28 found
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  1.  64
    Modal Languages and Bounded Fragments of Predicate Logic.Hajnal Andréka, István Németi & Johan van Benthem - 1998 - Journal of Philosophical Logic 27 (3):217 - 274.
    What precisely are fragments of classical first-order logic showing “modal” behaviour? Perhaps the most influential answer is that of Gabbay 1981, which identifies them with so-called “finite-variable fragments”, using only some fixed finite number of variables (free or bound). This view-point has been endorsed by many authors (cf. van Benthem 1991). We will investigate these fragments, and find that, illuminating and interesting though they are, they lack the required nice behaviour in our sense. (Several new negative results support this claim.) (...)
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  2.  71
    A Logic Road From Special Relativity to General Relativity.Hajnal Andréka, Judit X. Madarász, István Németi & Gergely Székely - 2012 - Synthese 186 (3):633 - 649.
    We present a streamlined axiom system of special relativity in first-order logic. From this axiom system we "derive" an axiom system of general relativity in two natural steps. We will also see how the axioms of special relativity transform into those of general relativity. This way we hope to make general relativity more accessible for the non-specialist.
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  3.  25
    Mutual Definability Does Not Imply Definitional Equivalence, a Simple Example.Hajnal Andréka, Judit X. Madarász & István Németi - 2005 - Mathematical Logic Quarterly 51 (6):591-597.
    We give two theories, Th1 and Th2, which are explicitly definable over each other , but are not definitionally equivalent. The languages of the two theories are disjoint.
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  4.  18
    Complexity of Equations Valid in Algebras of Relations Part I: Strong Non-Finitizability.Hajnal Andréka - 1997 - Annals of Pure and Applied Logic 89 (2):149-209.
    We study algebras whose elements are relations, and the operations are natural “manipulations” of relations. This area goes back to 140 years ago to works of De Morgan, Peirce, Schröder . Well known examples of algebras of relations are the varieties RCAn of cylindric algebras of n-ary relations, RPEAn of polyadic equality algebras of n-ary relations, and RRA of binary relations with composition. We prove that any axiomatization, say E, of RCAn has to be very complex in the following sense: (...)
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  5.  7
    A Representation Theorem for Measurable Relation Algebras.Steven Givant & Hajnal Andréka - 2018 - Annals of Pure and Applied Logic 169 (11):1117-1189.
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  6.  57
    Axiomatizing Relativistic Dynamics Without Conservation Postulates.Hajnal Andréka, Judit Madarász X., István Németi & Gergely Székely - 2008 - Studia Logica 89 (2):163 - 186.
    A part of relativistic dynamics is axiomatized by simple and purely geometrical axioms formulated within first-order logic. A geometrical proof of the formula connecting relativistic and rest masses of bodies is presented, leading up to a geometric explanation of Einstein’s famous E = mc 2. The connection of our geometrical axioms and the usual axioms on the conservation of mass, momentum and four-momentum is also investigated.
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  7. Expressibility of Properties of Relations.Hajnal Andréka, Ivo Düntsch & István Németi - 1995 - Journal of Symbolic Logic 60 (3):970-991.
    We investigate in an algebraic setting the question of which logical languages can express the properties integral, permutational, and rigid for algebras of relations.
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  8.  20
    Lambek Calculus and its Relational Semantics: Completeness and Incompleteness. [REVIEW]Hajnal Andréka & Szabolcs Mikulás - 1994 - Journal of Logic, Language and Information 3 (1):1-37.
    The problem of whether Lambek Calculus is complete with respect to (w.r.t.) relational semantics, has been raised several times, cf. van Benthem (1989a) and van Benthem (1991). In this paper, we show that the answer is in the affirmative. More precisely, we will prove that that version of the Lambek Calculus which does not use the empty sequence is strongly complete w.r.t. those relational Kripke-models where the set of possible worlds,W, is a transitive binary relation, while that version of the (...)
