Results for ' Weihrauch reducibility'

999 found
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  1.  19
    The characterization of Weihrauch reducibility in systems containing.Patrick Uftring - 2021 - Journal of Symbolic Logic 86 (1):224-261.
    We characterize Weihrauch reducibility in $ \operatorname {\mathrm {E-PA^{\omega }}} + \operatorname {\mathrm {QF-AC^{0,0}}}$ and all systems containing it by the provability in a linear variant of the same calculus using modifications of Gödel’s Dialectica interpretation that incorporate ideas from linear logic, nonstandard arithmetic, higher-order computability, and phase semantics.
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  2.  36
    On Weihrauch reducibility and intuitionistic reverse mathematics.Rutger Kuyper - 2017 - Journal of Symbolic Logic 82 (4):1438-1458.
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  3.  7
    The characterization of Weihrauch reducibility in systems containing e-pa ω + qf-ac0;0.Patrick Uftring - forthcoming - Journal of Symbolic Logic:1-35.
  4.  16
    Weihrauch Goes Brouwerian.Vasco Brattka & Guido Gherardi - 2020 - Journal of Symbolic Logic 85 (4):1614-1653.
    We prove that the Weihrauch lattice can be transformed into a Brouwer algebra by the consecutive application of two closure operators in the appropriate order: first completion and then parallelization. The closure operator of completion is a new closure operator that we introduce. It transforms any problem into a total problem on the completion of the respective types, where we allow any value outside of the original domain of the problem. This closure operator is of interest by itself, as (...)
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  5.  30
    Weihrauch degrees, omniscience principles and weak computability.Vasco Brattka & Guido Gherardi - 2011 - Journal of Symbolic Logic 76 (1):143 - 176.
    In this paper we study a reducibility that has been introduced by Klaus Weihrauch or, more precisely, a natural extension for multi-valued functions on represented spaces. We call the corresponding equivalence classes Weihrauch degrees and we show that the corresponding partial order induces a lower semi-lattice. It turns out that parallelization is a closure operator for this semi-lattice and that the parallelized Weihrauch degrees even form a lattice into which the Medvedev lattice and the Turing degrees (...)
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  6.  17
    The open and clopen Ramsey theorems in the Weihrauch lattice.Alberto Marcone & Manlio Valenti - 2021 - Journal of Symbolic Logic 86 (1):316-351.
    We investigate the uniform computational content of the open and clopen Ramsey theorems in the Weihrauch lattice. While they are known to be equivalent to $\mathrm {ATR_0}$ from the point of view of reverse mathematics, there is not a canonical way to phrase them as multivalued functions. We identify eight different multivalued functions and study their degree from the point of view of Weihrauch, strong Weihrauch, and arithmetic Weihrauch reducibility. In particular one of our functions (...)
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  7.  20
    On the (semi)lattices induced by continuous reducibilities.Arno Pauly - 2010 - Mathematical Logic Quarterly 56 (5):488-502.
    Continuous reducibilities are a proven tool in Computable Analysis, and have applications in other fields such as Constructive Mathematics or Reverse Mathematics. We study the order-theoretic properties of several variants of the two most important definitions, and especially introduce suprema for them. The suprema are shown to commutate with several characteristic numbers.
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  8.  45
    Effective Borel measurability and reducibility of functions.Vasco Brattka - 2005 - Mathematical Logic Quarterly 51 (1):19-44.
    The investigation of computational properties of discontinuous functions is an important concern in computable analysis. One method to deal with this subject is to consider effective variants of Borel measurable functions. We introduce such a notion of Borel computability for single-valued as well as for multi-valued functions by a direct effectivization of the classical definition. On Baire space the finite levels of the resulting hierarchy of functions can be characterized using a notion of reducibility for functions and corresponding complete (...)
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  9.  16
    Reduction games, provability and compactness.Damir D. Dzhafarov, Denis R. Hirschfeldt & Sarah Reitzes - 2022 - Journal of Mathematical Logic 22 (3).
    Journal of Mathematical Logic, Volume 22, Issue 03, December 2022. Hirschfeldt and Jockusch (2016) introduced a two-player game in which winning strategies for one or the other player precisely correspond to implications and non-implications between [math] principles over [math]-models of [math]. They also introduced a version of this game that similarly captures provability over [math]. We generalize and extend this game-theoretic framework to other formal systems, and establish a certain compactness result that shows that if an implication [math] between two (...)
