Results for 'Takayuki Arai'

188 found
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  1.  4
    Some People Are “More Lexical” Than Others.Mako Ishida, Arthur G. Samuel & Takayuki Arai - 2016 - Cognition 151:68-75.
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  2.  4
    Perceptual Restoration of Temporally Distorted Speech in L1 Vs. L2: Local Time Reversal and Modulation Filtering.Mako Ishida, Takayuki Arai & Makio Kashino - 2018 - Frontiers in Psychology 9.
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  3.  5
    Proof Theory for Theories of Ordinals—I: Recursively Mahlo Ordinals.Toshiyasu Arai - 2003 - Annals of Pure and Applied Logic 122 (1-3):1-85.
    This paper deals with a proof theory for a theory T22 of recursively Mahlo ordinals in the form of Π2-reflecting on Π2-reflecting ordinals using a subsystem Od of the system O of ordinal diagrams in Arai 353). This paper is the first published one in which a proof-theoretic analysis à la Gentzen–Takeuti of recursively large ordinals is expounded.
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  4.  6
    Proof Theory for Theories of Ordinals II: Π3-Reflection.Toshiyasu Arai - 2004 - Annals of Pure and Applied Logic 129 (1-3):39-92.
    This paper deals with a proof theory for a theory T3 of Π3-reflecting ordinals using the system O of ordinal diagrams in Arai 1375). This is a sequel to the previous one 1) in which a theory for recursively Mahlo ordinals is analyzed proof-theoretically.
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  5.  49
    Gerhard Jäger and Robert F. Stärk. A Proof-Theoretic Framework for Logic Programming. Handbook of Proof Theory, Edited by Samuel R. Buss, Studies in Logic and the Foundations of Mathematics, Vol. 137, Elsevier, Amsterdam Etc. 1998, Pp. 639–682. [REVIEW]Toshiyasu Arai - 2000 - Bulletin of Symbolic Logic 6 (4):475-476.
  6.  46
    Matt Fairtlough and Stanley S. Wainer. Hierarchies of Provably Recursive Functions. Handbook of Proof Theory, Edited by Samuel R. Buss, Studies in Logic and the Foundations of Mathematics, Vol. 137, Elsevier, Amsterdam Etc. 1998, Pp. 149–207. [REVIEW]Toshiyasu Arai - 2000 - Bulletin of Symbolic Logic 6 (4):466-467.
  7.  32
    Robert L. Constable. Types in Logic, Mathematics and Programming. Handbook of Proof Theory, Edited by Samuel R. Buss, Studies in Logic and the Foundations of Mathematics, Vol. 137, Elsevier, Amsterdam Etc. 1998, Pp. 683–786. [REVIEW]Toshiyasu Arai - 2000 - Bulletin of Symbolic Logic 6 (4):476-477.
  8.  32
    Wilfried Buchholz. Notation Systems for Infinitary Derivations. Archive for Mathematical Logic, Vol. 30 No. 5–6 , Pp. 277–296. - Wilfried Buchholz. Explaining Gentzen's Consistency Proof Within Infinitary Proof Theory. Computational Logic and Proof Theory, 5th Kurt Gödel Colloquium, KGC '97, Vienna, Austria, August 25–29, 1997, Proceedings, Edited by Georg Gottlob, Alexander Leitsch, and Daniele Mundici, Lecture Notes in Computer Science, Vol. 1289, Springer, Berlin, Heidelberg, New York, Etc., 1997, Pp. 4–17. - Sergei Tupailo. Finitary Reductions for Local Predicativity, I: Recursively Regular Ordinals. Logic Colloquium '98, Proceedings of the Annual European Summer Meeting of the Association for Symbolic Logic, Held in Prague, Czech Republic, August 9–15, 1998, Edited by Samuel R. Buss, Petr Háajek, and Pavel Pudlák, Lecture Notes in Logic, No. 13, Association for Symbolic Logic, Urbana, and A K Peters, Natick, Mass., Etc., 2000, Pp. 465–499. [REVIEW]Toshiyasu Arai - 2002 - Bulletin of Symbolic Logic 8 (3):437-439.
