Search results for 'Computable functions Data processing' (try it on Scholar)

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  1.  14
    Lawrence C. Paulson (1987). Logic and Computation: Interactive Proof with Cambridge Lcf. Cambridge University Press.
    Logic and Computation is concerned with techniques for formal theorem-proving, with particular reference to Cambridge LCF (Logic for Computable Functions). Cambridge LCF is a computer program for reasoning about computation. It combines methods of mathematical logic with domain theory, the basis of the denotational approach to specifying the meaning of statements in a programming language. This book consists of two parts. Part I outlines the mathematical preliminaries: elementary logic and domain theory. They are explained at an intuitive level, (...)
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  2.  6
    Michael J. C. Gordon (1979). Edinburgh Lcf: A Mechanised Logic of Computation. Springer-Verlag.
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  3.  1
    Richard L. Epstein & Walter A. Carnielli (1989). Computability Computable Functions, Logic, and the Foundations of Mathematics. Monograph Collection (Matt - Pseudo).
    This book is dedicated to a classic presentation of the theory of computable functions in the context of the foundations of mathematics. Part I motivates the study of computability with discussions and readings about the crisis in the foundations of mathematics in the early 20th century, while presenting the basic ideas of whole number, function, proof, and real number. Part II starts with readings from Turing and Post leading to the formal theory of recursive functions. Part III (...)
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  4.  80
    Martin Davis (ed.) (1965). The Undecidable: Basic Papers on Undecidable Propositions, Unsolvable Problems, and Computable Functions. Dover Publication.
    "A valuable collection both for original source material as well as historical formulations of current problems."-- The Review of Metaphysics "Much more than a mere collection of papers . . . a valuable addition to the literature."-- Mathematics of Computation An anthology of fundamental papers on undecidability and unsolvability by major figures in the field, this classic reference opens with Godel's landmark 1931 paper demonstrating that systems of logic cannot admit proofs of all true assertions of arithmetic. Subsequent papers by (...)
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  5.  17
    Manuel L. Campagnolo & Kerry Ojakian (2008). The Elementary Computable Functions Over the Real Numbers: Applying Two New Techniques. [REVIEW] Archive for Mathematical Logic 46 (7-8):593-627.
    The basic motivation behind this work is to tie together various computational complexity classes, whether over different domains such as the naturals or the reals, or whether defined in different manners, via function algebras (Real Recursive Functions) or via Turing Machines (Computable Analysis). We provide general tools for investigating these issues, using two techniques we call approximation and lifting. We use these methods to obtain two main theorems. First, we provide an alternative proof of the result from Campagnolo (...)
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  6.  11
    Joost J. Joosten (2010). Consistency Statements and Iterations of Computable Functions in IΣ1 and PRA. Archive for Mathematical Logic 49 (7-8):773-798.
    In this paper we will state and prove some comparative theorems concerning PRA and IΣ1. We shall provide a characterization of IΣ1 in terms of PRA and iterations of a class of functions. In particular, we prove that for this class of functions the difference between IΣ1 and PRA is exactly that, where PRA is closed under iterations of these functions, IΣ1 is moreover provably closed under iteration. We will formulate a sufficient condition for a model of (...)
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  7.  21
    Hagen Lindstädt (2001). More Nonconcavities in Information Processing Functions. Theory and Decision 51 (2/4):351-365.
    The productivity of (human) information processing as an economic activity is a question that is raising some interest. Using Marschak's evaluation framework, Radner and Stiglitz have shown that, under certain conditions, the production function of this activity has increasing marginal returns in its initial stage. This paper shows that, under slightly different conditions, this information processing function has repeated convexities with ongoing processing activity. Even for smooth changes in the signals' likelihoods, the function is only piecewise smooth (...)
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  8.  1
    Timothy H. McNicholl (2008). Uniformly Computable Aspects of Inner Functions: Estimation and Factorization. Mathematical Logic Quarterly 54 (5):508-518.
