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  1. Numerical Infinities and Infinitesimals: Methodology, Applications, and Repercussions on Two Hilbert Problems.Yaroslav Sergeyev - 2017 - EMS Surveys in Mathematical Sciences 4 (2):219–320.
    In this survey, a recent computational methodology paying a special attention to the separation of mathematical objects from numeral systems involved in their representation is described. It has been introduced with the intention to allow one to work with infinities and infinitesimals numerically in a unique computational framework in all the situations requiring these notions. The methodology does not contradict Cantor’s and non-standard analysis views and is based on the Euclid’s Common Notion no. 5 “The whole is greater than the (...)
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  2. Notes on Measure and Category in Recursion Theory.Hisao Tanaka - 1970 - Annals of the Japan Association for Philosophy of Science 3 (5):231-241.
  3. A Note on Continuous Functionals. Tugu^|^Eacute, Tosiyuki & Sigeru Hinata - 1969 - Annals of the Japan Association for Philosophy of Science 3 (4):138-145.
  4. Turing’s Algorithmic Lens: From Computability to Complexity Theory.Josep Díaz & Carme Torras - 2013 - Arbor 189 (764):a080.
  5. Physical Computation: A Mechanistic Account. [REVIEW]Joe Dewhurst - 2016 - Philosophical Psychology 29 (5):795-797.
    Physical Computation is the summation of Piccinini’s work on computation and mechanistic explanation over the past decade. It draws together material from papers published during that time, but also provides additional clarifications and restructuring that make this the definitive presentation of his mechanistic account of physical computation. This review will first give a brief summary of the account that Piccinini defends, followed by a chapter-by-chapter overview of the book, before finally discussing one aspect of the account in more critical detail.
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  6. Computing and Philosophy: Selected Papers From IACAP 2014.Vincent C. Müller (ed.) - 2016 - Springer.
    This volume offers very selected papers from the 2014 conference of the “International Association for Computing and Philosophy” (IACAP) - a conference tradition of 28 years. - - - Table of Contents - 0 Vincent C. Müller: - Editorial - 1) Philosophy of computing - 1 Çem Bozsahin: - What is a computational constraint? - 2 Joe Dewhurst: - Computing Mechanisms and Autopoietic Systems - 3 Vincenzo Fano, Pierluigi Graziani, Roberto Macrelli and Gino Tarozzi: - Are Gandy Machines really local? (...)
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  7. What is Morphological Computation? On How the Body Contributes to Cognition and Control.Vincent C. Müller & Matej Hoffmann - 2017 - Artificial Life 23 (1):1-24.
    The contribution of the body to cognition and control in natural and artificial agents is increasingly described as “off-loading computation from the brain to the body”, where the body is said to perform “morphological computation”. Our investigation of four characteristic cases of morphological computation in animals and robots shows that the ‘off-loading’ perspective is misleading. Actually, the contribution of body morphology to cognition and control is rarely computational, in any useful sense of the word. We thus distinguish (1) morphology that (...)
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  8. Realizability Semantics for Quantified Modal Logic: Generalizing Flagg's 1985 Construction.Benjamin G. Rin & Sean Walsh - 2016 - Review of Symbolic Logic 9 (4):752-809.
    A semantics for quantified modal logic is presented that is based on Kleene's notion of realizability. This semantics generalizes Flagg's 1985 construction of a model of a modal version of Church's Thesis and first-order arithmetic. While the bulk of the paper is devoted to developing the details of the semantics, to illustrate the scope of this approach, we show that the construction produces (i) a model of a modal version of Church's Thesis and a variant of a modal set theory (...)
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  9. Ramsey-Type Graph Coloring and Diagonal Non-Computability.Ludovic Patey - 2015 - Archive for Mathematical Logic 54 (7-8):899-914.
  10. Variable Binding Term Operators.John Corcoran, William Hatcher & John Herring - 1972 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 18 (12):177-182.
    Chapin reviewed this 1972 ZEITSCHRIFT paper that proves the completeness theorem for the logic of variable-binding-term operators created by Corcoran and his student John Herring in the 1971 LOGIQUE ET ANALYSE paper in which the theorem was conjectured. This leveraging proof extends completeness of ordinary first-order logic to the extension with vbtos. Newton da Costa independently proved the same theorem about the same time using a Henkin-type proof. This 1972 paper builds on the 1971 “Notes on a Semantic Analysis of (...)
