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Dimiter Vakarelov [29]D. Vakarelov [5]Dimitar Vakarelov [1]
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  1.  36
    Elementary Canonical Formulae: Extending Sahlqvist’s Theorem.Valentin Goranko & Dimiter Vakarelov - 2006 - Annals of Pure and Applied Logic 141 (1):180-217.
    We generalize and extend the class of Sahlqvist formulae in arbitrary polyadic modal languages, to the class of so called inductive formulae. To introduce them we use a representation of modal polyadic languages in a combinatorial style and thus, in particular, develop what we believe to be a better syntactic approach to elementary canonical formulae altogether. By generalizing the method of minimal valuations à la Sahlqvist–van Benthem and the topological approach of Sambin and Vaccaro we prove that all inductive formulae (...)
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  2.  23
    Notes on N-Lattices and Constructive Logic with Strong Negation.D. Vakarelov - 1977 - Studia Logica 36 (1-2):109-125.
  3. A Modal Approach to Dynamic Ontology: Modal Mereotopology.Dimiter Vakarelov - 2008 - Logic and Logical Philosophy 17 (1-2):163-183.
    In this paper we show how modal logic can be applied in the axiomatizations of some dynamic ontologies. As an example we consider the case of mereotopology, which is an extension of mereology with some relations of topological nature like contact relation. We show that in the modal extension of mereotopology we may define some new mereological and mereotopological relations with dynamic nature like stable part-of and stable contact. In some sense such “stable” relations can be considered as approximations of (...)
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  4.  64
    Sahlqvist Formulas Unleashed in Polyadic Modal Languages.Valentin Goranko & Dimiter Vakarelov - 2002 - In Frank Wolter, Heinrich Wansing, Maarten de Rijke & Michael Zakharyaschev (eds.), Advances in Modal Logic, Volume 3. World Scientific. pp. 221-240.
    We propose a generalization of Sahlqvist formulae to polyadic modal languages by representing modal polyadic languages in a combinatorial style and thus, in particular, developing what we believe to be the right approach to Sahlqvist formulae at all. The class of polyadic Sahlqvist formulae PSF defined here expands essentially the so far known one. We prove first-order definability and canonicity for the class PSF.
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  5.  20
    Maarten Marx and Yde Venema. Multi-Dimensional Modal Logic. Applied Logic Series, Vol. 4. Kluwer Academic Publishers, Dordrecht, Boston, and London, 1997, Xiii + 239 Pp. [REVIEW]Dimiter Vakarelov - 2000 - Bulletin of Symbolic Logic 6 (4):490-495.
  6.  48
    Non-Classical Negation in the Works of Helena Rasiowa and Their Impact on the Theory of Negation.Dimiter Vakarelov - 2006 - Studia Logica 84 (1):105-127.
    The paper is devoted to the contributions of Helena Rasiowa to the theory of non-classical negation. The main results of Rasiowa in this area concerns–constructive logic with strong (Nelson) negation.
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  7.  39
    Nelson's Negation on the Base of Weaker Versions of Intuitionistic Negation.Dimiter Vakarelov - 2005 - Studia Logica 80 (2-3):393-430.
    Constructive logic with Nelson negation is an extension of the intuitionistic logic with a special type of negation expressing some features of constructive falsity and refutation by counterexample. In this paper we generalize this logic weakening maximally the underlying intuitionistic negation. The resulting system, called subminimal logic with Nelson negation, is studied by means of a kind of algebras called generalized N-lattices. We show that generalized N-lattices admit representation formalizing the intuitive idea of refutation by means of counterexamples giving in (...)
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  8.  19
    A Proximity Approach to Some Region-Based Theories of Space.Dimiter Vakarelov, Georgi Dimov, Ivo Düntsch & Brandon Bennett - 2002 - Journal of Applied Non-Classical Logics 12 (3-4):527-559.
    This paper is a continuation of [VAK 01]. The notion of local connection algebra, based on the primitive notions of connection and boundedness, is introduced. It is slightly different but equivalent to Roeper's notion of region-based topology [ROE 97]. The similarity between the local proximity spaces of Leader [LEA 67] and local connection algebras is emphasized. Machinery, analogous to that introduced by Efremovi?c [EFR 51],[EFR 52], Smirnov [SMI 52] and Leader [LEA 67] for proximity and local proximity spaces, is developed. (...)
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  9.  32
    A System of Relational Syllogistic Incorporating Full Boolean Reasoning.Nikolay Ivanov & Dimiter Vakarelov - 2012 - Journal of Logic, Language and Information 21 (4):433-459.
