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  1. Representation of grossone-based arithmetic in Simulink for scientific computing.Alberto Falcone, Alfredo Garro, Marat Mukhametzhanov & Yaroslav Sergeyev - 2020 - Soft Computing 24:17525-17539.
    Numerical computing is a key part of the traditional computer architecture. Almost all traditional computers implement the IEEE 754-1985 binary floating point standard to represent and work with numbers. The architectural limitations of traditional computers make impossible to work with infinite and infinitesimal quantities numerically. This paper is dedicated to the Infinity Computer, a new kind of a supercomputer that allows one to perform numerical computations with finite, infinite, and infinitesimal numbers. The already available software simulator of the Infinity Computer (...)
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  2. A Simulink-based software solution using the Infinity Computer methodology for higher order differentiation.Alberto Falcone, Alfredo Garro, Marat Mukhametzhanov & Yaroslav Sergeyev - 2021 - Applied Mathematics and Computation 409:article 125606.
    This paper is dedicated to numerical computation of higher order derivatives in Simulink. In this paper, a new module has been implemented to achieve this purpose within the Simulink-based Infinity Computer solution, recently introduced by the authors. This module offers several blocks to calculate higher order derivatives of a function given by the arithmetic operations and elementary functions. Traditionally, this can be done in Simulink using finite differences only, for which it is well-known that they can be characterized by instability (...)
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  3. Introduction to the Theory of Computation.Michael Sipser - 2012 - Course Technology Cengage Learning.
    Now you can clearly present even the most complex computational theory topics to your students with Sipser’s distinct, market-leading INTRODUCTION TO THE THEORY OF COMPUTATION, 3E. The number one choice for today’s computational theory course, this highly anticipated revision retains the unmatched clarity and thorough coverage that make it a leading text for upper-level undergraduate and introductory graduate students. This edition continues author Michael Sipser’s well-known, approachable style with timely revisions, additional exercises, and more memorable examples in key areas. A (...)
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  4. Exploit Programming: From Buffer Overflows to “ Weird Machines ” and Theory of Computation.S. Bratus, Me Locasto & Ml Patterson - 2011 - Usenix; Login:13–21.
    It is hard to say exactly when their story began; chances are that at the beginning they were thought of as just handy tricks to assist more important techniques rather than the essence of exploitation. The classic " Smashing the Stack for Fun and Profit " by Aleph One 11 manages to explain the conversion of an implicit input data flow into altered program control flow in two short paragraphs: So a buffer overflow allows us to change the return address (...)
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  5. Review of Postdigital Theologies: Technology, Belief, and Practice, Maggi Savin-Baden, and John Reader (eds), Springer, 2022. [REVIEW]Ryan Haecker - unknown - Reviews in Religion and Theology 30 (3):197-200.
  6. On Pearl's Hierarchy and the Foundations of Causal Inference.Elias Bareinboim, Juan Correa, Duligur Ibeling & Thomas Icard - 2022 - In Hector Geffner, Rina Dechter & Joseph Y. Halpern (eds.), Probabilistic and Causal Inference: the Works of Judea Pearl. ACM Books. pp. 507-556.
    Cause and effect relationships play a central role in how we perceive and make sense of the world around us, how we act upon it, and ultimately, how we understand ourselves. Almost two decades ago, computer scientist Judea Pearl made a breakthrough in understanding causality by discovering and systematically studying the “Ladder of Causation” [Pearl and Mackenzie 2018], a framework that highlights the distinct roles of seeing, doing, and imagining. In honor of this landmark discovery, we name this the Pearl (...)
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  7. An Algebra for Tracing Categories of Social Processes: From a Surprising Fact to Middle-Range Theory using Categorical-Generative Analysis.Bruno da Rocha Braga - manuscript
    This paper describes a method for the analysis of the evolutionary path of a complex, dynamic, and contingent social phenomenon in an empirical setting. Given empirical evidence of a surprising or anomalous fact, which contradicts the prediction of the wide-acknowledged theory, the goal is to formulate a plausible explanation based on the context of occurrence, taking a holistic and historical point of view. The procedure begins by translating theoretical propositions into grammar rules to describe patterns of either individual action or (...)
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  8. Implementing a Computing System: A Pluralistic Approach.Syed AbuMusab - 2023 - Global Philosophy 33 (1):1-19.
    In chapter eleven of "On The Foundation of Computing," Primiero takes on the implementation debate in computer science. He contrasts his theory with two other views—the Semantic and the specification—artifact. In this paper, I argue that there is a way to fine-tune the implementation concept further. Firstly, contrary to Primiero, I claim it is problematic to separate the implementation relationship from the conditions which make it correct. Secondly, by taking a pluralistic approach to implementation, I claim it is a mistake (...)
