66 found
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  1.  2
    Philip Kremer & Grigori Mints (2005). Dynamic Topological Logic. Annals of Pure and Applied Logic 131 (1-3):133-158.
    Dynamic topological logic provides a context for studying the confluence of the topological semantics for S4, topological dynamics, and temporal logic. The topological semantics for S4 is based on topological spaces rather than Kripke frames. In this semantics, □ is interpreted as topological interior. Thus S4 can be understood as the logic of topological spaces, and □ can be understood as a topological modality. Topological dynamics studies the asymptotic properties of continuous maps on topological spaces. Let a dynamic topological system (...)
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  2. Grigori Mints (1996). Strong Termination for the Epsilon Substitution Method. Journal of Symbolic Logic 61 (4):1193-1205.
    Ackermann proved termination for a special order of reductions in Hilbert's epsilon substitution method for the first order arithmetic. We establish termination for arbitrary order of reductions.
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  3.  29
    Grigori Mints (1997). Indexed Systems of Sequents and Cut-Elimination. Journal of Philosophical Logic 26 (6):671-696.
    Cut reductions are defined for a Kripke-style formulation of modal logic in terms of indexed systems of sequents. A detailed proof of the normalization (cutelimination) theorem is given. The proof is uniform for the propositional modal systems with all combinations of reflexivity, symmetry and transitivity for the accessibility relation. Some new transformations of derivations (compared to standard sequent formulations) are needed, and some additional properties are to be checked. The display formulations [1] of the systems considered can be presented as (...)
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  4.  7
    Grigori Mints, Sergei Tupailo & Wilfried Buchholz (1996). Epsilon Substitution Method for Elementary Analysis. Archive for Mathematical Logic 35 (2):103-130.
    We formulate epsilon substitution method for elementary analysisEA (second order arithmetic with comprehension for arithmetical formulas with predicate parameters). Two proofs of its termination are presented. One uses embedding into ramified system of level one and cutelimination for this system. The second proof uses non-effective continuity argument.
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  5.  6
    Grigori Mints & Ting Zhang (2005). Propositional Logic of Continuous Transformations in Cantor Space. Archive for Mathematical Logic 44 (6):783-799.
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  6.  1
    Grigori Mints (1992). A Short Introduction to Modal Logic. Center for the Study of Language and Inf.
    A Short Introduction to Modal Logic presents both semantic and syntactic features of the subject and illustrates them by detailed analyses of the three best-known modal systems S5, S4 and T. The book concentrates on the logical aspects of ...
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  7.  4
    Sam Buss & Grigori Mints (1999). The Complexity of the Disjunction and Existential Properties in Intuitionistic Logic. Annals of Pure and Applied Logic 99 (1-3):93-104.
    This paper considers the computational complexity of the disjunction and existential properties of intuitionistic logic. We prove that the disjunction property holds feasibly for intuitionistic propositional logic; i.e., from a proof of A v B, a proof either of A or of B can be found in polynomial time. For intuitionistic predicate logic, we prove superexponential lower bounds for the disjunction property, namely, there is a superexponential lower bound on the time required, given a proof of A v B, to (...)
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  8.  92
    Grigori Mints (2006). Notes on Constructive Negation. Synthese 148 (3):701 - 717.
    We put together several observations on constructive negation. First, Russell anticipated intuitionistic logic by clearly distinguishing propositional principles implying the law of the excluded middle from remaining valid principles. He stated what was later called Peirce’s law. This is important in connection with the method used later by Heyting for developing his axiomatization of intuitionistic logic. Second, a work by Dragalin and his students provides easy embeddings of classical arithmetic and analysis into intuitionistic negationless systems. In the last section, we (...)
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  9.  2
    Makoto Tatsuta & Grigori Mints (2005). A Simple Proof of Second-Order Strong Normalization with Permutative Conversions. Annals of Pure and Applied Logic 136 (1-2):134-155.
    A simple and complete proof of strong normalization for first- and second-order intuitionistic natural deduction including disjunction, first-order existence and permutative conversions is given. The paper follows the Tait–Girard approach via computability predicates and saturated sets. Strong normalization is first established for a set of conversions of a new kind, then deduced for the standard conversions. Difficulties arising for disjunction are resolved using a new logic where disjunction is restricted to atomic formulas.
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  10. Grigori Mints (2002). A Short Introduction to Intuitionistic Logic. Bulletin of Symbolic Logic 8 (4):520-521.
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  11. Philip Kremer, Grigori Mints & V. Rybakov (1997). Axiomatizing the Next-Interior Fragment of Dynamic Topological Logic. Bulletin of Symbolic Logic 3:376-377.
     
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  12.  31
    Grigori Mints (1991). Proof Theory in the USSR 1925-1969. Journal of Symbolic Logic 56 (2):385-424.
