Results for 'Recursion'

922 found
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  1. Pierre mounoud.P. Rochat & A. Recursive Model - 1995 - In Philippe Rochat, The Self in Infancy: Theory and Research. Elsevier. pp. 112--141.
     
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  2.  63
    Classical recursion theory: the theory of functions and sets of natural numbers.Piergiorgio Odifreddi - 1989 - New York, N.Y., USA: Sole distributors for the USA and Canada, Elsevier Science Pub. Co..
    Volume II of Classical Recursion Theory describes the universe from a local (bottom-up or synthetical) point of view, and covers the whole spectrum, from the recursive to the arithmetical sets. The first half of the book provides a detailed picture of the computable sets from the perspective of Theoretical Computer Science. Besides giving a detailed description of the theories of abstract Complexity Theory and of Inductive Inference, it contributes a uniform picture of the most basic complexity classes, ranging from (...)
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  3.  57
    Recursion Isn’t Necessary for Human Language Processing: NEAR (Non-iterative Explicit Alternatives Rule) Grammars are Superior.Kenneth R. Paap & Derek Partridge - 2014 - Minds and Machines 24 (4):389-414.
    Language sciences have long maintained a close and supposedly necessary coupling between the infinite productivity of the human language faculty and recursive grammars. Because of the formal equivalence between recursion and non-recursive iteration; recursion, in the technical sense, is never a necessary component of a generative grammar. Contrary to some assertions this equivalence extends to both center-embedded relative clauses and hierarchical parse trees. Inspection of language usage suggests that recursive rule components in fact contribute very little, and likely (...)
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  4.  17
    Recursive functionals.Luis E. Sanchis - 1992 - New York: North-Holland.
    This work is a self-contained elementary exposition of the theory of recursive functionals, that also includes a number of advanced results.
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  5.  11
    E-recursion, forcing and C*-algebras.Chi-Tat Chong (ed.) - 2014 - New Jersey: World Scientific.
    This volume presents the lecture notes of short courses given by three leading experts in mathematical logic at the 2012 Asian Initiative for Infinity Logic Summer School. The major topics cover set-theoretic forcing, higher recursion theory, and applications of set theory to C*-algebra. This volume offers a wide spectrum of ideas and techniques introduced in contemporary research in the field of mathematical logic to students, researchers and mathematicians.
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  6.  8
    Recursion theory and complexity: proceedings of the Kazan '97 Workshop, Kazan, Russia, July 14-19, 1997.Marat Mirzaevich Arslanov & Steffen Lempp (eds.) - 1999 - New York: W. de Gruyter.
    This volume contains papers from the recursion theory session of the Kazan Workshop on Recursion and Complexity Theory. Recursion theory, the study of computability, is an area of mathematical logic that has traditionally been particularly strong in the United States and the former Soviet Union. This was the first workshop ever to bring together about 50 international experts in recursion theory from the United States, the former Soviet Union and Western Europe.
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  7.  37
    Recursive Functions and Metamathematics: Problems of Completeness and Decidability, Gödel's Theorems.Rod J. L. Adams & Roman Murawski - 1999 - Dordrecht, Netherland: Springer Verlag.
    Traces the development of recursive functions from their origins in the late nineteenth century to the mid-1930s, with particular emphasis on the work and influence of Kurt Gödel.
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  8.  17
    Handbook of recursive mathematics.I︠U︡riĭ Leonidovich Ershov (ed.) - 1998 - New York: Elsevier.
    v. 1. Recursive model theory -- v. 2. Recursive algebra, analysis and combinatorics.
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  9.  47
    Rudimentary Recursion, Gentle Functions and Provident Sets.A. R. D. Mathias & N. J. Bowler - 2015 - Notre Dame Journal of Formal Logic 56 (1):3-60.
    This paper, a contribution to “micro set theory”, is the study promised by the first author in [M4], as improved and extended by work of the second. We use the rudimentarily recursive functions and the slightly larger collection of gentle functions to initiate the study of provident sets, which are transitive models of $\mathsf{PROVI}$, a subsystem of $\mathsf{KP}$ whose minimal model is Jensen’s $J_{\omega}$. $\mathsf{PROVI}$ supports familiar definitions, such as rank, transitive closure and ordinal addition—though not ordinal multiplication—and Shoenfield’s unramified (...)