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  9.  11
    Notions of Density That Imply Representability in Algebraic Logic.Hajnal Andréka, Steven Givant, Szabolcs Mikulás, István Németi & András Simon - 1998 - Annals of Pure and Applied Logic 91 (2-3):93-190.
    Henkin and Tarski proved that an atomic cylindric algebra in which every atom is a rectangle must be representable . This theorem and its analogues for quasi-polyadic algebras with and without equality are formulated in Henkin, Monk and Tarski [13]. We introduce a natural and more general notion of rectangular density that can be applied to arbitrary cylindric and quasi-polyadic algebras, not just atomic ones. We then show that every rectangularly dense cylindric algebra is representable, and we extend this result (...)
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  10.  6
    On Tarski’s Axiomatic Foundations of the Calculus of Relations.Hajnal Andréka, Steven Givant, Peter Jipsen & István Németi - 2017 - Journal of Symbolic Logic 82 (3):966-994.
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  11.  6
    Complexity of Equations Valid in Algebras of Relations Part II: Finite Axiomatizations.Hajnal Andréka - 1997 - Annals of Pure and Applied Logic 89 (2-3):211-229.
    We study algebras whose elements are relations, and the operations are natural “manipulations” of relations. This area goes back to 140 years ago to works of De Morgan, Peirce, Schröder . Well known examples of algebras of relations are the varieties RCAn of cylindric algebras of n-ary relations, RPEAn of polyadic equality algebras of n-ary relations, and RRA of binary relations with composition. We prove that any axiomatization, say E, of RCAn has to be very complex in the following sense: (...)
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  12.  15
    General Algebraic Logic: A Perspective on “What is Logic”.Istvan Nemeti & Hajnal Andreka - 1994 - In Dov M. Gabbay (ed.), What is a Logical System? Oxford University Press.
  13.  6
    Back and Forth Between Modal Logic and Classical Logic.Hajnal Andreka, Johan van Benthem & Istvan Nemeti - 1995 - Logic Journal of the IGPL 3 (5):685-720.
  14.  76
    A Logic Road From Special to General Relativity.Hajnal Andréka, Judit X. Madarász, István Németi & Gergely Székely - unknown
    We present a streamlined axiom system of special relativity in firs-order logic. From this axiom system we ``derive'' an axiom system of general relativity in two natural steps. We will also see how the axioms of special relativity transform into those of general relativity. This way we hope to make general relativity more accessible for the non-specialist.
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  15.  19
    The Lattice of Varieties of Representable Relation Algebras.Hajnal Andréka, Steven Givant & István Németi - 1994 - Journal of Symbolic Logic 59 (2):631-661.
    We shall show that certain natural and interesting intervals in the lattice of varieties of representable relation algebras embed the lattice of all subsets of the natural numbers, and therefore must have a very complicated lattice-theoretic structure.
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  16. A Twist in the Geometry of Rotating Black Holes: Seeking the Cause of Acausality.Christian Wüthrich, Hajnal Andréka & István Németi - manuscript
    We investigate Kerr–Newman black holes in which a rotating charged ring-shaped singularity induces a region which contains closed timelike curves (CTCs). Contrary to popular belief, it turns out that the time orientation of the CTC is oppo- site to the direction in which the singularity or the ergosphere rotates. In this sense, CTCs “counter-rotate” against the rotating black hole. We have similar results for all spacetimes sufficiently familiar to us in which rotation induces CTCs. This motivates our conjecture that perhaps (...)
     
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  17.  32
    Not All Representable Cylindric Algebras Are Neat Reducts.Hajnal Andréka & István Németi - 1979 - Bulletin of the Section of Logic 8 (3):145-147.
  18.  18
    On Universal Algebraic Logic and Cylindric Algebras.Hajnal Andréka & István Németi - 1978 - Bulletin of the Section of Logic 7 (4):152-158.
  19.  5
    Representations for Small Relation Algebras.Hajnal Andréka & Roger D. Maddux - 1994 - Notre Dame Journal of Formal Logic 35 (4):550-562.