    The theory of inner functions plays an important role in the study of bounded analytic functions. Inner functions are also useful in applied mathematics. Two foundational results in this theory are Frostman's Theorem and the Factorization Theorem. We prove a uniformly computable version of Frostman's Theorem. We then show that the Factorization Theorem is not uniformly computably true. We then show that for an inner function u with infinitely many zeros, the Blaschke sum of u provides (...)
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  9. Ning Zhong (1998). Derivatives of Computable Functions. Mathematical Logic Quarterly 44 (3):304-316.
    As is well known the derivative of a computable and C1 function may not be computable. For a computable and C∞ function f, the sequence {f} of its derivatives may fail to be computable as a sequence, even though its derivative of any order is computable. In this paper we present a necessary and sufficient condition for the sequence {f} of derivatives of a computable and C∞ function f to be computable. We also (...)
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  10.  4
    Melvin Fitting (1987). Computability Theory, Semantics, and Logic Programming. Clarendon Press.
    This book describes computability theory and provides an extensive treatment of data structures and program correctness. It makes accessible some of the author's work on generalized recursion theory, particularly the material on the logic programming language PROLOG, which is currently of great interest. Fitting considers the relation of PROLOG logic programming to the LISP type of language.
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  11.  1
    H. Richard Blackwell (1952). The Influence of Data Collection Procedures Upon Psychophysical Measurement of Two Sensory Functions. Journal of Experimental Psychology 44 (5):306.
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  12.  58
    Peter Smith, Basic Reading on Computable Functions.
    This is an annotated reading list on the beginning elements of the theory of computable functions. It is now structured so as to complement the first eight lectures of Thomas Forster’s Part III course in Lent 2011 (see the first four chapters of his evolving handouts).
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  13.  2
    M. Patharkar (2011). From Data Processing to Mental Organs: An Interdisciplinary Path to Cognitive Neuroscience. Mens Sana Monographs 9 (1):218.
    Human brain is a highly evolved coordinating mechanism in the species Homo sapiens. It is only in the last 100 years that extensive knowledge of the intricate structure and complex functioning of the human brain has been acquired, though a lot is yet to be known. However, from the beginning of civilisation, people have been conscious of a 'mind' which has been considered the origin of all scientific and cultural development. Philosophers have discussed at length the various attributes of consciousness. (...)
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  14.  8
    Stefano Mazzanti (1997). Iterative Characterizations of Computable Unary Functions: A General Method. Mathematical Logic Quarterly 43 (1):29-38.
    Iterative characterizations of computable unary functions are useful patterns for the definition of programming languages based on iterative constructs. The features of such a characterization depend on the pairing producing it: this paper offers an infinite class of pairings involving very nice features.
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  15. Qing Zhou (1996). Computable Real‐Valued Functions on Recursive Open and Closed Subsets of Euclidean Space. Mathematical Logic Quarterly 42 (1):379-409.
    In this paper we study intrinsic notions of “computability” for open and closed subsets of Euclidean space. Here we combine together the two concepts, computability on abstract metric spaces and computability for continuous functions, and delineate the basic properties of computable open and closed sets. The paper concludes with a comprehensive examination of the Effective Riemann Mapping Theorem and related questions.
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  16.  4
    Marian B. Pour‐El & Ning Zhong (1997). The Wave Equation with Computable Initial Data Whose Unique Solution is Nowhere Computable. Mathematical Logic Quarterly 43 (4):499-509.
    We give a rough statement of the main result. Let D be a compact subset of ℝ3× ℝ. The propagation u of a wave can be noncomputable in any neighborhood of any point of D even though the initial conditions which determine the wave propagation uniquely are computable. A precise statement of the result appears below.
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  17.  2
    Philippe Moser (2010). On the Convergence of Fourier Series of Computable Lebesgue Integrable Functions. Mathematical Logic Quarterly 56 (5):461-469.
