschev - 2002 - Annals of Pure and Applied Logic 118 (1-2):133-145.
    It is known that even seemingly small fragments of the first-order temporal logic over the natural numbers are not recursively enumerable. In this paper we show that the monodic fragment is an exception by constructing its finite Hilbert-style axiomatization. We also show that the monodic fragment with equality is not recursively axiomatizable.
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  12.  71
    Undecidability of first-order intuitionistic and modal logics with two variables.Roman Kontchakov, Agi Kurucz & Michael Zakharyaschev - 2005 - Bulletin of Symbolic Logic 11 (3):428-438.
    We prove that the two-variable fragment of first-order intuitionistic logic is undecidable, even without constants and equality. We also show that the two-variable fragment of a quantified modal logic L with expanding first-order domains is undecidable whenever there is a Kripke frame for L with a point having infinitely many successors (such are, in particular, the first-order extensions of practically all standard modal logics like K, K4, GL, S4, S5, K4.1, S4.2, GL.3, etc.). For many quantified modal logics, including those (...)
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  13.  31
    On Dynamic Topological and Metric Logics.B. Konev, R. Kontchakov, F. Wolter & M. Zakharyaschev - 2006 - Studia Logica 84 (1):129-160.
    We investigate computational properties of propositional logics for dynamical systems. First, we consider logics for dynamic topological systems (W.f), fi, where W is a topological space and f a homeomorphism on W. The logics come with ‘modal’ operators interpreted by the topological closure and interior, and temporal operators interpreted along the orbits {w, f(w), f2 (w), ˙˙˙} of points w ε W. We show that for various classes of topological spaces the resulting logics are not recursively enumerable (and so not (...)
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  14.  17
    Logic-based ontology comparison and module extraction, with an application to DL-Lite.Roman Kontchakov, Frank Wolter & Michael Zakharyaschev - 2010 - Artificial Intelligence 174 (15):1093-1141.
  15.  71
    A modal logic framework for reasoning about comparative distances and topology.Mikhail Sheremet, Frank Wolter & Michael Zakharyaschev - 2010 - Annals of Pure and Applied Logic 161 (4):534-559.
    We propose and investigate a uniform modal logic framework for reasoning about topology and relative distance in metric and more general distance spaces, thus enabling the comparison and combination of logics from distinct research traditions such as Tarski’s for topological closure and interior, conditional logics, and logics of comparative similarity. This framework is obtained by decomposing the underlying modal-like operators into first-order quantifier patterns. We then show that quite a powerful and natural fragment of the resulting first-order logic can be (...)
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  16.  21
    Query inseparability for ALC ontologies.Elena Botoeva, Carsten Lutz, Vladislav Ryzhikov, Frank Wolter & Michael Zakharyaschev - 2019 - Artificial Intelligence 272 (C):1-51.
  17.  11
    Games for query inseparability of description logic knowledge bases.Elena Botoeva, Roman Kontchakov, Vladislav Ryzhikov, Frank Wolter & Michael Zakharyaschev - 2016 - Artificial Intelligence 234 (C):78-119.
  18.  17
    -Connections of abstract description systems.Oliver Kutz, Carsten Lutz, Frank Wolter & Michael Zakharyaschev - 2004 - Artificial Intelligence 156 (1):1-73.
  19. Temporalising tableaux.Roman Kontchakov, Carsten Lutz, Frank Wolter & Michael Zakharyaschev - 2004 - Studia Logica 76 (1):91 - 134.
    As a remedy for the bad computational behaviour of first-order temporal logic (FOTL), it has recently been proposed to restrict the application of temporal operators to formulas with at most one free variable thereby obtaining so-called monodic fragments of FOTL. In this paper, we are concerned with constructing tableau algorithms for monodic fragments based on decidable fragments of first-order logic like the two-variable fragment or the guarded fragment. We present a general framework that shows how existing decision procedures for first-order (...)
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  20. Modal companions of intermediate logics: A survey.A. V. Chagrov & M. V. Zakharyaschev - forthcoming - Studia Logica.
  21.  49
    Axiomatizing Distance Logics.Oliver Kutz, Holger Sturm, Nobu-Yuki Suzuki, Frank Wolter & Michael Zakharyaschev - 2002 - Journal of Applied Non-Classical Logics 12 (3-4):425-439.
    In [STU 00, KUT 03] we introduced a family of ‘modal' languages intended for talking about distances. These languages are interpreted in ‘distance spaces' which satisfy some of the standard axioms of metric spaces. Among other things, we singled out decidable logics of distance spaces and proved expressive completeness results relating classical and modal languages. The aim of this paper is to axiomatize the modal fragments of the semantically defined distance logics of [KUT 03] and give a new proof of (...)
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  22.  41
    Canonical formulas for k4. part III: The finite model property.Michael Zakharyaschev - 1997 - Journal of Symbolic Logic 62 (3):950-975.