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  11. A Jump Operator in Set Recursion.Dag Normann - 1979 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 25 (13-18):251-264.
  12. Sets Completely Creative Via Recursive Permutations.Bruce M. Horowitz - 1978 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 24 (25-30):445-452.
  13. Strong Computability and Variants of the Uniform Halting Problem.Gabor T. Herman - 1971 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 17 (1):115-131.
  14. The Physical Church-Turing Thesis: Modest or Bold?Gualtiero Piccinini - 2011 - British Journal for the Philosophy of Science 62 (4):733-769.
    This article defends a modest version of the Physical Church-Turing thesis (CT). Following an established recent trend, I distinguish between what I call Mathematical CT—the thesis supported by the original arguments for CT—and Physical CT. I then distinguish between bold formulations of Physical CT, according to which any physical process—anything doable by a physical system—is computable by a Turing machine, and modest formulations, according to which any function that is computable by a physical system is computable by a Turing machine. (...)
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  15. Information and Computation: Essays on Scientific and Philosophical Understanding of Foundations of Information and Computation.Gordana Dodig Crnkovic & Mark Burgin (eds.) - 2011 - World Scientific.
    Information is a basic structure of the world, while computation is a process of the dynamic change of information. This book provides a cutting-edge view of world's leading authorities in fields where information and computation play a central role. It sketches the contours of the future landscape for the development of our understanding of information and computation, their mutual relationship and the role in cognition, informatics, biology, artificial intelligence, and information technology. -/- This book is an utterly enjoyable and engaging (...)
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  16. Computability and Analysis: The Legacy of Alan Turing.Jeremy Avigad & Vasco Brattka - unknown
    We discuss the legacy of Alan Turing and his impact on computability and analysis.
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  17. Susan Stuart & Gordana Dodig Crnkovic : 'Computation, Information, Cognition: The Nexus and the Liminal'. [REVIEW]Vincent C. Müller - 2009 - Cybernetics and Human Knowing 16 (3-4):201-203.
    Review of: "Computation, Information, Cognition: The Nexus and the Liminal", Ed. Susan Stuart & Gordana Dodig Crnkovic, Newcastle: Cambridge Scholars Publishing, September 2007, xxiv+340pp, ISBN: 9781847180902, Hardback: £39.99, $79.99 ---- Are you a computer? Is your cat a computer? A single biological cell in your stomach, perhaps? And your desk? You do not think so? Well, the authors of this book suggest that you think again. They propose a computational turn, a turn towards computational explanation and towards the explanation of (...)
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  18. Representation in Digital Systems.Vincent C. Müller - 2008 - In Adam Briggle, Katinka Waelbers & Brey Philip (eds.), Current Issues in Computing and Philosophy. IOS Press. pp. 116-121.
    Cognition is commonly taken to be computational manipulation of representations. These representations are assumed to be digital, but it is not usually specified what that means and what relevance it has for the theory. I propose a specification for being a digital state in a digital system, especially a digital computational system. The specification shows that identification of digital states requires functional directedness, either for someone or for the system of which it is a part. In the case or digital (...)
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  19. Weak Computability and Representation of Reals.Xizhong Zheng & Robert Rettinger - 2004 - Mathematical Logic Quarterly 50 (45):431-442.
    The computability of reals was introduced by Alan Turing [20] by means of decimal representations. But the equivalent notion can also be introduced accordingly if the binary expansion, Dedekind cut or Cauchy sequence representations are considered instead. In other words, the computability of reals is independent of their representations. However, as it is shown by Specker [19] and Ko [9], the primitive recursiveness and polynomial time computability of the reals do depend on the representation. In this paper, we explore how (...)
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  20. Density and Baire Category in Recursive Topology.Iraj Kalantari & Larry Welch - 2004 - Mathematical Logic Quarterly 50 (45):381-391.
    We develop the concepts of recursively nowhere dense sets and sets that are recursively of first category and study closed sets of points in light of Baire's Category Theorem. Our theorems are primarily concerned with exdomains of recursive quantum functions and hence with avoidable points . An avoidance function is a recursive function which can be used to expel avoidable points from domains of recursive quantum functions. We define an avoidable set of points to be an arbitrary subset of the (...)
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  21. Computational Complexity of Solving Equation Systems.Przemysław Broniek - unknown
    We present conclusions and open problems raising from studying solving equations over unary algebras. We suggest areas that are most promising for expanding our knowledge.