  9.  28
    A. S. Troelstra. Realizability. Handbook of Proof Theory, Edited by Samuel R. Buss, Studies in Logic and the Foundations of Mathematics, Vol. 137, Elsevier, Amsterdam Etc. 1998, Pp. 407–473. [REVIEW]Toshiyasu Arai - 2000 - Bulletin of Symbolic Logic 6 (4):470-471.
  10.  27
    Giorgi Japaridze and Dick de Jongh. The Logic of Provability. Handbook of Proof Theory, Edited by Samuel R. Buss, Studies in Logic and the Foundations of Mathematics, Vol. 137, Elsevier, Amsterdam Etc. 1998, Pp. 475–546. [REVIEW]Toshiyasu Arai - 2000 - Bulletin of Symbolic Logic 6 (4):472-473.
  11.  27
    Sam Buss. Preface. Handbook of Proof Theory, Edited by Samuel R. Buss, Studies in Logic and the Foundations of Mathematics, Vol. 137, Elsevier, Amsterdam Etc. 1998, P. V. [REVIEW]Toshiyasu Arai - 2000 - Bulletin of Symbolic Logic 6 (4):463-464.
  12.  24
    Wolfram Pohlers. Subsystems of Set Theory and Second-Order Number Theory. Handbook of Proof Theory, Edited by Samuel R. Buss, Studies in Logic and the Foundations of Mathematics, Vol. 137, Elsevier, Amsterdam Etc. 1998, Pp. 209–335. [REVIEW]Toshiyasu Arai - 2000 - Bulletin of Symbolic Logic 6 (4):467-469.
  13.  24
    Jeremy Avigad and Solomon Feferman. Gödel's Functional Interpretation. Handbook of Proof Theory, Edited by Samuel R. Buss, Studies in Logic and the Foundations of Mathematics, Vol. 137, Elsevier, Amsterdam Etc. 1998, Pp. 337–405. [REVIEW]Toshiyasu Arai - 2000 - Bulletin of Symbolic Logic 6 (4):469-470.
  14.  23
    Pavel Pudlák. The Lengths of Proofs. Handbook of Proof Theory, Edited by Samuel R. Buss, Studies in Logic and the Foundations of Mathematics, Vol. 137, Elsevier, Amsterdam Etc. 1998, Pp. 547–637. [REVIEW]Toshiyasu Arai - 2000 - Bulletin of Symbolic Logic 6 (4):473-475.
  15.  6
    Epsilon Substitution Method for ID1.Toshiyasu Arai - 2003 - Annals of Pure and Applied Logic 121 (2-3):163-208.
    Hilbert proposed the epsilon substitution method as a basis for consistency proofs. Hilbert's Ansatz for finding a solving substitution for any given finite set of transfinite axioms is, starting with the null substitution S0, to correct false values step by step and thereby generate the process S0,S1,… . The problem is to show that the approximating process terminates. After Gentzen's innovation, Ackermann 162) succeeded to prove termination of the process for first order arithmetic. Inspired by G. Mints as an Ariadne's (...)
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  16.  21
    Samuel R. Buss. An Introduction to Proof Theory. Handbook of Proof Theory, Edited by Samuel R. Buss, Studies in Logic and the Foundations of Mathematics, Vol. 137, Elsevier, Amsterdam Etc. 1998, P. V., Pp. 1–78. [REVIEW]Toshiyasu Arai - 2000 - Bulletin of Symbolic Logic 6 (4):464-465.
  17.  21
    Jeremy Avigad. Update Procedures and the 1-Consistency of Arithmetic. Mathematical Logic Quarterly, Vol. 48 , Pp. 3–13.Toshiyasu Arai - 2003 - Bulletin of Symbolic Logic 9 (1):45-47.