    We present a survey of proof theory in the USSR beginning with the paper by Kolmogorov [1925] and ending (mostly) in 1969; the last two sections deal with work done by A. A. Markov and N. A. Shanin in the early seventies, providing a kind of effective interpretation of negative arithmetic formulas. The material is arranged in chronological order and subdivided according to topics of investigation. The exposition is more detailed when the work is little known in the West or (...)
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  13.  1
    S. Ghilardi & G. Mints (2014). The Logic of Transitive and Dense Frames: From the Step-Frame Analysis to Full Cut-Elimination. Logic Journal of the IGPL 22 (4):585-596.
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  14.  10
    Grigori Mints, Vladimir Orevkov & Tanel Tammet (1996). Transfer of Sequent Calculus Strategies to Resolution for S4. In H. Wansing (ed.), Proof Theory of Modal Logic. Kluwer 2--17.
  15.  4
    Grigori Mints & Ting Zhang (2005). A Proof of Topological Completeness for S4 In. Annals of Pure and Applied Logic 133 (1-3):231-245.
    The completeness of the modal logic S4 for all topological spaces as well as for the real line , the n-dimensional Euclidean space and the segment etc. was proved by McKinsey and Tarski in 1944. Several simplified proofs contain gaps. A new proof presented here combines the ideas published later by G. Mints and M. Aiello, J. van Benthem, G. Bezhanishvili with a further simplification. The proof strategy is to embed a finite rooted Kripke structure for S4 into a subspace (...)
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  16.  8
    G. Mints (1998). Linear Lambda-Terms and Natural Deduction. Studia Logica 60 (1):209-231.
  17.  4
    G. E. Mints & Darko Sarenac (2003). Completeness of Indexed Ε-Calculus. Archive for Mathematical Logic 42 (7):617-625.
    Epsilon terms indexed by contexts were used by K. von Heusinger to represent definite and indefinite noun phrases as well as some other constructs of natural language. We provide a language and a complete first order system allowing to formalize basic aspects of this representation. The main axiom says that for any finite collection S 1,…,S k of distinct definable sets and elements a 1,…,a k of these sets there exists a choice function assigning a i to S i for (...)
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  18.  13
    S. Artemov, B. Kushner, G. Mints, E. Nogina & A. Troelstra (1999). In Memoriam: Albert G. Dragalin, 1941-1998. Bulletin of Symbolic Logic 5 (3):389-391.
  19.  10
    Grigori Mints (1996). Thoralf Skolem and the Epsilon Substitution Method for Predicate Logic. Nordic Journal of Philosophical Logic 1 (2):133-146.
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  20.  11
    G. Mints (1998). Normal Deduction in the Intuitionistic Linear Logic. Archive for Mathematical Logic 37 (5-6):415-425.
    We describe a natural deduction system NDIL for the second order intuitionistic linear logic which admits normalization and has a subformula property. NDIL is an extension of the system for !-free multiplicative linear logic constructed by the author and elaborated by A. Babaev. Main new feature here is the treatment of the modality !. It uses a device inspired by D. Prawitz' treatment of S4 combined with a construction $<\Gamma>$ introduced by the author to avoid cut-like constructions used in $\otimes$ (...)
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  21.  3
    G. Mints (2001). Interpolation Theorems for Intuitionistic Predicate Logic. Annals of Pure and Applied Logic 113 (1-3):225-242.
    Craig interpolation theorem implies that the derivability of X,X′ Y′ implies existence of an interpolant I in the common language of X and X′ Y′ such that both X I and I,X′ Y′ are derivable. For classical logic this extends to X,X′ Y,Y′, but for intuitionistic logic there are counterexamples. We present a version true for intuitionistic propositional logic, and more complicated version for the predicate case.
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  22.  11
    Michael Detlefsen, Erich Reck, Colin McLarty, Rohit Parikh, Larry Moss, Scott Weinstein, Gabriel Uzquiano, Grigori Mints & Richard Zach (2001). The Minneapolis Hyatt Regency, Minneapolis, Minnesota May 3–4, 2001. Bulletin of Symbolic Logic 7 (3).
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  23.  28
    Grigori Mints (2006). Cut Elimination for S4c: A Case Study. Studia Logica 82 (1):121 - 132.
    S4C is a logic of continuous transformations of a topological space. Cut elimination for it requires new kind of rules and new kinds of reductions.
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  24.  7
    Grigori Mints (2013). Epsilon Substitution for First-and Second-Order Predicate Logic. Annals of Pure and Applied Logic 164 (6):733-739.
    The epsilon substitution method was proposed by D. Hilbert as a tool for consistency proofs. A version for first order predicate logic had been described and proved to terminate in the monograph “Grundlagen der Mathematik”. As far as the author knows, there have been no attempts to extend this approach to the second order case. We discuss possible directions for and obstacles to such extensions.