    There are eighteen isomorphism types of finite relation algebras with eight or fewer elements, and all of them are representable. We determine all the cardinalities of sets on which these algebras have representations.
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  20.  16
    Relativised Quantification: Some Canonical Varieties of Sequence-Set Algebras.Hajnal Andréka, Robert Goldblatt & István Németi - 1998 - Journal of Symbolic Logic 63 (1):163-184.
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  21.  13
    Binary Relations and Permutation Groups.Hajnal Andréka & Ivo Düntsch - 1995 - Mathematical Logic Quarterly 41 (2):197-216.
    We discuss some new properties of the natural Galois connection among set relation algebras, permutation groups, and first order logic. In particular, we exhibit infinitely many permutational relation algebras without a Galois closed representation, and we also show that every relation algebra on a set with at most six elements is Galois closed and essentially unique. Thus, we obtain the surprising result that on such sets, logic with three variables is as powerful in expression as full first order logic.
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  22.  14
    Omitting Types for Finite Variable Fragments and Complete Representations of Algebras.Hajnal Andréka, István Németi & Tarek Sayed Ahmed - 2008 - Journal of Symbolic Logic 73 (1):65-89.
    We give a novel application of algebraic logic to first order logic. A new, flexible construction is presented for representable but not completely representable atomic relation and cylindric algebras of dimension n (for finite n > 2) with the additional property that they are one-generated and the set of all n by n atomic matrices forms a cylindric basis. We use this construction to show that the classical Henkin-Orey omitting types theorem fails for the finite variable fragments of first order (...)
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  23.  17
    Groups and Algebras of Binary Relations.Steven Givant & Hajnal Andreka - 2002 - Bulletin of Symbolic Logic 8 (1):38-64.
    In 1941, Tarski published an abstract, finitely axiomatized version of the theory of binary relations, called the theory of relation algebras, He asked whether every model of his abstract theory could be represented as a concrete algebra of binary relations. He and Jonsson obtained some initial, positive results for special classes of abstract relation algebras. But Lyndon showed, in 1950, that in general the answer to Tarski's question is negative. Monk proved later that the answer remains negative even if one (...)
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  24.  4
    Perfect Extensions and Derived Algebras.Hajnal Andréka, Steven Givant & István Németi - 1995 - Journal of Symbolic Logic 60 (3):775-796.
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  25.  1
    Relativised Quantification: Some Canonical Varieties of Sequence-Set Algebras.Hajnal Andreka, Robert Goldblatt & Istvan Nemeti - 1998 - Journal of Symbolic Logic 63 (1):163-184.
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  26. Completeness of Floyd Logic.Hajnal Andreka & Istvan Nemeti - 1978 - Bulletin of the Section of Logic 7 (3):115-119.
    This is an abstract of our paper \A characterisation of Floyd-provable programs" submitted to Theoretical Computer Science. ! denotes the set of natural numbers. Y =d fyi : i 2 !g is the set of variable symbols. L denotes the set of classical rst order formulas of type t possibly with free variables , where t is the similarity type of arithmetic, i.e. it consists of \+; ; 0; 1" with arities \2; 2; 0; 0".
     
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  27. Program Verification Within and Without Logic.Hajnal Andreka, Istvan Nemeti & Ildiko Sain - 1979 - Bulletin of the Section of Logic 8 (3):124-128.
    Theorem 1 states a negative result about the classical semantics j= ! of program schemes. Theorem 2 investigates the reason for this. We conclude that Theorem 2 justies the Henkin-type semantics j= for which the opposite of the present Theorem 1 was proved in [1]{[3] and also in a dierent form in part III of [5]. The strongest positive result on j= is Corollary 6 in [3].
     
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  28. Quasi Equational Logic Of Partial Algebras.Hajnal Andreka, Peter Burmeister & Istvan Nemeti - 1980 - Bulletin of the Section of Logic 9 (4):193-197.
     
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