  18.  19
    Samuel R. Buss. First-Order Proof Theory of Arithmetic. Handbook of Proof Theory, Edited by Samuel R. Buss, Studies in Logic and the Foundations of Mathematics, Vol. 137, Elsevier, Amsterdam Etc. 1998, Pp. 79–147. [REVIEW]Toshiyasu Arai - 2000 - Bulletin of Symbolic Logic 6 (4):465-466.
  19.  7
    Epsilon Substitution Method for Theories of Jump Hierarchies.Toshiyasu Arai - 2002 - Archive for Mathematical Logic 41 (2):123-153.
    We formulate epsilon substitution method for theories (H)α0 of absolute jump hierarchies, and give two termination proofs of the H-process: The first proof is an adaption of Mints M, Mints-Tupailo-Buchholz MTB, i.e., based on a cut-elimination of a specially devised infinitary calculus. The second one is an adaption of Ackermann Ack. Each termination proof is based on transfinite induction up to an ordinal θ(α0+ ω)0, which is best possible.
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  20.  11
    Derivatives of Normal Functions and $$\Omega $$ Ω -Models.Toshiyasu Arai - 2018 - Archive for Mathematical Logic 57 (5-6):649-664.
    In this note the well-ordering principle for the derivative \ of normal functions \ on ordinals is shown to be equivalent to the existence of arbitrarily large countable coded \-models of the well-ordering principle for the function \.
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  21.  20
    Proof Theory of Weak Compactness.Toshiyasu Arai - 2013 - Journal of Mathematical Logic 13 (1):1350003.
    We show that the existence of a weakly compact cardinal over the Zermelo–Fraenkel's set theory ZF is proof-theoretically reducible to iterations of Mostowski collapsings and Mahlo operations.
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  22.  11
    Predicatively Computable Functions on Sets.Toshiyasu Arai - 2015 - Archive for Mathematical Logic 54 (3-4):471-485.
  23.  17
    Some Results on Cut-Elimination, Provable Well-Orderings, Induction and Reflection.Toshiyasu Arai - 1998 - Annals of Pure and Applied Logic 95 (1-3):93-184.
    We gather the following miscellaneous results in proof theory from the attic.1. 1. A provably well-founded elementary ordering admits an elementary order preserving map.2. 2. A simple proof of an elementary bound for cut elimination in propositional calculus and its applications to separation problem in relativized bounded arithmetic below S21.3. 3. Equivalents for Bar Induction, e.g., reflection schema for ω logic.4. 4. Direct computations in an equational calculus PRE and a decidability problem for provable inequations in PRE.5. 5. Intuitionistic fixed (...)
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  24.  18
    Wellfoundedness Proofs by Means of Non-Monotonic Inductive Definitions I: Π₂⁰-Operators.Toshiyasu Arai - 2004 - Journal of Symbolic Logic 69 (3):830-850.
    In this paper, we prove the wellfoundedness of recursive notation systems for reflecting ordinals up to Π₃-reflection by relevant inductive definitions.
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  25.  9
    A Slow Growing Analogue to Buchholz' Proof.Toshiyasu Arai - 1991 - Annals of Pure and Applied Logic 54 (2):101-120.
    In this, journal, W. Buchholz gave an elegant proof of a characterization theorem for provably total recursive functions in the theory IDv for the v-times iterated inductive definitions . He characterizes the classes of functions by Hardy functions. In this note we will show that a slow growing analogue to the theorem can be obtained by a slight modification of Buchholz' proof.
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  26.  18
    Epsilon Substitution Method for [Image] -FIX.Toshiyasu Arai - 2006 - Journal of Symbolic Logic 71 (4):1155 - 1188.
    In this paper we formulate epsilon substitution method for a theory $\Pi _{2}^{0}$-FIX for non-monotonic $\Pi _{2}^{0}$ inductive definitions. Then we give a termination proof of the H-processes based on Ackermann [1].