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  10.  19
    Difference Sets and Recursion Theory.James H. Schmerl - 1998 - Mathematical Logic Quarterly 44 (4):515-521.
    There is a recursive set of natural numbers which is the difference set of some recursively enumerable set but which is not the difference set of any recursive set.
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  11.  29
    Recursion-theoretic hierarchies.Peter G. Hinman - 1978 - New York: Springer Verlag.
  12. Recursion theory: its generalisations and applications: proceedings of Logic Colloquium '79, Leeds, August 1979.F. R. Drake & S. S. Wainer (eds.) - 1980 - New York: Cambridge University Press.
  13.  15
    Higher recursion theory.Gerald E. Sacks - 1990 - New York, NY, USA: Cambridge University Press.
    This almost self-contained introduction to higher recursion theory is essential reading for all researchers in the field.
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  14.  50
    Recursion, Language, and Starlings.Michael C. Corballis - 2007 - Cognitive Science 31 (4):697-704.
    It has been claimed that recursion is one of the properties that distinguishes human language from any other form of animal communication. Contrary to this claim, a recent study purports to demonstrate center‐embedded recursion in starlings. I show that the performance of the birds in this study can be explained by a counting strategy, without any appreciation of center‐embedding. To demonstrate that birds understand center‐embedding of sequences of the form AnBn (such as A1A2B2B1, or A3A4A5B5B4B3) would require not (...)
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  15.  53
    Recursive Differentiation Arithmetic.Denys Spirin - manuscript
    This paper introduces Recursive Differentiation Arithmetic (RDA), a formal system that redefines the foundations of arithmetic, geometry, and computation in terms of ontological differentiation rather than set-theoretic or numerical primitives. Instead of assuming numbers, space, or time as given, RDA constructs these structures from stabilized differences within a field of potentiality. The basic elements of RDA are differentiation nodes, which emerge through recursive operations of unfolding and composition. We show how natural numbers arise as a special case of recursive differentiation, (...)
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  16.  15
    Recursive Polish spaces.Tyler Arant - 2023 - Archive for Mathematical Logic 62 (7):1101-1110.
    This paper is concerned with the proper way to effectivize the notion of a Polish space. A theorem is proved that shows the recursive Polish space structure is not found in the effectively open subsets of a space X{\mathcal {X}} X, and we explore strong evidence that the effective structure is instead captured by the effectively open subsets of the product space N×X\mathbb {N}\times {\mathcal {X}} N × X.
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  17.  26
    A recursion-theoretic approach to NP.Isabel Oitavem - 2011 - Annals of Pure and Applied Logic 162 (8):661-666.
    An implicit characterization of the class NP is given, without using any minimization scheme. This is the first purely recursion-theoretic formulation of NP.
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  18.  18
    Recursive analysis.R. L. Goodstein - 1961 - Mineola, N.Y.: Dover Publications.
    This graduate-level_text by a master in the field builds a function theory of the rational field that combines aspects of classical and intuitionist analysis. Topics include recursive convergence, recursive and relative continuity, recursive and relative differentiability, the relative integral, elementary functions, and transfinite ordinals. 1961 edition.
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  19.  47
    Recursive Ontology: A Systemic Theory of Reality.Valerio Velardo - 2016 - Axiomathes 26 (1):89-114.
    The article introduces recursive ontology, a general ontology which aims to describe how being is organized and what are the processes that drive it. In order to answer those questions, I use a multidisciplinary approach that combines the theory of levels, philosophy and systems theory. The main claim of recursive ontology is that being is the product of a single recursive process of generation that builds up all of reality in a hierarchical fashion from fundamental physical particles to human societies. (...)
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  20.  42
    A Recursive Measure of Voting Power with Partial Decisiveness or Efficacy.Arash Abizadeh - 2022 - Journal of Politics 84 (3):1652-1666.
    The current literature standardly conceives of voting power in terms of decisiveness: the ability to change the voting outcome by unilaterally changing one’s vote. I argue that this classic conception of voting power, which fails to account for partial decisiveness or efficacy, produces erroneous results because it saddles the concept of voting power with implausible microfoundations. This failure in the measure of voting power in turn reflects a philosophical mistake about the concept of social power in general: a failure to (...)