    This paper studies how well computable functions can be approximated by their Fourier series. To this end, we equip the space of Lp-computable functions with a size notion, by introducing Lp-computable Baire categories. We show that Lp-computable Baire categories satisfy the following three basic properties. Singleton sets {f } are meager, suitable infinite unions of meager sets are meager, and the whole space of Lp-computable functions is not meager. We give an alternative (...)
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  18.  2
    Iraj Kalantari & Larry Welch (2013). When Series of Computable Functions with Varying Domains Are Computable. Mathematical Logic Quarterly 59 (6):471-493.
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  19.  5
    C. L. Haynes, G. A. Cook & M. A. Jones (2007). Legal and Ethical Considerations in Processing Patient-Identifiable Data Without Patient Consent: Lessons Learnt From Developing a Disease Register. Journal of Medical Ethics 33 (5):302-307.
    The legal requirements and justifications for collecting patient-identifiable data without patient consent were examined. The impetus for this arose from legal and ethical issues raised during the development of a population-based disease register. Numerous commentaries and case studies have been discussing the impact of the Data Protection Act 1998 and Caldicott principles of good practice on the uses of personal data. But uncertainty still remains about the legal requirements for processing patient-identifiable data without patient consent (...)
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  20.  1
    Klaus Weirauch (2003). Computational Complexity on Computable Metric Spaces. Mathematical Logic Quarterly 49 (1):3-21.
    We introduce a new Turing machine based concept of time complexity for functions on computable metric spaces. It generalizes the ordinary complexity of word functions and the complexity of real functions studied by Ko [19] et al. Although this definition of TIME as the maximum of a generally infinite family of numbers looks straightforward, at first glance, examples for which this maximum exists seem to be very rare. It is the main purpose of this paper to (...)
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  21.  18
    Dag Elgesem (1999). The Structure of Rights in Directive 95/46/EC on the Protection of Individuals with Regard to the Processing of Personal Data and the Free Movement of Such Data. [REVIEW] Ethics and Information Technology 1 (4):283-293.
    The paper has three parts. First, a survey and analysis is given ofthe structure of individual rights in the recent EU Directive ondata protection. It is argued that at the core of this structure isan unexplicated notion of what the data subject can `reasonablyexpect' concerning the further processing of information about himor herself. In the second part of the paper it is argued thattheories of privacy popular among philosophers are not able to shed much light on the issues (...)
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  22.  12
    P. Boyd (2003). The Requirements of the Data Protection Act 1998 for the Processing of Medical Data. Journal of Medical Ethics 29 (1):34-35.
    The Data Protection Act 1998 presents a number of significant challenges to data controllers in the health sector. To assist data controllers in understanding their obligations under the act, the Information Commissioner has published guidance, The Use and Disclosure of Health Data, which is reproduced here. The guidance deals, among other things, with the steps that must be taken to obtain patient data fairly, the implied requirements of the act to use anonymised or psuedonymised (...) where possible, an exemption applicable principally to records based research, the right of patients to object to the processing of their data, and the interface of the act and the common law duty of confidence. (shrink)
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  23.  11
    Rodney G. Downey & Asher M. Kach (2010). Euclidean Functions of Computable Euclidean Domains. Notre Dame Journal of Formal Logic 52 (2):163-172.
    We study the complexity of (finitely-valued and transfinitely-valued) Euclidean functions for computable Euclidean domains. We examine both the complexity of the minimal Euclidean function and any Euclidean function. Additionally, we draw some conclusions about the proof-theoretical strength of minimal Euclidean functions in terms of reverse mathematics.
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  24.  17
    Asher M. Kach & Daniel Turetsky (2010). Limitwise Monotonic Functions, Sets, and Degrees on Computable Domains. Journal of Symbolic Logic 75 (1):131-154.