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  27.  10
    Learning Cooperative Policy Among Self-Driving Vehicles for Reducing Traffic Jams渋滞低減に向けた路車間・車車間協調を実現する自動運転方策の学習法.Shota Ishikawa & Sachiyo Arai - 2019 - Transactions of the Japanese Society for Artificial Intelligence 34 (1):D-I55_1-9.
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  28.  6
    On the Slowly Well Orderedness of Ɛo.Toshiyasu Arai - 2002 - Mathematical Logic Quarterly 48 (1):125-130.
    For α < ε0, Nα denotes the number of occurrences of ω in the Cantor normal form of α with the base ω. For a binary number-theoretic function f let B denote the length n of the longest descending chain of ordinals <ε0 such that for all i < n, Nαi ≤ f . Simpson [2] called ε0 as slowly well ordered when B is totally defined for f = K · . Let |n| denote the binary length of the (...)
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  29.  15
    One-Dimensional Migration of Interstitial Clusters in SUS316L and its Model Alloys at Elevated Temperatures.Y. Satoh, H. Abe, Y. Matsukawa, T. Matsunaga, S. Kano, S. Arai, Y. Yamamoto & N. Tanaka - 2015 - Philosophical Magazine 95 (14):1587-1606.
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  30.  12
    Ordinal Diagrams for Recursively Mahlo Universes.Toshiyasu Arai - 2000 - Archive for Mathematical Logic 39 (5):353-391.
    In this paper we introduce a recursive notation system $O(\mu)$ of ordinals. An element of the notation system is called an ordinal diagram following G. Takeuti [25]. The system is designed for proof theoretic study of theories of recursively Mahlo universes. We show that for each $\alpha<\Omega$ in $O(\mu)$ KPM proves that the initial segment of $O(\mu)$ determined by $\alpha$ is a well ordering. Proof theoretic study for such theories will be reported in [9].
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  31.  36
    Derivability Conditions on Rosser's Provability Predicates.Toshiyasu Arai - 1990 - Notre Dame Journal of Formal Logic 31 (4):487-497.
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  32.  12
    Intuitionistic Fixed Point Theories Over Set Theories.Toshiyasu Arai - 2015 - Archive for Mathematical Logic 54 (5-6):531-553.
  33.  13
    Quick Cut-Elimination for Strictly Positive Cuts.Toshiyasu Arai - 2011 - Annals of Pure and Applied Logic 162 (10):807-815.
    In this paper we show that the intuitionistic theory for finitely many iterations of strictly positive operators is a conservative extension of Heyting arithmetic. The proof is inspired by the quick cut-elimination due to G. Mints. This technique is also applied to fragments of Heyting arithmetic.
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  34.  3
    Epsilon Substitution Method for< I> ID< Sub> 1(< I> Π_< Sub> 1< Sup> 0∨< I> Σ< Sub> 1< Sup> 0). [REVIEW]Toshiyasu Arai - 2003 - Annals of Pure and Applied Logic 121 (2):163-208.
  35.  27
    Ordinal Diagrams for Π3-Reflection.Toshiyasu Arai - 2000 - Journal of Symbolic Logic 65 (3):1375 - 1394.
    In this paper we introduce a recursive notation system O(Π 3 ) of ordinals. An element of the notation system is called an ordinal diagram. The system is designed for proof theoretic study of theories of Π 3 -reflection. We show that for each $\alpha in O(Π 3 ) a set theory KP Π 3 for Π 3 -reflection proves that the initial segment of O(Π 3 ) determined by α is a well ordering. Proof theoretic study for such theories (...)
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  36.  13
    Conservations of First-Order Reflections.Toshiyasu Arai - 2014 - Journal of Symbolic Logic 79 (3):814-825.
  37.  11
    Lifting Proof Theory to the Countable Ordinals: Zermelo-Fraenkel Set Theory.Toshiyasu Arai - 2014 - Journal of Symbolic Logic 79 (2):325-354.
  38.  17
    Consistency Proof Via Pointwise Induction.Toshiyasu Arai - 1998 - Archive for Mathematical Logic 37 (3):149-165.