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  9. On the Foundations of Computing. Computing as the Fourth Great Domain of Science. [REVIEW]Gordana Dodig-Crnkovic - 2023 - Global Philosophy 33 (1):1-12.
    This review essay analyzes the book by Giuseppe Primiero, On the foundations of computing. Oxford: Oxford University Press (ISBN 978-0-19-883564-6/hbk; 978-0-19-883565-3/pbk). xix, 296 p. (2020). It gives a critical view from the perspective of physical computing as a foundation of computing and argues that the neglected pillar of material computation (Stepney) should be brought centerstage and computing recognized as the fourth great domain of science (Denning).
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  10. Lower and Upper Estimates of the Quantity of Algebraic Numbers.Yaroslav Sergeyev - 2023 - Mediterranian Journal of Mathematics 20:12.
    It is well known that the set of algebraic numbers (let us call it A) is countable. In this paper, instead of the usage of the classical terminology of cardinals proposed by Cantor, a recently introduced methodology using ①-based infinite numbers is applied to measure the set A (where the number ① is called grossone). Our interest to this methodology is explained by the fact that in certain cases where cardinals allow one to say only whether a set is countable (...)
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  11. Link Uncertainty, Implementation, and ML Opacity: A Reply to Tamir and Shech.Emily Sullivan - 2022 - In Insa Lawler, Kareem Khalifa & Elay Shech (eds.), Scientific Understanding and Representation. Routledge. pp. 341-345.
    This chapter responds to Michael Tamir and Elay Shech’s chapter “Understanding from Deep Learning Models in Context.”.
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  12. Simulating Halt Decider Applied to the Halting Theorem.P. Olcott - manuscript
    The novel concept of a simulating halt decider enables halt decider H to to correctly determine the halt status of the conventional “impossible” input D that does the opposite of whatever H decides. This works equally well for Turing machines and “C” functions. The algorithm is demonstrated using “C” functions because all of the details can be shown at this high level of abstraction. ---------------------------------------------------------------------------------------------------- ---- Simulating halt decider H correctly determines that D correctly simulated by H would remain stuck in (...)
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  13. Bold because humble, humble because bold. Yann LeCun's path.Giovanni Landi - 2022 - Www.Intelligenzaartificialecomefilosofia.Com.
  14. Understanding from Machine Learning Models.Emily Sullivan - 2022 - British Journal for the Philosophy of Science 73 (1):109-133.
    Simple idealized models seem to provide more understanding than opaque, complex, and hyper-realistic models. However, an increasing number of scientists are going in the opposite direction by utilizing opaque machine learning models to make predictions and draw inferences, suggesting that scientists are opting for models that have less potential for understanding. Are scientists trading understanding for some other epistemic or pragmatic good when they choose a machine learning model? Or are the assumptions behind why minimal models provide understanding misguided? In (...)
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  15. Elements of the Theory of Computation.Harry Ralph Lewis & Christos H. Papadimitriou - 1981 - Englewood Cliffs, NJ, USA: Prentice-Hall.
    A general, yet comprehensive, introduction to the classical and contemporary theory of computation.
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  16. Halting problem undecidability and infinitely nested simulation (V2).P. Olcott - manuscript
    The halting theorem counter-examples present infinitely nested simulation (non-halting) behavior to every simulating halt decider. Whenever the pure simulation of the input to simulating halt decider H(x,y) never stops running unless H aborts its simulation H correctly aborts this simulation and returns 0 for not halting.
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  17. Solving equation systems in ω-categorical algebras.Manuel Bodirsky & Thomas Quinn-Gregson - 2021 - Journal of Mathematical Logic 21 (3).
    We study the computational complexity of deciding whether a given set of term equalities and inequalities has a solution in an ω-categorical algebra ????. There are ω-categorical groups where this pro...
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  18. Natural morphological computation as foundation of learning to learn in humans, other living organisms, and intelligent machines.Gordana Dodig-Crnkovic - 2020 - Philosophies 5 (3):17-32.
    The emerging contemporary natural philosophy provides a common ground for the integrative view of the natural, the artificial, and the human-social knowledge and practices. Learning process is central for acquiring, maintaining, and managing knowledge, both theoretical and practical. This paper explores the relationships between the present advances in understanding of learning in the sciences of the artificial, natural sciences, and philosophy. The question is, what at this stage of the development the inspiration from nature, specifically its computational models such as (...)
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  19. Towards a Theory of Computation similar to some other scientific theories.Antonino Drago - manuscript
    At first sight the Theory of Computation i) relies on a kind of mathematics based on the notion of potential infinity; ii) its theoretical organization is irreducible to an axiomatic one; rather it is organized in order to solve a problem: “What is a computation?”; iii) it makes essential use of doubly negated propositions of non-classical logic, in particular in the word expressions of the Church-Turing’s thesis; iv) its arguments include ad absurdum proofs. Under such aspects, it is like many (...)