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  10.  24
    Completion of choice.Vasco Brattka & Guido Gherardi - 2021 - Annals of Pure and Applied Logic 172 (3):102914.
    We systematically study the completion of choice problems in the Weihrauch lattice. Choice problems play a pivotal rôle in Weihrauch complexity. For one, they can be used as landmarks that characterize important equivalences classes in the Weihrauch lattice. On the other hand, choice problems also characterize several natural classes of computable problems, such as finite mind change computable problems, non-deterministically computable problems, Las Vegas computable problems and effectively Borel measurable functions. The closure operator of completion generates the (...)
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  11.  3
    Computability Theory: Constructive Applications of the Lefthanded Local Lemma and Characterizations of Some Classes of Cohesive Powers.Daniel Mourad - 2023 - Bulletin of Symbolic Logic 29 (4):664-665.
    The Lovász local lemma (LLL) is a technique from combinatorics for proving existential results. There are many different versions of the LLL. One of them, the lefthanded local lemma, is particularly well suited for applications to two player games. There are also constructive and computable versions of the LLL. The chief object of this thesis is to prove an effective version of the lefthanded local lemma and to apply it to effectivise constructions of non-repetitive sequences.The second goal of this thesis (...)
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  12.  25
    Embeddings between well-orderings: Computability-theoretic reductions.Jun Le Goh - 2020 - Annals of Pure and Applied Logic 171 (6):102789.
    We study the computational content of various theorems with reverse mathematical strength around Arithmetical Transfinite Recursion (ATR_0) from the point of view of computability-theoretic reducibilities, in particular Weihrauch reducibility. Our main result states that it is equally hard to construct an embedding between two given well-orderings, as it is to construct a Turing jump hierarchy on a given well-ordering. This answers a question of Marcone. We obtain a similar result for Fraïssé's conjecture restricted to well-orderings.
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  13.  92
    Effective choice and boundedness principles in computable analysis.Vasco Brattka & Guido Gherardi - 2011 - Bulletin of Symbolic Logic 17 (1):73-117.
    In this paper we study a new approach to classify mathematical theorems according to their computational content. Basically, we are asking the question which theorems can be continuously or computably transferred into each other? For this purpose theorems are considered via their realizers which are operations with certain input and output data. The technical tool to express continuous or computable relations between such operations is Weihrauch reducibility and the partially ordered degree structure induced by it. We have identified (...)
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  14.  23
    Using Ramsey’s theorem once.Jeffry L. Hirst & Carl Mummert - 2019 - Archive for Mathematical Logic 58 (7-8):857-866.
    We show that \\) cannot be proved with one typical application of \\) in an intuitionistic extension of \ to higher types, but that this does not remain true when the law of the excluded middle is added. The argument uses Kohlenbach’s axiomatization of higher order reverse mathematics, results related to modified reducibility, and a formalization of Weihrauch reducibility.
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  15.  24
    A journey through computability, topology and analysis.Manlio Valenti - 2022 - Bulletin of Symbolic Logic 28 (2):266-267.
    This thesis is devoted to the exploration of the complexity of some mathematical problems using the framework of computable analysis and descriptive set theory. We will especially focus on Weihrauch reducibility as a means to compare the uniform computational strength of problems. After a short introduction of the relevant background notions, we investigate the uniform computational content of problems arising from theorems that lie at the higher levels of the reverse mathematics hierarchy.We first analyze the strength of the (...)
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  16.  14
    The Discontinuity Problem.Vasco Brattka - 2023 - Journal of Symbolic Logic 88 (3):1191-1212.
    Matthias Schröder has asked the question whether there is a weakest discontinuous problem in the topological version of the Weihrauch lattice. Such a problem can be considered as the weakest unsolvable problem. We introduce the discontinuity problem, and we show that it is reducible exactly to the effectively discontinuous problems, defined in a suitable way. However, in which sense this answers Schröder’s question sensitively depends on the axiomatic framework that is chosen, and it is a positive answer if we (...)
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  17.  10
    Placebo treatment is effective differently in different diseases — but is it also harmless? A brief synopsis.Thomas R. Weihrauch - 2004 - Science and Engineering Ethics 10 (1):151-155.
