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Agi Kurucz [24]A. Kurucz [9]Ágnes Kurucz [7]Á Kurucz [3]
  1. 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.  9
    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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  3.  7
    Non-Finitely Axiomatisable Modal Product Logics with Infinite Canonical Axiomatisations.Christopher Hampson, Stanislav Kikot, Agi Kurucz & Sérgio Marcelino - 2020 - Annals of Pure and Applied Logic 171 (5):102786.
    Our concern is the axiomatisation problem for modal and algebraic logics that correspond to various fragments of two-variable first-order logic with counting quantifiers. In particular, we consider modal products with Diff, the propositional unimodal logic of the difference operator. We show that the two-dimensional product logic $Diff \times Diff$ is non-finitely axiomatisable, but can be axiomatised by infinitely many Sahlqvist axioms. We also show that its ‘square’ version (the modal counterpart of the substitution and equality free fragment of two-variable first-order (...)
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  4. On Modal Logics Between K × K × K and S5 × S5 × S.R. Hirsch, I. Hodkinson & A. Kurucz - 2002 - Journal of Symbolic Logic 67 (1):221-234.
    We prove that everyn-modal logic betweenKnandS5nis undecidable, whenever n ≥ 3. We also show that each of these logics is non-finitely axiomatizable, lacks the product finite model property, and there is no algorithm deciding whether a finite frame validates the logic. These results answer several questions of Gabbay and Shehtman. The proofs combine the modal logic technique of Yankov–Fine frame formulas with algebraic logic results of Halmos, Johnson and Monk, and give a reduction of the representation problem of finite relation (...)
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  5.  25
    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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  6.  39
    Non-Finitely Axiomatisable Two-Dimensional Modal Logics.Agi Kurucz & Sérgio Marcelino - 2012 - Journal of Symbolic Logic 77 (3):970-986.
    We show the first examples of recursively enumerable (even decidable) two-dimensional products of finitely axiomatisable modal logics that are not finitely axiomatisable. In particular, we show that any axiomatisation of some bimodal logics that are determined by classes of product frames with linearly ordered first components must be infinite in two senses: It should contain infinitely many propositional variables, and formulas of arbitrarily large modal nesting-depth.
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  7.  37
    On Axiomatising Products of Kripke Frames.Ágnes Kurucz - 2000 - Journal of Symbolic Logic 65 (2):923-945.
    It is shown that the many-dimensional modal logic K n , determined by products of n-many Kripke frames, is not finitely axiomatisable in the n-modal language, for any $n > 2$ . On the other hand, K n is determined by a class of frames satisfying a single first-order sentence.
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  8.  7
    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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  9.  16
    Weakly Associative Relation Algebras with Projections.Agi Kurucz - 2009 - Mathematical Logic Quarterly 55 (2):138-153.
    Built on the foundations laid by Peirce, Schröder, and others in the 19th century, the modern development of relation algebras started with the work of Tarski and his colleagues [21, 22]. They showed that relation algebras can capture strong first-order theories like ZFC, and so their equational theory is undecidable. The less expressive class WA of weakly associative relation algebras was introduced by Maddux [7]. Németi [16] showed that WA's have a decidable universal theory. There has been extensive research on (...)
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  10.  5
    On Modal Logics Between {$\Roman K\Times\Roman K\Times \Roman K$} and {${\Rm S}5\Times{\Rm S}5\Times{\Rm S}5$}.R. Hirsch, I. Hodkinson & A. Kurucz - 2002 - Journal of Symbolic Logic 67 (1):221-234.
    We prove that everyn-modal logic betweenKnandS5nis undecidable, whenever n ≥ 3. We also show that each of these logics is non-finitely axiomatizable, lacks the product finite model property, and there is no algorithm deciding whether a finite frame validates the logic. These results answer several questions of Gabbay and Shehtman. The proofs combine the modal logic technique of Yankov–Fine frame formulas with algebraic logic results of Halmos, Johnson and Monk, and give a reduction of the representation problem of finite relation (...)
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  11.  10
    On Modal Logics Between K × K × K and S5 × S5 × S5.Robin Hirsch, I. Hodkinson & A. Kurucz - 2002 - Journal of Symbolic Logic 67 (1):221-234.
    We prove that everyn-modal logic betweenKnandS5nis undecidable, whenever n ≥ 3. We also show that each of these logics is non-finitely axiomatizable, lacks the product finite model property, and there is no algorithm deciding whether a finite frame validates the logic. These results answer several questions of Gabbay and Shehtman. The proofs combine the modal logic technique of Yankov–Fine frame formulas with algebraic logic results of Halmos, Johnson and Monk, and give a reduction of the representation problem of finite relation (...)
