22 found
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  1.  8
    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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  2.  10
    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.  26
    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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  4.  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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  5.  8
    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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  6.  33
    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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  7.  10
    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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  8.  3
    On the Complexity of Modal Axiomatisations Over Many-Dimensional Structures.Agi Kurucz - 2010 - In Lev Beklemishev, Valentin Goranko & Valentin Shehtman (eds.), Advances in Modal Logic, Volume 8. CSLI Publications. pp. 256-270.
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  9.  17
    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.  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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  11.  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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  12.  4
    On Axiomatisting Products of Kripke Frames, Part II.Agi Kurucz - 2008 - In Carlos Areces & Robert Goldblatt (eds.), Advances in Modal Logic, Volume 7. CSLI Publications. pp. 219-230.
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  13.  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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  14. A Tetrachotomy of Ontology-Mediated Queries with a Covering Axiom.Olga Gerasimova, Stanislav Kikot, Agi Kurucz, Vladimir Podolskii & Michael Zakharyaschev - 2022 - Artificial Intelligence 309:103738.
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  15.  3
    Advances in Modal Logic, Volume 10: Papers From the Tenth Aiml Conference, Held in Groningen, the Netherlands, August 2014.Rajeev Goré, Barteld Kooi & Agi Kurucz (eds.) - 2014 - London, England: CSLI Publications.
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  16.  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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  17.  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.
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  18.  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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  19.  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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  20.  10
    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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  21.  1
    On Modal Products with Th Logic of 'Elsewhere'.Christopher Hampson & Agi Kurucz - 2012 - In Thomas Bolander, Torben Braüner, Silvio Ghilardi & Lawrence Moss (eds.), Advances in Modal Logic, Volume 9. CSLI Publications. pp. 339-347.
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  22.  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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