    The placebo drug reactions from controlled trials were studied for the first time systematically for efficacy and the safety in drug data pooled from randomized, placebo-controlled, multicentre studies. Results: The efficacy of placebo on clinical symptoms and outcome varied between the therapeutic indications. However, no placebo effects on laboratory values, as e.g. blood glucose or Hb1c in diabetics, were noted. The frequency and type of placebo-induced adverse reactions also varied between indication groups. The placebo side effect profile was largely similar (...)
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  18.  33
    Computable analysis of the abstract Cauchy problem in a Banach space and its applications I.Klaus Weihrauch & Ning Zhong - 2007 - Mathematical Logic Quarterly 53 (4‐5):511-531.
    We study computability of the abstract linear Cauchy problem equation image)where A is a linear operator, possibly unbounded, on a Banach space X. We give necessary and sufficient conditions for A such that the solution operator K: x ↦ u of the problem is computable. For studying computability we use the representation approach to computable analysis developed by Weihrauch and others. This approach is consistent with the model used by Pour-El/Richards.
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  19.  37
    Placebo treatment is effective differently in different diseases — but is it also harmless? A brief synopsis.Prof Dr Thomas R. Weihrauch - 2004 - Science and Engineering Ethics 10 (1):151-155.
    The placebo drug reactions from controlled trials were studied for the first time systematically for efficacy and the safety in drug data pooled from randomized, placebo-controlled, multicentre studies. Results: The efficacy of placebo on clinical symptoms and outcome varied between the therapeutic indications. However, no placebo effects on laboratory values, as e.g. blood glucose or Hb1c in diabetics, were noted. The frequency and type of placebo-induced adverse reactions also varied between indication groups. The placebo side effect profile was largely similar (...)
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  20.  20
    Representations of the real numbers and of the open subsets of the set of real numbers.Klaus Weihrauch & Christoph Kreitz - 1987 - Annals of Pure and Applied Logic 35 (C):247-260.
  21.  20
    Göran Collste: Global Rectificatory Justice. Palgrave Macmillan, 2014, ISBN-9781137466129. Hardcover € 81.Tobias Weihrauch - 2016 - Ethical Theory and Moral Practice 19 (2):527-529.
  22. Parallel Monte Carlo Algorithms for Diverse Applications in a Distributed Setting-Comparison of the Computational Cost of a Monte Carlo and Deterministic Algorithm for Computing Bilinear Forms of.Christian Weihrauch, Ivan Dimov, Simon Branford & Vassil Alexandrov - 2006 - In O. Stock & M. Schaerf (eds.), Lecture Notes In Computer Science. Springer Verlag. pp. 640-647.
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  23.  29
    The Arithmetical Hierarchy of Real Numbers.Xizhong Zheng & Klaus Weihrauch - 2001 - Mathematical Logic Quarterly 47 (1):51-66.
    A real number x is computable iff it is the limit of an effectively converging computable sequence of rational numbers, and x is left computable iff it is the supremum of a computable sequence of rational numbers. By applying the operations “sup” and “inf” alternately n times to computable sequences of rational numbers we introduce a non-collapsing hierarchy {Σn, Πn, Δn : n ∈ ℕ} of real numbers. We characterize the classes Σ2, Π2 and Δ2 in various ways and give (...)
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  24.  22
    Compactness in constructive analysis revisited.Christoph Kreitz & Klaus Weihrauch - 1987 - Annals of Pure and Applied Logic 36:29-38.
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  25.  18
    Computable Riesz representation for the dual of C [0; 1].Hong Lu & Klaus Weihrauch - 2007 - Mathematical Logic Quarterly 53 (4):415-430.
    By the Riesz representation theorem for the dual of C [0; 1], if F: C [0; 1] → ℝ is a continuous linear operator, then there is a function g: [0;1] → ℝ of bounded variation such that F = ∫ f dg . The function g can be normalized such that V = ‖F ‖. In this paper we prove a computable version of this theorem. We use the framework of TTE, the representation approach to computable analysis, which allows (...)
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  26.  20
    Computable metrization.Tanja Grubba, Matthias Schröder & Klaus Weihrauch - 2007 - Mathematical Logic Quarterly 53 (4‐5):381-395.
    Every second-countable regular topological space X is metrizable. For a given “computable” topological space satisfying an axiom of computable regularity M. Schröder [10] has constructed a computable metric. In this article we study whether this metric space can be considered computationally as a subspace of some computable metric space [15]. While Schröder's construction is “pointless”, i. e., only sets of a countable base but no concrete points are known, for a computable metric space a concrete dense set of computable points (...)