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  25.  26
    Grigori Mints (1993). Resolution Calculus for the First Order Linear Logic. Journal of Logic, Language and Information 2 (1):59-83.
    This paper presents a formulation and completeness proof of the resolution-type calculi for the first order fragment of Girard's linear logic by a general method which provides the general scheme of transforming a cutfree Gentzen-type system into a resolution type system, preserving the structure of derivations. This is a direct extension of the method introduced by Maslov for classical predicate logic. Ideas of the author and Zamov are used to avoid skolomization. Completeness of strategies is first established for the Gentzen-type (...)
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  26.  25
    G. Mints (1999). Cut-Elimination for Simple Type Theory with an Axiom of Choice. Journal of Symbolic Logic 64 (2):479-485.
    We present a cut-elimination proof for simple type theory with an axiom of choice formulated in the language with an epsilon-symbol. The proof is modeled after Takahashi's proof of cut-elimination for simple type theory with extensionality. The same proof works when types are restricted, for example for second-order classical logic with an axiom of choice.
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  27. Grigori Mints & S. Tupailo (1999). Epsilon-Substitution Method for the Ramified Language and Δ 1 1 -Comprehension Rule. In ¸ Itecantini1999. Springer
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  28.  5
    Michael Detlefsen, Erich Reck, Colin McLarty, Rohit Parikh, Larry Moss, Scott Weinstein, Gabriel Uzquiano, Grigori Mints & Richard Zach (2001). 2000-2001 Spring Meeting of the Association for Symbolic Logic. Bulletin of Symbolic Logic 7 (3):413-419.
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  29.  2
    Grigori Mints (2006). Cut Elimination for S4C: A Case Study. Studia Logica 82 (1):121-132.
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  30.  7
    Grigori Mints (2010). Cut-Free Formulations for a Quantified Logic of Here and There. Annals of Pure and Applied Logic 162 (3):237-242.
    A predicate extension SQHT= of the logic of here-and-there was introduced by V. Lifschitz, D. Pearce, and A. Valverde to characterize strong equivalence of logic programs with variables and equality with respect to stable models. The semantics for this logic is determined by intuitionistic Kripke models with two worlds with constant individual domain and decidable equality. Our sequent formulation has special rules for implication and for pushing negation inside formulas. The soundness proof allows us to establish that SQHT= is a (...)
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  31. G. Mints, M. Otero, S. Ronchi Della Rocca & K. Segerberg (1997). Donostia-San Sebastián, Spain, July 9–15, 1996. Bulletin of Symbolic Logic 3 (2).
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  32.  1
    G. Mints (1993). A Normal Form for Logical Derivations Implying One for Arithmetic Derivations. Annals of Pure and Applied Logic 62 (1):65-79.
    We describe a short model-theoretic proof of an extended normal form theorem for derivations in predicate logic which implies in PRA a normal form theorem for the arithmetic derivations . Consider the Gentzen-type formulation of predicate logic with invertible rules. A derivation with proper variables is one where a variable b can occur in the premiss of an inference L but not below this premiss only in the case when L is () or () and b is its eigenvariable. Free (...)
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  33.  11
    Grigori Mints (2012). Effective Cut-Elimination for a Fragment of Modal Mu-Calculus. Studia Logica 100 (1-2):279-287.
    A non-effective cut-elimination proof for modal mu-calculus has been given by G. Jäger, M. Kretz and T. Studer. Later an effective proof has been given for a subsystem M 1 with non-iterated fixpoints and positive endsequents. Using a new device we give an effective cut-elimination proof for M 1 without restriction to positive sequents.
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  34. G. E. Mints (1989). The Completeness of Provable Realizability. Notre Dame Journal of Formal Logic 30 (3):420-441.
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  35.  2
    Sergei Artemov, Yuri Matiyasevich, Grigori Mints & Anatol Slissenko (2010). Preface. Annals of Pure and Applied Logic 162 (3):173-174.
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  36.  2
    G. E. Mints & Darko Sarenac (2003). Completeness of Indexed Ε-Calculus. Archive for Mathematical Logic 42 (7):617-625.
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  37.  4
    Grigori Mints (2008). Cut Elimination for a Simple Formulation of Epsilon Calculus. Annals of Pure and Applied Logic 152 (1):148-160.
    A simple cut elimination proof for arithmetic with the epsilon symbol is used to establish the termination of a modified epsilon substitution process. This opens a possibility of extension to much stronger systems.