    Related Works: Part I: Michael Zakharyaschev. Canonical Formulas for $K4$. Part I: Basic Results. J. Symbolic Logic, Volume 57, Issue 4 , 1377--1402. Project Euclid: euclid.jsl/1183744119 Part II: Michael Zakharyaschev. Canonical Formulas for K4. Part II: Cofinal Subframe Logics. J. Symbolic Logic, Volume 61, Issue 2 , 421--449. Project Euclid: euclid.jsl/1183745008.
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  23.  28
    Willem Blok and Modal Logic.W. Rautenberg, M. Zakharyaschev & F. Wolter - 2006 - Studia Logica 83 (1):15-30.
    We present our personal view on W.J. Blok's contribution to modal logic.
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  24.  52
    A Logic for Metric and Topology.Frank Wolter & Michael Zakharyaschev - 2005 - Journal of Symbolic Logic 70 (3):795 - 828.
    We propose a logic for reasoning about metric spaces with the induced topologies. It combines the 'qualitative' interior and closure operators with 'quantitative' operators 'somewhere in the sphere of radius r.' including or excluding the boundary. We supply the logic with both the intended metric space semantics and a natural relational semantics, and show that the latter (i) provides finite partial representations of (in general) infinite metric models and (ii) reduces the standard '∈-definitions' of closure and interior to simple constraints (...)
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  25.  13
    (1 other version)Dynamic topological logics over spaces with continuous functions.B. Konev, R. Kontchakov, F. Wolter & M. Zakharyaschev - 1998 - In Marcus Kracht, Maarten de Rijke, Heinrich Wansing & Michael Zakharyaschev (eds.), Advances in Modal Logic. CSLI Publications. pp. 299-318.
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  26.  25
    Canonical formulas for modal and superintuitionistic logics: a short outline.Michael Zakharyaschev - 1997 - In Maarten de Rijke (ed.), Advances in Intensional Logic. Dordrecht, Netherland: Kluwer Academic Publishers. pp. 195--248.
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  27. Advances in Modal Logic, Volume.F. Wolter, H. Wansing, M. de Rijke & M. Zakharyaschev - unknown
    We study a propositional bimodal logic consisting of two S4 modalities £ and [a], together with the interaction axiom scheme a £ϕ → £ aϕ. In the intended semantics, the plain £ is given the McKinsey-Tarski interpretation as the interior operator of a topology, while the labelled [a] is given the standard Kripke semantics using a reflexive and transitive binary relation a. The interaction axiom expresses the property that the Ra relation is lower semi-continuous with respect to the topology. The (...)
     
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  28.  16
    Spatial reasoning with RCC 8 and connectedness constraints in Euclidean spaces.Roman Kontchakov, Ian Pratt-Hartmann & Michael Zakharyaschev - 2014 - Artificial Intelligence 217 (C):43-75.
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  29.  21
    (1 other version)Topology, connectedness, and modal logic.Roman Kontchakov, Ian Pratt-Hartmann, Frank Wolter & Michael Zakharyaschev - 1998 - In Marcus Kracht, Maarten de Rijke, Heinrich Wansing & Michael Zakharyaschev (eds.), Advances in Modal Logic. CSLI Publications. pp. 151-176.
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  30. (1 other version)Dynamic Description Logics.Frank Wolter & Michael Zakharyaschev - 1998 - In Marcus Kracht, Maarten de Rijke, Heinrich Wansing & Michael Zakharyaschev (eds.), Advances in Modal Logic. CSLI Publications. pp. 449-463.
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  31.  67
    The greatest extension of s4 into which intuitionistic logic is embeddable.Michael Zakharyaschev - 1997 - Studia Logica 59 (3):345-358.
    This paper gives a characterization of those quasi-normal extensions of the modal system S4 into which intuitionistic propositional logic Int is embeddable by the Gödel translation. It is shown that, as in the normal case, the set of quasi-normal modal companions of Int contains the greatest logic, M*, for which, however, the analog of the Blok-Esakia theorem does not hold. M* is proved to be decidable and Halldén-complete; it has the disjunction property but does not have the finite model property.
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  32. A tableau decision algorithm for modalized ALC with constant domains.Carsten Lutz, Holger Sturm, Frank Wolter & Michael Zakharyaschev - 2002 - Studia Logica 72 (2):199-232.
    The aim of this paper is to construct a tableau decision algorithm for the modal description logic K ALC with constant domains. More precisely, we present a tableau procedure that is capable of deciding, given an ALC-formula with extra modal operators (which are applied only to concepts and TBox axioms, but not to roles), whether is satisfiable in a model with constant domains and arbitrary accessibility relations. Tableau-based algorithms have been shown to be practical even for logics of rather high (...)
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  33.  25
    First-order rewritability of ontology-mediated queries in linear temporal logic.Alessandro Artale, Roman Kontchakov, Alisa Kovtunova, Vladislav Ryzhikov, Frank Wolter & Michael Zakharyaschev - 2021 - Artificial Intelligence 299 (C):103536.
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  34.  49
    Philadelphia, PA, USA May 18–20, 2011.Anjolina G. de Oliveira, Ruy de Queiroz, Rajeev Alur, Max Kanovich, John Mitchell, Vladimir Voevodsky, Yoad Winter & Michael Zakharyaschev - 2012 - Bulletin of Symbolic Logic 18 (1).