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  27.  23
    Editorial: Math. Log. Quart. 4–5/2007.Ker-I. Ko, Klaus Weihrauch & Xizhong Zheng - 2007 - Mathematical Logic Quarterly 53 (4‐5):325-325.
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  28.  32
    Connectivity properties of dimension level sets.Jack H. Lutz & Klaus Weihrauch - 2008 - Mathematical Logic Quarterly 54 (5):483-491.
    This paper initiates the study of sets in Euclidean spaces ℝn that are defined in terms of the dimensions of their elements. Specifically, given an interval I ⊆ [0, n ], we are interested in the connectivity properties of the set DIMI, consisting of all points in ℝn whose dimensions lie in I, and of its dual DIMIstr, consisting of all points whose strong dimensions lie in I. If I is [0, 1) or.
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  29.  22
    Approaches to Effective Semi‐Continuity of Real Functions.Xizhong Zheng, Vasco Brattka & Klaus Weihrauch - 1999 - Mathematical Logic Quarterly 45 (4):481-496.
    For semi-continuous real functions we study different computability concepts defined via computability of epigraphs and hypographs. We call a real function f lower semi-computable of type one, if its open hypograph hypo is recursively enumerably open in dom × ℝ; we call f lower semi-computable of type two, if its closed epigraph Epi is recursively enumerably closed in dom × ℝ; we call f lower semi-computable of type three, if Epi is recursively closed in dom × ℝ. We show that (...)
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  30.  17
    Je subjektívna skúsenosť redukovateľná?M. Bednáriková & Is Subjective Experience Reducible - 2003 - Filozofia 58 (7):495.
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  31.  41
    Linear orderings under one-one reducibility.Paul R. Young - 1966 - Journal of Symbolic Logic 31 (1):70-85.
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  32.  6
    Quiné W. V.. On the axiom of reducibility. Mind, n.s., vol. 45 , pp. 498–500.C. H. Langford - 1937 - Journal of Symbolic Logic 2 (1):60-60.
  33.  17
    Some properties of r-maximal sets and Q 1,N -reducibility.R. Sh Omanadze - 2015 - Archive for Mathematical Logic 54 (7-8):941-959.
    We show that the c.e. Q1,N\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${Q_{1,N}}$$\end{document}-degrees are not an upper semilattice. We prove that if M is an r-maximal set, A is an arbitrary set and M≡Q1,NA\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${M \equiv{}_ {Q_{1,N}}A}$$\end{document}, then M≤mA\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${M\leq{}_{m} A}$$\end{document}. Also, if M1 and M2 are r-maximal sets, A and B are major subsets of M1 and M2, respectively, and M1\A≡Q1,NM2\B\documentclass[12pt]{minimal} \usepackage{amsmath} (...)
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  34.  44
    Additive Property and the Physical Reducibility of the Mind.Kwangho Hyun - 2014 - Open Journal of Philosophy 4 (2):91-95.
  35. Axiomatization of set theory by extensionality, separation, and reducibility.Harvey Friedman - manuscript
    We discuss several axiomatizations of set theory in first order predicate calculus with epsilon and a constant symbol W, starting with the simple system K(W) which has a strong equivalence with ZF without Foundation. The other systems correspond to various extensions of ZF by certain large cardinal hypotheses. These axiomatizations are unusually simple and uncluttered, and are highly suggestive of underlying philosophical principles that generate higher set theory.
     
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  36.  12
    Church‐Rosser Property for Some Extensions of λβ‐Reducibility Relation.Andrei A. Kuzichev - 1991 - Mathematical Logic Quarterly 37 (33‐35):547-559.
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  37.  27
    Church‐Rosser Property for Some Extensions of λβ‐Reducibility Relation.Andrei A. Kuzichev - 1991 - Mathematical Logic Quarterly 37 (33-35):547-559.
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  38.  7
    On restricted forms of enumeration reducibility.Phil Watson - 1990 - Annals of Pure and Applied Logic 49 (1):75-96.
  39.  49
    Carnap’s Aufbau and Physicalism: What Does the “Mutual Reducibility” of Psychological and Physical Objects Amount to?Thomas Uebel - 2014 - Vienna Circle Institute Yearbook 17:45-56.