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  38.  2
    John Baldwin, Lev Beklemishev, Anuj Dawar, Mirna Dzamonja, David Evans, Erich Grädel, Denis Hirschfeldt, Hannes Leitgeb, Roger Maddux & Grigori Mints (2008). Vassar College, 124 Raymond Avenue, Poughkeepsie, Ny 12604, Usa. In a Review, a Reference “Jsl Xliii 148,” for Example, Refers Either to the Publication Reviewed on Page 148 of Volume 43 of the Journal, or to the Review Itself (Which Contains Full Bibliographical Information for the Reviewed Publication). Analogously, a Reference “Bsl VII 376” Refers to the Review Beginning on Page 376 in Volume 7 of This Bulletin, Or. [REVIEW] Bulletin of Symbolic Logic 14 (1).
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  39.  3
    S. J. Maslov, G. E. Mints & V. P. Orevkov (1971). Mechanical Proof-Search and the Theory of Logical Deduction in the Ussr. Revue Internationale de Philosophie 25 (4=98):575-584.
    A survey of works on automatic theorem-proving in the ussr 1964-1970. the philosophical problems are not touched.
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  40. Anuj Dawar Beklemishev, Mirna Dzamonja, David Evans, Erich Grädel, Denis Hirschfeldt, Hannes Leitgeb, Roger Maddux, Grigori Mints, Volker Peckhaus & Sławomir Solecki (2008). Vassar College, 124 Raymond Avenue, Poughkeepsie, Ny 12604, Usa. In a Review, a Reference “Jsl Xliii 148,” for Example, Refers Either to the Publication Reviewed on Page 148 of Volume 43 of the Journal, or to the Review Itself (Which Contains Full Bibliographical Information for the Reviewed Publication). Analogously, a Reference “Bsl VII 376” Refers to the Review Beginning on Page 376 in Volume 7 of This Bulletin, Or. [REVIEW] Bulletin of Symbolic Logic 14 (4).
     
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  41. G. E. Mints (1969). Variation in the Deduction Search Tactics in Sequential Calculi. In A. O. Slisenko (ed.), Studies in Constructive Mathematics and Mathematical Logic. New York, Consultants Bureau 52--59.
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  42.  2
    G. Mints (1998). Review: Wolfram Pohlers, Pure Proof Theory. Aims, Methods and Results. [REVIEW] Journal of Symbolic Logic 63 (3):1185-1185.
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  43.  1
    Grigori Mints (2006). S4 Is Topologically Complete For : A Short Proof. Logic Journal of the IGPL 14 (1):63-71.
    Ideas of previous constructions are combined into a short proof of topological completeness of modal logic S4 first for rational numbers and after that for real numbers in the interval.
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  44.  2
    Denis Hirschfeldt, Hannes Leitgeb, Roger Maddux, Grigori Mints & Volker Peckhaus (2008). Reviewed on Page 148 of Volume 43 of the Journal, or to the Review Itself (Which Contains Full Bibliographical Information for the Reviewed Publication). Analogously, a Reference" Bsl VII 376" Refers to the Review Beginning on Page 376 in Volume 7 of This Bulletin, or to the Publication There Reviewed." Jsl Lv 347" Refers to One of the Reviews or One of the Publications Reviewed or Listed on Page 347 of Volume 55 of the Journal, with Reliance On. [REVIEW] Bulletin of Symbolic Logic 14 (3).
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  45.  2
    Grigori Mints (1994). Review: Marianne Winslett, Updating Logical Databases. [REVIEW] Journal of Symbolic Logic 59 (3):1110-1114.
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  46.  1
    G. Mints, M. Otero, S. Ronchi Della Rocca & K. Segerberg (1997). 1996 European Summer Meeting of the Association for Symbolic Logic. Bulletin of Symbolic Logic 3 (2):242-277.
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  47.  1
    G. E. Mints & V. P. Orevkov (1969). On Imbedding Operators. In A. O. Slisenko (ed.), Studies in Constructive Mathematics and Mathematical Logic. New York, Consultants Bureau 64--66.
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  48. M. Borisavljevit, S. Buss, G. Mints, T. Coquand, A. A. Ivanov & D. Macpherson (1999). Kearnes, KA, Kiss, EW and Valeriote, MA, A Geometric. Annals of Pure and Applied Logic 99:261.
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  49. Denis Hirschfeldt, Hannes Leitgeb, Roger Maddux, Grigori Mints & Volker Peckhaus (2008). The Association for Symbolic Logic Publishes Analytical Reviews of Selected Books and Articles in the Field of Symbolic Logic. The Reviews Were Published in The Journal of Symbolic Logic From the Founding of the Journal in 1936 Until the End of 1999. The Association Moved the Reviews to This Bulletin, Beginning in 2000. The Reviews Section is Edited by Alasdair Urquhart (Managing Editor), Steve Awodey. [REVIEW] Bulletin of Symbolic Logic 14 (2).
     
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  50. Per Martin-löf & G. E. Mints (1990). Colog-88 International Conference on Computer Logic, Tallinn, Ussr, December 12-16, 1988 : Proceedings.
     
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