    We extend the notion of limitwise monotonic functions to include arbitrary computable domains. We then study which sets and degrees are support increasing limitwise monotonic on various computable domains. As applications, we provide a characterization of the sets S with computable increasing η-representations using support increasing limitwise monotonic sets on ℚ and note relationships between the class of order-computable sets and the class of support increasing limitwise monotonic sets on certain domains.
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  25.  10
    E. F. Bradley & O. T. Denmead (eds.) (1967). The Collection and Processing of Field Data. New York, Interscience Publishers.
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  26.  47
    Carol E. Cleland (1995). Effective Procedures and Computable Functions. Minds and Machines 5 (1):9-23.
    Horsten and Roelants have raised a number of important questions about my analysis of effective procedures and my evaluation of the Church-Turing thesis. They suggest that, on my account, effective procedures cannot enter the mathematical world because they have a built-in component of causality, and, hence, that my arguments against the Church-Turing thesis miss the mark. Unfortunately, however, their reasoning is based upon a number of misunderstandings. Effective mundane procedures do not, on my view, provide an analysis of ourgeneral concept (...)
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  27.  1
    Manuel Lerman & Richard Watnick (2003). Computable Choice Functions for Computable Linear Orderings. Mathematical Logic Quarterly 49 (5):485-510.
    A choice set for a computable linear ordering is a set which contains one element from each maximal block of the ordering. We obtain a partial characterization of the computable linear order-types for which each computable model has a computable choice set, and a full characterization in the relativized case; Every model of the linear order-type α of degree ≤ d has a choice set of degree ≤ d iff α can written as a finite sum (...)
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  28.  6
    Toshiyasu Arai (2015). Predicatively Computable Functions on Sets. Archive for Mathematical Logic 54 (3-4):471-485.
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  29. M. A. Nielsen, Computable Functions, Quantum Measurements, and Quantum Dynamics.
    Quantum mechanical measurements on a physical system are represented by observables - Hermitian operators on the state space of the observed system. It is an important question whether all observables may be realized, in principle, as measurements on a physical system. Dirac’s influential text ( [1], page 37) makes the following assertion on the question: The question now presents itself – Can every observable be measured? The answer theoretically is yes. In practice it may be very awkward, or perhaps even (...)
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  30.  9
    R. Zach (2002). Computability. Computable Functions, Logic, and the Foundations of Mathematics. [REVIEW] History and Philosophy of Logic 23 (1):67-69.
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  31.  7
    G. Kreisel (1982). Review: Marian Boykan Pour-El, Ian Richards, A Computable Ordinary Differential Equation with Possesses No Computable Solution; Marian Boykan Pour-El, Ian Richards, The Wave Equation with Computable Initial Data Such That its Unique Solution is Not Computable. [REVIEW] Journal of Symbolic Logic 47 (4):900-902.
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  32.  11
    Judith Slein (1984). Philosophy and Data Processing. International Journal of Applied Philosophy 2 (1):75-84.
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  33. P. Eklof (1984). Review: Jerome Malitz, Introduction to Mathematical Logic. Set Theory, Computable Functions, Model Theory. [REVIEW] Journal of Symbolic Logic 49 (2):672-673.
     
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  34.  11
    Samuel Alexander (2006). Formulas for Computable and Non-Computable Functions. Rose-Hulman Undergraduate Mathematics Journal 7 (2).
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  35.  2
    Edmund F. Byrne (1996). The Two-Tiered Ethics of Electronic Data Processing. Techné: Research in Philosophy and Technology 2 (1):18-27.
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  36.  4
    Simon Thompson (2001). Resenha de 'Propositional Logic: The Semantic Foundations of Logic' (R. L. Epstein) - 'Predicate Logic: The Semantic Foundations of Logic' (R. L. Epstein) - 'Computable Functions, Logic, and the Foundations of Mathematics' (R. L. Epstein and W. A. Carniel). [REVIEW] Manuscrito 24 (1).