    The present paper is part of a larger project of investigating how far puzzling questions about Carnap’s philosophical deflationism – as expressed most prominently in “Empricism, Semantics and Ontology”1 – can be answered by reference to his own preferred position in areas upon which this meta-philosophical position can be expected to have a bearing. For that project the explorations below provide a starting point; on the present occasion they will, I hope, be found to be of independent interest. At issue (...)
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  40.  10
    r‐Maximal sets and Q1,N‐reducibility.Roland Sh Omanadze & Irakli O. Chitaia - 2021 - Mathematical Logic Quarterly 67 (2):138-148.
    We show that if M is an r‐maximal set, A is a major subset of M, B is an arbitrary set and, then. We prove that the c.e. ‐degrees are not dense. We also show that there exist infinite collections of ‐degrees and such that the following hold: (i) for every i, j,, and,(ii) each consists entirely of r‐maximal sets, and(iii) each consists entirely of non‐r‐maximal hyperhypersimple sets.
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  41.  11
    On Constructively Non‐Morphisms of Enumerated Sets and Constructive Non‐Reducibility of Enumerations.Andrzej Orlicki - 1987 - Mathematical Logic Quarterly 33 (6):485-496.
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  42.  23
    On Constructively Non-Morphisms of Enumerated Sets and Constructive Non-Reducibility of Enumerations.Andrzej Orlicki - 1987 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 33 (6):485-496.
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  43.  13
    Liu Shih-Chao. A note on many-one reducibility.Gerald E. Sacks - 1966 - Journal of Symbolic Logic 31 (3):512.
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  44.  12
    Addendum to “computably enumerable sets and quasi-reducibility”.R. Downey, G. LaForte & A. Nies - 1999 - Annals of Pure and Applied Logic 98 (1-3):295.
  45.  51
    Bounded fixed-parameter tractability and reducibility.Rod Downey, Jörg Flum, Martin Grohe & Mark Weyer - 2007 - Annals of Pure and Applied Logic 148 (1):1-19.
    We study a refined framework of parameterized complexity theory where the parameter dependence of fixed-parameter tractable algorithms is not arbitrary, but restricted by a function in some family . For every family of functions, this yields a notion of -fixed-parameter tractability. If is the class of all polynomially bounded functions, then -fixed-parameter tractability coincides with polynomial time decidability and if is the class of all computable functions, -fixed-parameter tractability coincides with the standard notion of fixed-parameter tractability. There are interesting choices (...)
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  46.  6
    Churchland, Kandel and Dooyeweerd on the reducibility of mind states.Gerrit Glas - 2002 - Philosophia Reformata 67 (2):148-172.
    This article is devoted to the conceptual analysis of two texts of leading scholars in cognitive neuroscience and its philosophy, Patricia Churchland and Eric Kandel. After a short introduction about the notion of reduction, I give a detailed account of the way both scientists view the relationship between theories about brain functioning on the one hand and consciousness and psychopathology, respectively, on the other hand. The analysis not only reveals underlying philosophical mind/brain conceptions and their inner tensions, but also the (...)
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  47.  5
    Bounds in weak truth-table reducibility.Karol Habart - 1991 - Notre Dame Journal of Formal Logic 32 (2):233-241.
  48.  4
    Weihrauch und Schwefel: ein Monolog.Adolf Holl - 2003 - Graz: Styria.
    *Weitere Angaben Inhalt: Mit der Frage nach der Zuständigkeit der eigenen Nase in Religionsangelegenheiten beginnt diese ungewöhnliche Reise in Erfahrungsbereiche, die von Theologen bislang eher gemieden wurden. Nicht der Inhalt von Glaubensbekenntnissen ist Gegenstand des Interesses, sondern der Tonfall, in dem sie vorgetragen werden. Von bestimmten Kirchengerüchen geht die Rede, von Körperhaltungen beim Gottesdienst, von Kindheitserinnerungen und vom Läuten der Glocken. Dabei stellt sich heraus, dass mit dem abgenützten Etikett des Religiösen die Sinnenfälligkeit des Erlebten nur sehr oberflächlich bezeichnet wird.
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  49.  2
    On subcreative sets and s-reducibility.I. I. I. Gill & Paul H. Morris - 1974 - Journal of Symbolic Logic 39 (4):669-677.
  50.  6
    A note on many·one reducibility.Shih-Chao Liu - 1963 - Journal of Symbolic Logic 28 (1):35-42.
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