36 found
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  1.  66
    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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  2.  52
    Modal Languages and Bounded Fragments of Predicate Logic.Andréka Hajnal, Németi István & Benthem Johan van - 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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  3.  16
    Algebraization of Quantifier Logics, an Introductory Overview.István Németi - 1991 - Studia Logica 50 (3-4):485 - 569.
    This paper is an introduction: in particular, to algebras of relations of various ranks, and in general, to the part of algebraic logic algebraizing quantifier logics. The paper has a survey character, too. The most frequently used algebras like cylindric-, relation-, polyadic-, and quasi-polyadic algebras are carefully introduced and intuitively explained for the nonspecialist. Their variants, connections with logic, abstract model theory, and further algebraic logics are also reviewed. Efforts were made to make the review part relatively comprehensive. In some (...)
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  4.  45
    Twin Paradox and the Logical Foundation of Relativity Theory.Judit X. Madarász, István Németi & Gergely Székely - 2006 - Foundations of Physics 36 (5):681-714.
    We study the foundation of space-time theory in the framework of first-order logic (FOL). Since the foundation of mathematics has been successfully carried through (via set theory) in FOL, it is not entirely impossible to do the same for space-time theory (or relativity). First we recall a simple and streamlined FOL-axiomatization Specrel of special relativity from the literature. Specrel is complete with respect to questions about inertial motion. Then we ask ourselves whether we can prove the usual relativistic properties of (...)
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  5.  53
    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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  6.  22
    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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  7. Non-Turing Computations Via Malament-Hogarth Space-Times.Gábor Etesi & István Németi - 2002 - International Journal of Theoretical Physics 41:341--70.
  8. Relativistic Computers and the Turing Barrier.István Németi & Gyula Dávid - 2006 - Journal of Applied Mathematics and Computation 178:118--42.
  9. 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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  10.  23
    On Neat Reducts of Algebras of Logic.Tarek Sayed Ahmed & Istvan Németi - 2001 - Studia Logica 68 (2):229-262.
    SC , CA , QA and QEA stand for the classes of Pinter's substitution algebras, Tarski's cylindric algebras, Halmos' quasipolyadic algebras, and quasipolyadic equality algebras of dimension , respectively. Generalizing a result of Németi on cylindric algebras, we show that for K {SC, CA, QA, QEA} and ordinals , the class Nr K of -dimensional neat reducts of -dimensional K algebras, though closed under taking homomorphic images and products, is not closed under forming subalgebras (i.e. is not a variety) if (...)
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  11.  12
    On the Equational Theory of Representable Polyadic Equality Algebras.István Németi & Gábor Sági - 2000 - Journal of Symbolic Logic 65 (3):1143-1167.
    Among others we will prove that the equational theory of ω dimensional representable polyadic equality algebras (RPEA ω 's) is not schema axiomatizable. This result is in interesting contrast with the Daigneault-Monk representation theorem, which states that the class of representable polyadic algebras is finite schema-axiomatizable (and hence the equational theory of this class is finite schema-axiomatizable, as well). We will also show that the complexity of the equational theory of RPEA ω is also extremely high in the recursion theoretic (...)
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  12.  3
    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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  13.  14
    On Generalizing the Logic-Approach to Space-Time Towards General Relativity: First Steps.Judit X. Madarász, István Németi & Csaba Toke - 2004 - In Vincent F. Hendricks (ed.), First-Order Logic Revisited. Logos. pp. 225--268.
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  14.  12
    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.
  15.  22
    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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  16.  5
    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.
  17.  30
    Not All Representable Cylindric Algebras Are Neat Reducts.Hajnal Andréka & István Németi - 1979 - Bulletin of the Section of Logic 8 (3):145-147.
  18.  17
    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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  19.  67
    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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  20. 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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  21.  14
    Problems with the Category Theoretic Notions of Ultraproducts.Hien Huy Bui & István Németi - 1981 - Bulletin of the Section of Logic 10 (3):122-126.
    In this paper we try to initiate a search for an explicite and direct denition of ultraproducts in categories which would share some of the attractive properties of products, coproducts, limits, and related category theoretic notions. Consider products as a motivating example.
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  22.  17
    On Universal Algebraic Logic and Cylindric Algebras.Hajnal Andréka & István Németi - 1978 - Bulletin of the Section of Logic 7 (4):152-158.
  23.  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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  24. The Class of Neat-Reducts of Cylindric Algebras is Not a Variety but is Closed with Respect to ${\Rm HP}$.István Németi - 1983 - Notre Dame Journal of Formal Logic 24 (3):399-409.
  25.  6
    Taming Logic.Maarten Marx, Szabolcs Mikul & István Németi - 1995 - Journal of Logic, Language and Information 4 (3):207-226.
    In this paper, we introduce a general technology, calledtaming, for finding well-behaved versions of well-investigated logics. Further, we state completeness, decidability, definability and interpolation results for a multimodal logic, calledarrow logic, with additional operators such as thedifference operator, andgraded modalities. Finally, we give a completeness proof for a strong version of arrow logic.
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  26.  32
    First-Order Logic Foundation of Relativity Theories.Judit X. Madarasz, Istvan Nemeti & Gergely Szekely - unknown
    Motivation and perspective for an exciting new research direction interconnecting logic, spacetime theory, relativity--including such revolutionary areas as black hole physics, relativistic computers, new cosmology--are presented in this paper. We would like to invite the logician reader to take part in this grand enterprise of the new century. Besides general perspective and motivation, we present initial results in this direction.
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  27. Review: Alfred Tarski, Steven Givant, A Formalization of Set Theory Without Variables. [REVIEW]Istvan Nemeti - 1990 - Journal of Symbolic Logic 55 (1):350-352.
     
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  28.  6
    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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  29.  3
    Perfect Extensions and Derived Algebras.Hajnal Andréka, Steven Givant & István Németi - 1995 - Journal of Symbolic Logic 60 (3):775-796.
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  30. 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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  31. 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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  32. 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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  33. 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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  34. On the Equational Theory of Representable Polyadic Equality Algebras.Istvan Nemeti & Gabor Sagi - 2000 - Journal of Symbolic Logic 65 (3):1143-1167.
    Among others we will prove that the equational theory of $\omega$ dimensional representable polyadic equality algebras is not schema axiomatizable. This result is in interesting contrast with the Daigneault-Monk representation theorem, which states that the class of representable polyadic algebras is finite schema-axiomatizable. We will also show that the complexity of the equational theory of RPEA$_\omega$ is also extremely high in the recursion theoretic sense. Finally, comparing the present negative results with the positive results of Ildiko Sain and Viktor Gyuris (...)
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  35. The Class of Neat-Reducts of Cylindric Algebras is Not a Variety but is Closed W.R.T. HP.Istvan Nemeti - 1983 - Notre Dame Journal of Formal Logic 24:399-409.
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  36. Tarski Alfred and Givant Steven. A Formalization of Set Theory Without Variables. American Mathematical Society Colloquium Publications, Vol. 41. American Mathematical Society, Providence 1987, Xxi + 318 Pp. [REVIEW]István Németi - 1990 - Journal of Symbolic Logic 55 (1):350-352.