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  21.  41
    Recursively Enumerable Equivalence Relations Modulo Finite Differences.André Nies - 1994 - Mathematical Logic Quarterly 40 (4):490-518.
    We investigate the upper semilattice Eq* of recursively enumerable equivalence relations modulo finite differences. Several natural subclasses are shown to be first-order definable in Eq*. Building on this we define a copy of the structure of recursively enumerable many-one degrees in Eq*, thereby showing that Th has the same computational complexity as the true first-order arithmetic.
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  22.  43
    Recursive Approximability of Real Numbers.Xizhong Zheng - 2002 - Mathematical Logic Quarterly 48 (S1):131-156.
    A real number is recursively approximable if there is a computable sequence of rational numbers converging to it. If some extra condition to the convergence is added, then the limit real number might have more effectivity. In this note we summarize some recent attempts to classify the recursively approximable real numbers by the convergence rates of the corresponding computable sequences ofr ational numbers.
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  23.  57
    Primitive Recursion and the Chain Antichain Principle.Alexander P. Kreuzer - 2012 - Notre Dame Journal of Formal Logic 53 (2):245-265.
    Let the chain antichain principle (CAC) be the statement that each partial order on $\mathbb{N}$ possesses an infinite chain or an infinite antichain. Chong, Slaman, and Yang recently proved using forcing over nonstandard models of arithmetic that CAC is $\Pi^1_1$-conservative over $\text{RCA}_0+\Pi^0_1\text{-CP}$ and so in particular that CAC does not imply $\Sigma^0_2$-induction. We provide here a different purely syntactical and constructive proof of the statement that CAC (even together with WKL) does not imply $\Sigma^0_2$-induction. In detail we show using a (...)
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  24.  18
    Synthesising recursive functions with side effects.Ria Follett - 1980 - Artificial Intelligence 13 (3):175-200.
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  25.  79
    A recursive model for arithmetic with weak induction.Zofia Adamowicz & Guillermo Morales-Luna - 1985 - Journal of Symbolic Logic 50 (1):49-54.
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  26. Theory of recursive functions and effective computability.Hartley Rogers - 1987 - Cambridge: MIT Press.
  27.  42
    Is recursion language-specific? Evidence of recursive mechanisms in the structure of intentional action.Giuseppe Vicari & Mauro Adenzato - 2014 - Consciousness and Cognition 26:169-188.
    In their 2002 seminal paper Hauser, Chomsky and Fitch hypothesize that recursion is the only human-specific and language-specific mechanism of the faculty of language. While debate focused primarily on the meaning of recursion in the hypothesis and on the human-specific and syntax-specific character of recursion, the present work focuses on the claim that recursion is language-specific. We argue that there are recursive structures in the domain of motor intentionality by way of extending John R. Searle’s analysis (...)
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  28. Computability, an introduction to recursive function theory.Nigel Cutland - 1980 - New York: Cambridge University Press.
    What can computers do in principle? What are their inherent theoretical limitations? These are questions to which computer scientists must address themselves. The theoretical framework which enables such questions to be answered has been developed over the last fifty years from the idea of a computable function: intuitively a function whose values can be calculated in an effective or automatic way. This book is an introduction to computability theory (or recursion theory as it is traditionally known to mathematicians). Dr (...)
  29. Joint attention without recursive mindreading: On the role of second-person engagement.Felipe León - 2021 - Philosophical Psychology 34 (4):550-580.
    On a widely held characterization, triadic joint attention is the capacity to perceptually attend to an object or event together with another subject. In the last four decades, research in developmental psychology has provided increasing evidence of the crucial role that this capacity plays in socio-cognitive development, early language acquisition, and the development of perspective-taking. Yet, there is a striking discrepancy between the general agreement that joint attention is critical in various domains, and the lack of theoretical consensus on how (...)
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  30.  32
    Cobham recursive set functions.Arnold Beckmann, Sam Buss, Sy-David Friedman, Moritz Müller & Neil Thapen - 2016 - Annals of Pure and Applied Logic 167 (3):335-369.
  31. Recursive analysis.Rl Goodsteest - 1959 - In A. Heyting, Constructivity in mathematics. Amsterdam,: North-Holland Pub. Co.. pp. 37.