    We show that the consistency of the first order arithmetic $PA$ follows from the pointwise induction up to the Howard ordinal. Our proof differs from U. Schmerl [Sc]: We do not need Girard's Hierarchy Comparison Theorem. A modification on the ordinal assignment to proofs by Gentzen and Takeuti [T] is made so that one step reduction on proofs exactly corresponds to the stepping down $\alpha\mapsto\alpha [1]$ in ordinals. Also a generalization to theories $ID_q$ of finitely iterated inductive definitions is proved.
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  39.  4
    A Bounded Arithmetic AID for Frege Systems.Toshiyasu Arai - 2000 - Annals of Pure and Applied Logic 103 (1-3):155-199.
    In this paper we introduce a system AID of bounded arithmetic. The main feature of AID is to allow a form of inductive definitions, which was extracted from Buss’ propositional consistency proof of Frege systems F in Buss 3–29). We show that AID proves the soundness of F , and conversely any Σ 0 b -theorem in AID yields boolean sentences of which F has polysize proofs. Further we define Σ 1 b -faithful interpretations between AID+Σ 0 b -CA and (...)
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  40.  6
    Proof Theory for Theories of Ordinals II:< I> Π_< Sub> 3-Reflection.Toshiyasu Arai - 2004 - Annals of Pure and Applied Logic 129 (1):39-92.
  41.  30
    Wellfoundedness Proofs by Means of Non-Monotonic Inductive Definitions II: First Order Operators.Toshiyasu Arai - 2010 - Annals of Pure and Applied Logic 162 (2):107-143.
  42.  21
    Epsilon Substitution Method for [Π0 1, Π0 1]-FIX.T. Arai - 2005 - Archive for Mathematical Logic 44 (8):1009-1043.
    We formulate epsilon substitution method for a theory [Π0 1, Π0 1]-FIX for two steps non-monotonic Π0 1 inductive definitions. Then we give a termination proof of the H-processes based on Ackermann [1].
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  43.  22
    Immediate Use of Prosody and Context in Predicting a Syntactic Structure.Chie Nakamura, Manabu Arai & Reiko Mazuka - 2012 - Cognition 125 (2):317-323.
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  44.  7
    Cut-Eliminability in Second Order Logic Calculus.Toshiyasu Arai - 2018 - Annals of the Japan Association for Philosophy of Science 27:45-60.
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  45.  3
    A Sneak Preview of Proof Theory of Ordinals.Toshiyasu Arai - 2012 - Annals of the Japan Association for Philosophy of Science 20:29-47.
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  46.  7
    Proof-Theoretic Strengths of Weak Theories for Positive Inductive Definitions.Toshiyasu Arai - 2018 - Journal of Symbolic Logic 83 (3):1091-1111.
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  47. Laforte, G., See Downey, R.T. Arai, Z. Chatzidakis & A. Pillay - 1998 - Annals of Pure and Applied Logic 95:287.
     
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  48.  11
    Perception of the Roles of Intelligent Machines and Systems「知的な機械・システム」と責任に関する意識.Koki Arai - 2018 - Transactions of the Japanese Society for Artificial Intelligence 33 (3):B-H32_1-7.
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  49. On the Slowly Well Orderedness of Ɛo.Toshiyasu Arai - 2002 - Mathematical Logic Quarterly 48 (1):125-130.
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  50.  11
    Non‐Elementary Speed‐Ups in Logic Calculi.Toshiyasu Arai - 2008 - Mathematical Logic Quarterly 54 (6):629-640.
    In this paper we show some non-elementary speed-ups in logic calculi: Both a predicative second-order logic and a logic for fixed points of positive formulas are shown to have non-elementary speed-ups over first-order logic. Also it is shown that eliminating second-order cut formulas in second-order logic has to increase sizes of proofs super-exponentially, and the same in eliminating second-order epsilon axioms. These are proved by relying on results due to P. Pudlák.
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