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  12. On Modal Logics Between K × K × K and $S5 \Times S5 \Times S5$.R. Hirsch, I. Hodkinson & A. Kurucz - 2002 - Journal of Symbolic Logic 67 (1):221 - 234.
    We prove that every n-modal logic between K n and S5 n is undecidable, whenever n ≥ 3. We also show that each of these logics is non- finitely axiomatizable, lacks the product finite model property, and there is no algorithm deciding whether a finite frame validates the logic. These results answer several questions of Gabbay and Shehtman. The proofs combine the modal logic technique of Yankov-Fine frame formulas with algebraic logic results of Halmos, Johnson and Monk, and give a (...)
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  13.  9
    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 can be decidable. In particular, if.
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  14.  63
    Combining Algebraizable Logics.A. Jánossy, Á Kurucz & Á. E. Eiben - 1996 - Notre Dame Journal of Formal Logic 37 (2):366-380.
    The general methodology of "algebraizing" logics is used here for combining different logics. The combination of logics is represented as taking the colimit of the constituent logics in the category of algebraizable logics. The cocompleteness of this category as well as its isomorphism to the corresponding category of certain first-order theories are proved.
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  15.  32
    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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  16.  47
    Decidable and Undecidable Logics with a Binary Modality.ágnes Kurucz, István Németi, Ildikó Sain & András Simon - 1995 - Journal of Logic, Language and Information 4 (3):191-206.
    We give an overview of decidability results for modal logics having a binary modality. We put an emphasis on the demonstration of proof-techniques, and hope that this will also help in finding the borderlines between decidable and undecidable fragments of usual first-order logic.
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  17.  1
    A Note on Relativised Products of Modal Logics.Agi Kurucz & Michael Zakharyaschev - 2003 - In Marcus Kracht, Maarten de Rijke, Heinrich Wansing & Michael Zakharyaschev (eds.), Advances in Modal Logic. CSLI Publications. pp. 221-242.
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  18.  1
    Finite Frames for K4.3 X S5 Are Decidable.Agi Kurucz & Sérgio Marcelino - 2012 - In Marcus Kracht, Maarten de Rijke, Heinrich Wansing & Michael Zakharyaschev (eds.), Advances in Modal Logic. CSLI Publications. pp. 411-436.
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  19.  5
    Islands of Tractability for Relational Constraints: Towards Dichotomy Results for the Description of Logic EL.Agi Kurucz, Frank Wolter & Michael Zakharyaschev - 2010 - In Lev Beklemishev, Valentin Goranko & Valentin Shehtman (eds.), Advances in Modal Logic, Volume 8. CSLI Publications. pp. 271-291.
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  20.  4
    Combining Algebraizable Logics.Á E. Eiben, A. Jánossy & Á Kurucz - 1996 - Notre Dame Journal of Formal Logic 37 (2):366-380.
    The general methodology of "algebraizing" logics is used here for combining different logics. The combination of logics is represented as taking the colimit of the constituent logics in the category of algebraizable logics. The cocompleteness of this category as well as its isomorphism to the corresponding category of certain first-order theories are proved.
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  21.  1
    Islands of Tractability for Relational Constraints: Towards Dichotomy Results for the Description of Logic EL.Agi Kurucz, Frank Wolter & Michael Zakharyaschev - 2010 - In Marcus Kracht, Maarten de Rijke, Heinrich Wansing & Michael Zakharyaschev (eds.), Advances in Modal Logic. CSLI Publications. pp. 271-291.
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  22.  9
    REVIEWS-Many-Dimensional Modal Logics: Theory and Applications.D. M. Gabbay, A. Kurucz, F. Wolter, M. Zakharyaschev & Mark Reynolds - 2005 - Bulletin of Symbolic Logic 11 (1):77-78.
  23.  38
    Arrow Logic and Infinite Counting.Ágnes Kurucz - 2000 - Studia Logica 65 (2):199-222.
    We consider arrow logics (i.e., propositional multi-modal logics having three -- a dyadic, a monadic, and a constant -- modal operators) augmented with various kinds of infinite counting modalities, such as 'much more', 'of good quantity', 'many times'. It is shown that the addition of these modal operators to weakly associative arrow logic results in finitely axiomatizable and decidable logics, which fail to have the finite base property.