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  20. A coinductive approach to proof search through typed lambda-calculi.José Espírito Santo, Ralph Matthes & Luís Pinto - 2021 - Annals of Pure and Applied Logic 172 (10):103026.
  21. Computing, Modelling, and Scientific Practice: Foundational Analyses and Limitations.Filippos A. Papagiannopoulos - 2018 - Dissertation, University of Western Ontario
    This dissertation examines aspects of the interplay between computing and scientific practice. The appropriate foundational framework for such an endeavour is rather real computability than the classical computability theory. This is so because physical sciences, engineering, and applied mathematics mostly employ functions defined in continuous domains. But, contrary to the case of computation over natural numbers, there is no universally accepted framework for real computation; rather, there are two incompatible approaches --computable analysis and BSS model--, both claiming to formalise algorithmic (...)
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  22. Квантовият компютър: квантовите ординали и типовете алгоритмична неразрешимост.Vasil Penchev - 2005 - Philosophical Alternatives 14 (6):59-71.
    A definition of quantum computer is supposed: as a countable set of Turing machines on the ground of: quantum parallelism, reversibility, entanglement. Qubit is the set of all the i–th binary location cells transforming in parallel by unitary matrices. The Church thesis is suggested in the form relevat to quantum computer. The notion of the non–finite (but not infinite) potency of a set is introduced .
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  23. We are less free than how we think: Regular patterns in nonverbal communication.".Alessandro Vinciarelli, Anna Esposito, Mohammad Tayarani, Giorgio Roffo, Filomena Scibelli, Perrone Francesco & Dong BachVo - 2019 - In Multimodal Behavior Analysis in the Wild Advances and Challenges Computer Vision and Pattern Recognition. pp. Pages 269-288.
    The goal of this chapter is to show that human behavior is not random but follows principles and laws that result into regular patterns that can be not only observed, but also automatically detected and analyzed. The word “behavior” accounts here for nonverbal behavioral cues (e.g., facial expressions, laughter, gestures, etc.) that people display, typically outside conscious awareness, during social interactions. In particular, the chapter shows that observable behavioral patterns typically account for social and psychological differences that cannot be observed (...)
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  24. Insights in How Computer Science can be a Science.Robert W. P. Luk - 2020 - Science and Philosophy 8 (2):17-46.
    Recently, information retrieval is shown to be a science by mapping information retrieval scientific study to scientific study abstracted from physics. The exercise was rather tedious and lengthy. Instead of dealing with the nitty gritty, this paper looks at the insights into how computer science can be made into a science by using that methodology. That is by mapping computer science scientific study to the scientific study abstracted from physics. To show the mapping between computer science and physics, we need (...)
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  25. Intuitionistic fixed point logic.Ulrich Berger & Hideki Tsuiki - 2021 - Annals of Pure and Applied Logic 172 (3):102903.
    We study the system IFP of intuitionistic fixed point logic, an extension of intuitionistic first-order logic by strictly positive inductive and coinductive definitions. We define a realizability interpretation of IFP and use it to extract computational content from proofs about abstract structures specified by arbitrary classically true disjunction free formulas. The interpretation is shown to be sound with respect to a domain-theoretic denotational semantics and a corresponding lazy operational semantics of a functional language for extracted programs. We also show how (...)
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  26. Absolutely No Free Lunches!Gordon Belot - forthcoming - Theoretical Computer Science.
    This paper is concerned with learners who aim to learn patterns in infinite binary sequences: shown longer and longer initial segments of a binary sequence, they either attempt to predict whether the next bit will be a 0 or will be a 1 or they issue forecast probabilities for these events. Several variants of this problem are considered. In each case, a no-free-lunch result of the following form is established: the problem of learning is a formidably difficult one, in that (...)
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  27. How to be concrete: mechanistic computation and the abstraction problem.Luke Kersten - 2020 - Philosophical Explorations 23 (3):251-266.
    This paper takes up a recent challenge to mechanistic approaches to computational implementation, the view that computational implementation is best explicated within a mechanistic framework. The challenge, what has been labelled “the abstraction problem”, claims that one of MAC’s central pillars – medium independence – is deeply confused when applied to the question of computational implementation. The concern is that while it makes sense to say that computational processes are abstract (i.e. medium-independent), it makes considerably less sense to say that (...)
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  28. Unrealistic models for realistic computations: how idealisations help represent mathematical structures and found scientific computing.Philippos Papayannopoulos - 2020 - Synthese 199 (1-2):249-283.
    We examine two very different approaches to formalising real computation, commonly referred to as “Computable Analysis” and “the BSS approach”. The main models of computation underlying these approaches—bit computation and BSS, respectively—have also been put forward as appropriate foundations for scientific computing. The two frameworks offer useful computability and complexity results about problems whose underlying domain is an uncountable space. Since typically the problems dealt with in physical sciences, applied mathematics, economics, and engineering are also defined in uncountable domains, it (...)