    We present a system of relational syllogistic, based on classical propositional logic, having primitives of the following form: $$\begin{array}{ll}\mathbf{Some}\, a \,{\rm are} \,R-{\rm related}\, {\rm to}\, \mathbf{some} \,b;\\ \mathbf{Some}\, a \,{\rm are}\,R-{\rm related}\, {\rm to}\, \mathbf{all}\, b;\\ \mathbf{All}\, a\, {\rm are}\,R-{\rm related}\, {\rm to}\, \mathbf{some}\, b;\\ \mathbf{All}\, a\, {\rm are}\,R-{\rm related}\, {\rm to}\, \mathbf{all} \,b.\end{array}$$ Such primitives formalize sentences from natural language like ‘ All students read some textbooks’. Here a, b denote arbitrary sets (of objects), and R denotes an (...)
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  10.  32
    Algorithmic Correspondence and Completeness in Modal Logic. V. Recursive Extensions of SQEMA.Willem Conradie, Valentin Goranko & Dimitar Vakarelov - 2010 - Journal of Applied Logic 8 (4):319-333.
    The previously introduced algorithm \sqema\ computes first-order frame equivalents for modal formulae and also proves their canonicity. Here we extend \sqema\ with an additional rule based on a recursive version of Ackermann's lemma, which enables the algorithm to compute local frame equivalents of modal formulae in the extension of first-order logic with monadic least fixed-points \mffo. This computation operates by transforming input formulae into locally frame equivalent ones in the pure fragment of the hybrid mu-calculus. In particular, we prove that (...)
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  11.  11
    Intuitive Semantics for Some Three-Valued Logics Connected with Information, Contrariety and Subcontrariety.Dimiter Vakarelov - 1989 - Studia Logica 48 (4):565 - 575.
    Four known three-valued logics are formulated axiomatically and several completeness theorems with respect to nonstandard intuitive semantics, connected with the notions of information, contrariety and subcontrariety is given.
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  12.  51
    Hyperboolean Algebras and Hyperboolean Modal Logic.Valentin Goranko & Dimiter Vakarelov - 1999 - Journal of Applied Non-Classical Logics 9 (2):345-368.
    Hyperboolean algebras are Boolean algebras with operators, constructed as algebras of complexes (or, power structures) of Boolean algebras. They provide an algebraic semantics for a modal logic (called here a {\em hyperboolean modal logic}) with a Kripke semantics accordingly based on frames in which the worlds are elements of Boolean algebras and the relations correspond to the Boolean operations. We introduce the hyperboolean modal logic, give a complete axiomatization of it, and show that it lacks the finite model property. The (...)
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  13.  20
    Elementary Canonical Formulae: A Survey on Syntactic, Algorithmic, and Modeltheoretic Aspects.W. Conradie, V. Goranko & D. Vakarelov - 2005 - In Renate Schmidt, Ian Pratt-Hartmann, Mark Reynolds & Heinrich Wansing (eds.), Advances in Modal Logic, Volume 5. Kings College London Publ.. pp. 17-51.
    In terms of validity in Kripke frames, a modal formula expresses a universal monadic second-order condition. Those modal formulae which are equivalent to first-order conditions are called elementary. Modal formulae which have a certain persistence property which implies their validity in all canonical frames of modal logics axiomatized with them, and therefore their completeness, are called canonical. This is a survey of a recent and ongoing study of the class of elementary and canonical modal formulae. We summarize main ideas and (...)
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  14.  10
    Dynamic Logics of the Region-Based Theory of Discrete Spaces.Philippe Balbiani, Tinko Tinchev & Dimiter Vakarelov - 2007 - Journal of Applied Non-Classical Logics 17 (1):39-61.
    The aim of this paper is to give new kinds of modal logics suitable for reasoning about regions in discrete spaces. We call them dynamic logics of the region-based theory of discrete spaces. These modal logics are linguistic restrictions of propositional dynamic logic with the global diamond E. Their formulas are equivalent to Boolean combinations of modal formulas like E where A and B are Boolean terms and α is a relational term. Examining what we can say about dynamic models (...)
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  15.  30
    Modal Logic and Universal Algebra I: Modal Axiomatizations of Structures.Valentin Goranko & Dimiter Vakarelov - 2000 - In Michael Zakharyaschev, Krister Segerberg, Maarten de Rijke & Heinrich Wansing (eds.), Advances in Modal Logic, Volume 2. CSLI Publications. pp. 265-292.
    We study the general problem of axiomatizing structures in the framework of modal logic and present a uniform method for complete axiomatization of the modal logics determined by a large family of classes of structures of any signature.