  35. Mathematical Problems from Applied Logic I.Dov M. Gabbay, Sergei S. Goncharov & Michael Zakharyaschev - 2007 - Studia Logica 87 (2-3):363-367.
     
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  36.  14
    A tetrachotomy of ontology-mediated queries with a covering axiom.Olga Gerasimova, Stanislav Kikot, Agi Kurucz, Vladimir Podolskii & Michael Zakharyaschev - 2022 - Artificial Intelligence 309 (C):103738.
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  37. Fragments of rst-order temporal logics.I. Hodkinson, F. Wolter & M. Zakharyaschev - forthcoming - Annals of Pure and Applied Logic.
     
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  38. Advances in Modal Logic, Vol. 1.Marcus Kracht, Maarten de Rijke, Heinrich Wansing & Michael Zakharyaschev - 2000 - Studia Logica 65 (3):440-442.
  39. Advances in Modal Logic.Marcus Kracht, Maarten de Rijke, Heinrich Wansing & Michael Zakharyaschev (eds.) - 1998 - CSLI Publications.
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  40.  14
    Advances in Modal Logic, Volume 1: Papers From the First Aiml Conference, Held at the Free University of Berlin, 1996.Marcus Kracht, Maarten de Rijke, Heinrich Wansing & Michael Zakharyaschev (eds.) - 1998 - Cambridge, England: Cambridge University Press.
    Modal logic originated in philosophy as the logic of necessity and possibility. Now it has reached a high level of mathematical sophistication and has many applications in a variety of disciplines, including theoretical and applied computer science, artificial intelligence, the foundations of mathematics, and natural language syntax and semantics. This volume represents the proceedings of the first international workshop on Advances in Modal Logic, held in Berlin, Germany, October 8-10, 1996. It offers an up-to-date perspective on the field, with contributions (...)
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  41.  16
    (1 other version)Islands of Tractability for Relational Constraints: Towards Dichotomy Results for the Description of Logic EL.Agi Kurucz, Frank Wolter & Michael Zakharyaschev - 1998 - In Marcus Kracht, Maarten de Rijke, Heinrich Wansing & Michael Zakharyaschev (eds.), Advances in Modal Logic. CSLI Publications. pp. 271-291.
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  42.  40
    A New Solution to a Problem of Hosoi and Ono.Michael Zakharyaschev - 1994 - Notre Dame Journal of Formal Logic 35 (3):450-457.
    This paper gives a new, purely semantic proof of the following theorem: if an intermediate propositional logic L has the disjunction property then a disjunction free formula is provable in L iff it is provable in intuitionistic logic. The main idea of the proof is to use the well-known semantic criterion of the disjunction property for "simulating" finite binary trees (which characterize the disjunction free fragment of intuitionistic logic) by general frames.
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  43.  14
    Preface.A. Kurucz, M. Zakharyaschev & F. Wolter - 2002 - Studia Logica 72 (2):145-146.
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  44.  8
    (1 other version)From topology to metric: modal logic and quantification in metric spaces.M. Sheremet, D. Tishkovsky, F. Wolter & M. Zakharyaschev - 1998 - In Marcus Kracht, Maarten de Rijke, Heinrich Wansing & Michael Zakharyaschev (eds.), Advances in Modal Logic. CSLI Publications. pp. 429-448.
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  45.  8
    Advances in Modal Logic, Volume 3: Papers From the Third Aiml Conference, Held at the University of Leipzig, October 2000.Frank Wolter, H. Wansing, Maarten de Rijke & Michael Zakharyaschev - 2002 - Singapore: World Scientific.
  46.  19
    Advances in Modal Logic, Volume 2: Papers From the Second Aiml Conference, Held at the University of Uppsala, Sweden, October 1998.Michael Zakharyaschev, Krister Segerberg, Maarten de Rijke & Heinrich Wansing (eds.) - 2001 - Stanford, CA, USA: Center for the Study of Language and Inf.
    Modal Logic, originally conceived as the logic of necessity and possibility, has developed into a powerful mathematical and computational discipline. It is the main source of formal languages aimed at analyzing complex notions such as common knowledge and formal provability. Modal and modal-like languages also provide us with families of restricted description languages for relational and topological structures; they are being used in many disciplines, ranging from artificial intelligence, computer science and mathematics via natural language syntax and semantics to philosophy. (...)
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  47. Maarten Marx and Yde Venema, Multi-Dimensional Modal Logic.M. Zakharyaschev - 2000 - Journal of Logic Language and Information 9 (1):128-131.
  48.  30
    Multi-dimensional modal logic, Maarten Marx and Yde Venema.Michael Zakharyaschev - 2000 - Journal of Logic, Language and Information 9 (1):128-131.
  49.  12
    (1 other version)G. E. Hughes and M. J. Cresswell. A new introduction to modal logic. Routledge, London and New York1996, x + 421 pp. [REVIEW]Michael Zakharyaschev - 1997 - Journal of Symbolic Logic 62 (4):1483-1484.