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  29. On the Foundations of Computing.Giuseppe Primiero - 2019 - Oxford University Press.
    Computing, today more than ever before, is a multi-faceted discipline which collates several methodologies, areas of interest, and approaches: mathematics, engineering, programming, and applications. Given its enormous impact on everyday life, it is essential that its debated origins are understood, and that its different foundations are explained. On the Foundations of Computing offers a comprehensive and critical overview of the birth and evolution of computing, and it presents some of the most important technical results and philosophical problems of the discipline, (...)
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  30. Why Be Random?Thomas Icard - 2021 - Mind 130 (517):111-139.
    When does it make sense to act randomly? A persuasive argument from Bayesian decision theory legitimizes randomization essentially only in tie-breaking situations. Rational behaviour in humans, non-human animals, and artificial agents, however, often seems indeterminate, even random. Moreover, rationales for randomized acts have been offered in a number of disciplines, including game theory, experimental design, and machine learning. A common way of accommodating some of these observations is by appeal to a decision-maker’s bounded computational resources. Making this suggestion both precise (...)
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  31. Richard Montague. Towards a general theory of computability. Synthese, vol. 12 no. 4 , pp. 429–438.Martin Davis - 1964 - Journal of Symbolic Logic 29 (1):63-64.
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  32. J. Hartmanis, P. M. LewisII, and R. E. Stearns. Classifications of computations by time and memory requirements. Information processing 1965, Proceedings of IFIP Congress 65, organized by the International Federation for Information Processing, New York City, May 24–29,1965, Volume 1, edited by Wayne A. Kalenich, Spartan Books, Inc., Washington, D.C., and Macmillan and Co., Ltd., London, 1965, pp. 31–35. [REVIEW]Jiří Bečvář - 1972 - Journal of Symbolic Logic 37 (3):624.
  33. Un Sistema di Creatività Computazionale basato su Logiche Non Monotòne per la Generazione di Nuovi Personaggi/Storie/Format in Ambienti Multi-Mediali.Antonio Lieto - forthcoming - In Proceedings of Ital-IA. Rome, Metropolitan City of Rome, Italy: pp. 123-135.
    In questo contributo descriviamo un sistema di creatività computazionale in grado di generare automaticamente nuovi concetti utilizzando una logica descrittiva non monotòna che integra tre ingredienti principali: una logica descrittiva della tipicalità, una estensione probabilistica basata sulla semantica distribuita nota come DISPONTE, e una euristica di ispirazione cognitiva per la combinazione di più concetti. Una delle applicazioni principali del sistema riguarda il campo della creatività computazionale e, più specificatamente, il suo utilizzo come sistema di supporto alla creatività in ambito mediale. (...)
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  34. 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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  35. Notes on Measure and Category in Recursion Theory.Hisao Tanaka - 1970 - Annals of the Japan Association for Philosophy of Science 3 (5):231-241.
  36. A Note on Continuous Functionals. Tugu^|^Eacute, Tosiyuki & Sigeru Hinata - 1969 - Annals of the Japan Association for Philosophy of Science 3 (4):138-145.
  37. Completeness properties of heyting's predicate calculus with respect to re models.Dov M. Gabbay - 1976 - Journal of Symbolic Logic 41 (1):81-94.
  38. Turing’s algorithmic lens: From computability to complexity theory.Josep Díaz & Carme Torras - 2013 - Arbor 189 (764):a080.
  39. 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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  40. Computing and philosophy: Selected papers from IACAP 2014.Vincent C. Müller (ed.) - 2016 - Cham: 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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  41. 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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  42. 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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  43. Ramsey-type graph coloring and diagonal non-computability.Ludovic Patey - 2015 - Archive for Mathematical Logic 54 (7-8):899-914.
    A function is diagonally non-computable if it diagonalizes against the universal partial computable function. D.n.c. functions play a central role in algorithmic randomness and reverse mathematics. Flood and Towsner asked for which functions h, the principle stating the existence of an h-bounded d.n.c. function implies Ramsey-type weak König’s lemma. In this paper, we prove that for every computable order h, there exists an ω\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\omega}$$\end{document} -model of h-DNR which is not a not (...)
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  44. 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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  45. A Jump Operator in Set Recursion.Dag Normann - 1979 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 25 (13-18):251-264.
  46. Sets Completely Creative Via Recursive Permutations.Bruce M. Horowitz - 1978 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 24 (25-30):445-452.
  47. Strong Computability and Variants of the Uniform Halting Problem.Gabor T. Herman - 1971 - Mathematical Logic Quarterly 17 (1):115-131.
  48. 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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  49. 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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  50. 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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