  37.  4
    Stefan Bauer-Mengelberg (1996). Davis Martin. On Formally Undecidable Propositions of the Principia Mathematica and Related Systems. I. The Undecidable, Basic Papers on Undecidable Propositions, Unsolvable Problems and Computable Functions, Edited by Davis Martin, Raven Press, Hewlett, New York, 1965, P. 4. Gödel Kurt. On Formally Undecidable Propositions of Principia Mathematica and Related Systems I. English Translation of 4183 by Elliott Mendelson. The Undecidable, Basic Papers on Undecidable Propositions, Unsolvable Problems and ... [REVIEW] Journal of Symbolic Logic 31 (3):484-494.
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  38.  8
    Harley Shands (1973). Other-Than-Neurological Components Basic to Human Data-Processing Operations. World Futures 14 (1):13-32.
  39.  3
    Tilman Lenssen-erz (1994). Facts or Fantasy? The Rock Paintings of the Brandberg, Namibia, and a Concept of Textualization for Purposes of Data Processing. Semiotica 100 (2-4):169-200.
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  40. C. C. Elgot (1963). Review: Robert W. Ritchie, Classes of Predictably Computable Functions. [REVIEW] Journal of Symbolic Logic 28 (3):252-253.
     
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  41. Eberhard Herrmann & Rodney Downey (1990). Review: Robert I. Soare, Recursively Enumerable Sets and Degrees. A Study of Computable Functions and Computably Generated Sets. [REVIEW] Journal of Symbolic Logic 55 (1):356-357.
     
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  42.  6
    Carlos Augusto Priscdio (2002). Review: Richard L. Epstein, Walter A. Carnielli, Computability. Computable Functions, Logic, and the Foundations of Mathematics ; Richard L. Epstein, Walter A. Carnielli, Computability. Computable Functions, Logic, and the Foundations of Mathematics. Second Edition of the Preceding. [REVIEW] Bulletin of Symbolic Logic 8 (1):101-104.
  43.  1
    Lyle R. Creamer (1963). Event Uncertainty, Psychological Refractory Period, and Human Data Processing. Journal of Experimental Psychology 66 (2):187.
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  44.  2
    Carlos Augusto Di Prisco (2002). Review: Richard L. Epstein, Walter A. Carnielli, Computability. Computable Functions, Logic, and the Foundations of Mathematics; Richard L. Epstein, Walter A. Carnielli, Computability. Computable Functions, Logic, and the Foundations of Mathematics. Second Edition of the Preceding. [REVIEW] Bulletin of Symbolic Logic 8 (1):101-104.
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  45. F. B. Cannonito (1967). Review: T. Rado, On Non-Computable Functions. [REVIEW] Journal of Symbolic Logic 32 (4):524-524.
     
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  46.  3
    Carlos Augusto Priscdio (2002). Review: Richard L. Epstein, Walter A. Carnielli, Computability. Computable Functions, Logic, and the Foundations of Mathematics ; Richard L. Epstein, Walter A. Carnielli, Computability. Computable Functions, Logic, and the Foundations of Mathematics. Second Edition of the Preceding. [REVIEW] Bulletin of Symbolic Logic 8 (1):101-104.
  47. F. B. Cannonito (1967). Review: Tibor Rado, On a Simple Source for Non-Computable Functions. [REVIEW] Journal of Symbolic Logic 32 (4):524-524.
     
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  48.  1
    Judy M. Reviewer-Myerson (1991). Book Review: English-Japanese, Japanese-English Dictionary of Computer and Data Processing Terms by George Ferber (MIT Press 1989). [REVIEW] Acm Sigcas Computers and Society 21 (2-4):51.
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  49.  1
    Arthur E. Parry (1983). Data Processing Risk. Acm Sigcas Computers and Society 13 (3):14-18.
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  50. Jiri Becvar (1969). Review: G. S. Matveeva, On a Theorem of Rabin Concerning the Complexity of Computable Functions. [REVIEW] Journal of Symbolic Logic 34 (1):133-134.
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