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  22. Levels of Discontinuity, Limit-Computability, and Jump Operators.de Brecht Matthew - 2014 - In Dieter Spreen, Hannes Diener & Vasco Brattka (eds.), Logic, Computation, Hierarchies. De Gruyter. pp. 79-108.
  23. Elements of the Theory of Computation Harry R. Lewis, Christos H. Papadimitriou.Harry R. Lewis & Christos H. Papadimitriou - 1998
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  24. Gary R. Collins, "Psychology Series for Church Leaders". Vol. II. "Effective Counselling". [REVIEW]William J. Nessel - 1973 - The Thomist 37 (1):262.
  25. Finite Automata, Formal Logic, and Circuit Complexity.Howard Straubing - 1994
  26. Communication Complexity.Eyal Kushilevitz & Noam Nisan - 1997
  27. Degrees of Unsolvability.Gerald E. Sacks - 1963 - Princeton University Press.
  28. Recursive Analysis. [REVIEW]H. T. R. - 1964 - Review of Metaphysics 18 (1):174-174.
  29. Formal Systems and Recursive Functions. [REVIEW]J. M. P. - 1965 - Review of Metaphysics 19 (1):161-162.
  30. The Equivalence of Bar Recursion and Open Recursion.Thomas Powell - 2014 - Annals of Pure and Applied Logic 165 (11):1727-1754.
    Several extensions of Gödel's system TT with new forms of recursion have been designed for the purpose of giving a computational interpretation to classical analysis. One can organise many of these extensions into two groups: those based on bar recursion , which include Spector's original bar recursion, modified bar recursion and the more recent products of selections functions, or those based on open recursion which in particular include the symmetric Berardi–Bezem–Coquand functional. We relate these two groups by showing that both (...)
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  31. Computable Symbolic Dynamics.Douglas Cenzer, S. Ali Dashti & Jonathan L. F. King - 2008 - Mathematical Logic Quarterly 54 (5):460-469.
    We investigate computable subshifts and the connection with effective symbolic dynamics. It is shown that a decidable Π01 class P is a subshift if and only if there exists a computable function F mapping 2ℕ to 2ℕ such that P is the set of itineraries of elements of 2ℕ. Π01 subshifts are constructed in 2ℕ and in 2ℤ which have no computable elements. We also consider the symbolic dynamics of maps on the unit interval.
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  32. Sequential Real Number Computation and Recursive Relations.J. Raymundo Marcial-Romero & M. Andrew Moshier - 2008 - Mathematical Logic Quarterly 54 (5):492-507.
    In the first author's thesis [10], a sequential language, LRT, for real number computation is investigated. That thesis includes a proof that all polynomials are programmable, but that work comes short of giving a complete characterization of the expressive power of the language even for first-order functions. The technical problem is that LRT is non-deterministic. So a natural characterization of its expressive power should be in terms of relations rather than in terms of functions. In [2], Brattka examines a formalization (...)
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  33. "Turing's\ Oracle": From Absolute to Relative Computability and Back.Solomon Feferman - 1992 - In Javier Echeverria, Andoni Ibarra & Thomas Mormann (eds.), The Space of Mathematics: Philosophical, Epistemological, and Historical Explorations. De Gruyter. pp. 314--348.
  34. The Complexity of Industrial Ecosystems: Classification and Computational Modelling.James S. Baldwin - 2011 - In Peter Allen, Steve Maguire & Bill McKelvey (eds.), The Sage Handbook of Complexity and Management. Sage Publications. pp. 299.
  35. Reducing Negative Complexity by a Computational Semiotic System.Gerd Doben-Henisch - 2007 - In R. Gudwin & J. Queiroz (eds.), Semiotics and Intelligent Systems Development. Idea Group. pp. 330.
  36. Reducing Negative Complexity by a Computational Semiotic System.Gerd Döben Henisch - 2007 - In R. Gudwin & J. Queiroz (eds.), Semiotics and Intelligent Systems Development. Idea Group.
  37. Computational Complexity Reduction and Interpretability Improvement of Distance-Based Decision Trees.Marcin Blachnik & Mirosław Kordos - 2012 - In Emilio Corchado, Vaclav Snasel, Ajith Abraham, Michał Woźniak, Manuel Grana & Sung-Bae Cho (eds.), Hybrid Artificial Intelligent Systems. Springer. pp. 288--297.