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  16.  20
    PDL with Intersection of Programs: A Complete Axiomatization.Philippe Balbiani & Dimiter Vakarelov - 2003 - Journal of Applied Non-Classical Logics 13 (3-4):231-276.
    One of the important extensions of PDL is PDL with intersection of programs. We devote this paper to its complete axiomatization.
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  17.  21
    A Mereotopology Based on Sequent Algebras.Dimiter Vakarelov - 2017 - Journal of Applied Non-Classical Logics 27 (3-4):342-364.
    Mereotopology is an extension of mereology with some relations of topological nature like contact. An algebraic counterpart of mereotopology is the notion of contact algebra which is a Boolean algebra whose elements are considered to denote spatial regions, extended with a binary relation of contact between regions. Although the language of contact algebra is quite expressive to define many useful mereological relations and mereotopological relations, there are, however, some interesting mereotopological relations which are not definable in it. Such are, for (...)
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  18.  33
    Intuitionistic Modal Logics Incompatible with the Law of the Excluded Middle.Dimiter Vakarelov - 1981 - Studia Logica 40 (2):103 - 111.
    In this paper, intuitionistic modal logics which do not admit the law of the excluded middle are studied. The main result is that there exista a continuum of such logics.
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  19.  4
    Dynamic Extensions of Arrow Logic.Philippe Balbiani & Dimiter Vakarelov - 2004 - Annals of Pure and Applied Logic 127 (1-3):1-15.
    This paper is devoted to the complete axiomatization of dynamic extensions of arrow logic based on a restriction of propositional dynamic logic with intersection. Our deductive systems contain an unorthodox inference rule: the inference rule of intersection. The proof of the completeness of our deductive systems uses the technique of the canonical model.
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  20.  20
    Lattices Related to Post Algebras and Their Applications to Some Logical Systems.D. Vakarelov - 1977 - Studia Logica 36 (1-2):89-107.
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  21.  8
    Many-Dimensional Arrow Logics.Dimiter Vakarelov - 1996 - Journal of Applied Non-Classical Logics 6 (4):303-345.
    ABSTRACT The notion of n-dimensional arrow structure is introduced, which for n = 2 coincides with the notion of directed multi-graph. In part I of the paper several first-order and modal languages connected with arrow structures are studied and their expressive power is compared. Part II is devoted to the axiomatization of some arrow logics. At the end some further perspectives of ?arrow approach? are discussed.
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  22.  15
    A Duality Between Pawlak's Knowledge Representation Systems and Bi-Consequence Systems.Dimiter Vakarelov - 1995 - Studia Logica 55 (1):205 - 228.
    A duality between Pawlak's knowledge representation systems and certain information systems of logical type, called bi-consequence systems is established. As an application a first-order characterization of some informational relations is given and a completeness theorem for the corresponding modal logic INF is proved. It is shown that INF possesses finite model property and hence is decidable.
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  23.  9
    Rough Polyadic Modal Logics.D. Vakarelov - 1991 - Journal of Applied Non-Classical Logics 1 (1):9-35.
  24.  25
    Review: Maarten Marx, Yde Venema, Multi-Dimensional Modal Logic. [REVIEW]Dimiter Vakarelov - 2000 - Bulletin of Symbolic Logic 6 (4):490-495.
  25.  26
    Dynamic Modalities.Dimiter Vakarelov - 2012 - Studia Logica 100 (1-2):385-397.
    A new modal logic containing four dynamic modalities with the following informal reading is introduced: $${\square^\forall}$$ – always necessary , $${\square^\exists}$$ – sometimes necessary , and their duals – $${\diamondsuit^\forall}$$ – always possibly , and $${\diamondsuit^\exists}$$ – sometimes possibly . We present a complete axiomatization with respect to the intended formal semantics and prove decidability via fmp.
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  26.  21
    An Application of Rieger-Nishimura Formulas to the Intuitionistic Modal Logics.Dimiter Vakarelov - 1985 - Studia Logica 44 (1):79 - 85.
    The main results of the paper are the following: For each monadic prepositional formula which is classically true but not intuitionistically so, there is a continuum of intuitionistic monotone modal logics L such that L+ is inconsistent.There exists a consistent intuitionistic monotone modal logic L such that for any formula of the kind mentioned above the logic L+ is inconsistent.
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  27.  3
    Modal Logics of Arrows.Dimiter Vakarelov - 1997 - In M. de Rijke (ed.), Advances in Intensional Logic. Kluwer Academic Publishers. pp. 137--171.