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Á. Kurucz [7]Agi Kurucz [7]Ágnes Kurucz [4]Á Kurucz [1]
  1. R. Hirsch, I. Hodkinson & A. Kurucz (forthcoming). On Modal Logics Between â â à and Ë¢ Ë¢ Ë. Journal of Symbolic Logic.
     
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  2. AgneS Kurucz & Arrow Logic (forthcoming). Infinite Counting. Studia Logica.
     
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  3. Agi Kurucz (2013). A Note on Axiomatisations of Two-Dimensional Modal Logics. In Kamal Lodaya (ed.), Logic and its Applications. Springer. 27--33.
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  4. Agi Kurucz & Sérgio Marcelino (2012). Non-Finitely Axiomatisable Two-Dimensional Modal Logics. 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. Agi Kurucz (2009). Weakly Associative Relation Algebras with Projections. Mlq 55 (2):138-153.
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  6. Miklós Erdélyi-Szabó, László Kálmán & Agi Kurucz (2008). Towards a Natural Language Semantics Without Functors and Operands. 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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  7. David Gabelaia, Agi Kurucz, Frank Wolter & Michael Zakharyaschev (2006). Non-Primitive Recursive Decidability of Products of Modal Logics with Expanding Domains. Annals of Pure and Applied Logic 142 (1):245-268.
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  8. D. M. Gabbay, A. Kurucz, F. Wolter, M. Zakharyaschev & Mark Reynolds (2005). REVIEWS-Many-Dimensional Modal Logics: Theory and Applications. Bulletin of Symbolic Logic 11 (1):77-78.
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  9. David Gabelaia, Agi Kurucz, Frank Wolter & Michael Zakharyaschev (2005). Products of 'Transitive' Modal Logics. 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. Roman Kontchakov, Agi Kurucz & Michael Zakharyaschev (2005). Undecidability of First-Order Intuitionistic and Modal Logics with Two Variables. 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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  11. R. Hirsch, I. Hodkinson & A. Kurucz (2002). On Modal Logics Between K × K × K and S5 × S5 × S. Journal of Symbolic Logic 67 (1):221-234.
  12. R. Hirsch, I. Hodkinson & A. Kurucz (2002). On Modal Logics Between K × K × K and $S5 \Times S5 \Times S5$. 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. R. Hirsch, I. Hodkinson & A. Kurucz (2002). On Modal Logics Between {$\Roman K\Times\Roman K\Times \Roman K$} and {${\Rm S}5\Times{\Rm S}5\Times{\Rm S}5$}. Journal of Symbolic Logic 67 (1):221-234.
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  14. A. Kurucz, M. Zakharyaschev & F. Wolter (2002). Preface. Studia Logica 72 (2):145-146.
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  15. Ágnes Kurucz (2000). Arrow Logic and Infinite Counting. 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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  16. Ágnes Kurucz (2000). On Axiomatising Products of Kripke Frames. 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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  17. A. Jánossy, Á Kurucz & Á. E. Eiben (1996). Combining Algebraizable Logics. 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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  18. ágnes Kurucz, István Németi, Ildikó Sain & András Simon (1995). Decidable and Undecidable Logics with a Binary Modality. 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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  19. H. Andréka, Á Kurucz & I. Németi (1994). Connections Between Axioms of Set Theory and Basic Theorems of Universal Algebra. 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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