  38. Turing Computable Embeddings and Coding Families of Sets.Víctor A. Ocasio-González - 2012 - In S. Barry Cooper (ed.), How the World Computes. pp. 539--548.
  39. Hierarchies of Provably Recursive Functions.Stanley S. Wainer - 1998 - In Samuel R. Buss (ed.), Bulletin of Symbolic Logic. Elsevier. pp. 149.
  40. Computability and Computational Complexity.Patrick Doyle - 2003 - In L. Nadel (ed.), Encyclopedia of Cognitive Science. Nature Publishing Group.
  41. Recursive Analysis.Rl Goodsteest - 1959 - In A. Heyting (ed.), Constructivity in Mathematics. Amsterdam: North-Holland Pub. Co.. pp. 37.
  42. Remarks on Church's Thesis and GOdel's Theorem.Stanisław Krajewski - 2006 - In A. Olszewski, J. Wole'nski & R. Janusz (eds.), Church's Thesis After Seventy Years. Ontos Verlag. pp. 1--269.
  43. Analog Computation and Church's Thesis.Jerzy Mycka - 2006 - In A. Olszewski, J. Wole'nski & R. Janusz (eds.), Church's Thesis After Seventy Years. Ontos Verlag. pp. 1--331.
  44. Algorithmic Randomness and Measures of Complexity.George Barmpalias - forthcoming - Association for Symbolic Logic: The Bulletin of Symbolic Logic.
    We survey recent advances on the interface between computability theory and algorithmic randomness, with special attention on measures of relative complexity. We focus on (weak) reducibilities that measure (a) the initial segment complexity of reals and (b) the power of reals to compress strings, when they are used as oracles. The results are put into context and several connections are made with various central issues in modern algorithmic randomness and computability.
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  45. Arithmetic of Infinity.Yaroslav D. Sergeyev - 2013 - E-book.
    This book presents a new type of arithmetic that allows one to execute arithmetical operations with infinite numbers in the same manner as we are used to do with finite ones. The problem of infinity is considered in a coherent way different from (but not contradicting to) the famous theory founded by Georg Cantor. Surprisingly, the introduced arithmetical operations result in being very simple and are obtained as immediate extensions of the usual addition, multiplication, and division of finite numbers to (...)
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  46. Two Splitting Theorems for Beta-Recursion Theory.Steven Homer - 1980 - Annals of Mathematical Logic 18 (2):137-151.
  47. On Suborderings of Degrees of Recursive Unsolvability.Gerald E. Sacks - 1961 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 7 (1-5):46-56.
  48. Hybrid Elections Broaden Complexity‐Theoretic Resistance to Control.Edith Hemaspaandra, Lane A. Hemaspaandra & Jörg Rothe - 2009 - Mathematical Logic Quarterly 55 (4):397-424.
    Electoral control refers to attempts by an election's organizer to influence the outcome by adding/deleting/partitioning voters or candidates. The important paper of Bartholdi, Tovey, and Trick [1] that introduces control proposes computational complexity as a means of resisting control attempts: Look for election systems where the chair's task in seeking control is itself computationally infeasible.We introduce and study a method of combining two or more candidate-anonymous election schemes in such a way that the combined scheme possesses all the resistances to (...)
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  49. On the Complexity of Finding Paths in a Two‐Dimensional Domain I: Shortest Paths.Arthur W. Chou & Ker-I. Ko - 2004 - Mathematical Logic Quarterly 50 (6):551-572.
    The computational complexity of finding a shortest path in a two-dimensional domain is studied in the Turing machine-based computational model and in the discrete complexity theory. This problem is studied with respect to two formulations of polynomial-time computable two-dimensional domains: domains with polynomialtime computable boundaries, and polynomial-time recognizable domains with polynomial-time computable distance functions. It is proved that the shortest path problem has the polynomial-space upper bound for domains of both type and type ; and it has a polynomial-space lower (...)
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  50. On the Relations Between Discrete and Continuous Complexity Theory.Klaus Meer - 1995 - Mathematical Logic Quarterly 41 (2):281-286.
    Relations between discrete and continuous complexity models are considered. The present paper is devoted to combine both models. In particular we analyze the 3-Satisfiability problem. The existence of fast decision procedures for this problem over the reals is examined based on certain conditions on the discrete setting. Moreover we study the behaviour of exponential time computations over the reals depending on the real complexity of 3-Satisfiability. This will be done using tools from complexity theory over the integers.
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