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  24.  5
    Undecidable Varieties of Semilattice—Ordered Semigroups, of Boolean Algebras with Operators, and Logics Extending Lambek Calculus.A. Kurucz, I. Nemeti, I. Sain & A. Simon - 1993 - Logic Journal of the IGPL 1 (1):91-98.
    We prove that the equational theory of a semigroups becomes undecidable if we add a semilattice structure with a ‘touch of symmetric difference’. As a corollary we obtain that the variety of all Boolean algebras with an associative binary operator has a ‘hereditarily’ undecidable equational theory. Our results have implications in logic, e.g. they imply undecidability of modal logics extending the Lambek Calculus and undecidability of Arrow Logics with an associative arrow modality.
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  25.  25
    Connections Between Axioms of Set Theory and Basic Theorems of Universal Algebra.H. Andréka, Á Kurucz & I. Németi - 1994 - Journal of Symbolic Logic 59 (3):912-923.
    One of the basic theorems in universal algebra is Birkhoff's variety theorem: the smallest equationally axiomatizable class containing a class K of algebras coincides with the class obtained by taking homomorphic images of subalgebras of direct products of elements of K. G. Gratzer asked whether the variety theorem is equivalent to the Axiom of Choice. In 1980, two of the present authors proved that Birkhoff's theorem can already be derived in ZF. Surprisingly, the Axiom of Foundation plays a crucial role (...)
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  26.  34
    Towards a Natural Language Semantics Without Functors and Operands.Miklós Erdélyi-Szabó, László Kálmán & Agi Kurucz - 2008 - Journal of Logic, Language and Information 17 (1):1-17.
    The paper sets out to offer an alternative to the function/argument approach to the most essential aspects of natural language meanings. That is, we question the assumption that semantic completeness (of, e.g., propositions) or incompleteness (of, e.g., predicates) exactly replicate the corresponding grammatical concepts (of, e.g., sentences and verbs, respectively). We argue that even if one gives up this assumption, it is still possible to keep the compositionality of the semantic interpretation of simple predicate/argument structures. In our opinion, compositionality presupposes (...)
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  27. Advances in Modal Logic, Volume 10.Rajeev Goré, Barteld Kooi & Agi Kurucz (eds.) - 2014 - CSLI Publications.
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  28.  27
    The Decision Problem of Modal Product Logics with a Diagonal, and Faulty Counter Machines.C. Hampson, S. Kikot & A. Kurucz - 2016 - Studia Logica 104 (3):455-486.
    In the propositional modal treatment of two-variable first-order logic equality is modelled by a ‘diagonal’ constant, interpreted in square products of universal frames as the identity relation. Here we study the decision problem of products of two arbitrary modal logics equipped with such a diagonal. As the presence or absence of equality in two-variable first-order logic does not influence the complexity of its satisfiability problem, one might expect that adding a diagonal to product logics in general is similarly harmless. We (...)
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  29.  22
    A Note on Axiomatisations of Two-Dimensional Modal Logics.Agi Kurucz - 2013 - In Kamal Lodaya (ed.), Logic and its Applications. Springer. pp. 27--33.
  30.  3
    A Note on Relativised Products of Modal Logics.Agi Kurucz & Michael Zakharyaschev - 2003 - In Philippe Balbiani, Nobu-Yuki Suzuki, Frank Wolter & Michael Zakharyaschev (eds.), Advances in Modal Logic, Volume 4. CSLI Publications. pp. 221-242.
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  31.  9
    Bimodal Logics with a “Weakly Connected” Component Without the Finite Model Property.Agi Kurucz - 2017 - Notre Dame Journal of Formal Logic 58 (2):287-299.
    There are two known general results on the finite model property of commutators [L0,L1]. If L is finitely axiomatizable by modal formulas having universal Horn first-order correspondents, then both [L,K] and [L,S5] are determined by classes of frames that admit filtration, and so they have the fmp. On the negative side, if both L0 and L1 are determined by transitive frames and have frames of arbitrarily large depth, then [L0,L1] does not have the fmp. In this paper we show that (...)
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  32.  4
    Finite Frames for K4.3 X S5 Are Decidable.Agi Kurucz & Sérgio Marcelino - 2012 - In Thomas Bolander, Torben Braüner, Silvio Ghilardi & Lawrence Moss (eds.), Advances in Modal Logic, Volume 9. CSLI Publications. pp. 411-436.
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  33. Infinite Counting.AgneS Kurucz & Arrow Logic - forthcoming - Studia Logica.
     
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