  32. Recursiveness of ω‐Operations.Victor L. Selivanov - 1994 - Mathematical Logic Quarterly 40 (2):204-206.
    It is well known that any finitary operation is recursive in a suitable total numeration. A. Orlicki showed that there is an ω-operation not recursive in any total numeration. We will show that any ω-operation is recursive in a partial numeration.
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  33.  41
    The Recursively Mahlo Property in Second Order Arithmetic.Michael Rathjen - 1996 - Mathematical Logic Quarterly 42 (1):59-66.
    The paper characterizes the second order arithmetic theorems of a set theory that features a recursively Mahlo universe; thereby complementing prior proof-theoretic investigations on this notion. It is shown that the property of being recursively Mahlo corresponds to a certain kind of β-model reflection in second order arithmetic. Further, this leads to a characterization of the reals recursively computable in the superjump functional.
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  34.  75
    Recursion theory for metamathematics.Raymond Merrill Smullyan - 1993 - New York: Oxford University Press.
    This work is a sequel to the author's Godel's Incompleteness Theorems, though it can be read independently by anyone familiar with Godel's incompleteness theorem for Peano arithmetic. The book deals mainly with those aspects of recursion theory that have applications to the metamathematics of incompleteness, undecidability, and related topics. It is both an introduction to the theory and a presentation of new results in the field.
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  35.  18
    Recursive Combination Has Adaptability in Diversifiability of Production and Material Culture.Genta Toya & Takashi Hashimoto - 2018 - Frontiers in Psychology 9.
    It has been suggested that hierarchically structured symbols, a remarkable feature of human language, are produced via the operation of recursive combination. Recursive combination is frequently observed in human behavior, not only in language but also in action sequences, mind-reading, technology, et cetera.; in contrast, it is rarely observed in animals. Why is it that only humans use this operation? What is the adaptability of recursive combination? We aim (1) to identify the environmental feature(s) in which recursive combination is effective (...)
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  36.  35
    Complete, Recursively Enumerable Relations in Arithmetic.Giovanna D'Agostino & Mario Magnago - 1995 - Mathematical Logic Quarterly 41 (1):65-72.
    Using only propositional connectives and the provability predicate of a Σ1-sound theory T containing Peano Arithmetic we define recursively enumerable relations that are complete for specific natural classes of relations, as the class of all r. e. relations, and the class of all strict partial orders. We apply these results to give representations of these classes in T by means of formulas.
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  37. Every recursive linear ordering has a copy in DTIMESPACE (n; log (n)).S. Gregorie - 1990 - Journal of Symbolic Logic 55:260-276.
  38.  53
    Automorphisms of Countable Short Recursively Saturated Models of PA.Erez Shochat - 2008 - Notre Dame Journal of Formal Logic 49 (4):345-360.
    A model of Peano Arithmetic is short recursively saturated if it realizes all its bounded finitely realized recursive types. Short recursively saturated models of $\PA$ are exactly the elementary initial segments of recursively saturated models of $\PA$. In this paper, we survey and prove results on short recursively saturated models of $\PA$ and their automorphisms. In particular, we investigate a certain subgroup of the automorphism group of such models. This subgroup, denoted $G|_{M(a)}$, contains all the automorphisms of a countable short (...)
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  39.  36
    General recursion theory: an axiomatic approach.Jens Erik Fenstad - 1980 - New York: Springer Verlag.
  40. Recursive Philosophy and Negative Machines.Luciana Parisi - 2022 - Critical Inquiry 48 (2):313-333.
    What has philosophy become after computation? Critical positions about what counts as intelligence, reason, and thinking have addressed this question by reenvisioning and pushing debates about the modern question of technology towards new radical visions. Artificial intelligence, it is argued, is replacing transcendental metaphysics with aggregates of data resulting in predictive modes of decision-making, replacing conceptual reflection with probabilities. This article discusses two main positions. While on the one hand, it is feared that philosophy has been replaced by cybernetic metaphysics, (...)
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  41.  46
    Bar recursion over finite partial functions.Paulo Oliva & Thomas Powell - 2017 - Annals of Pure and Applied Logic 168 (5):887-921.
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  42.  35
    Recursion theory.Anil Nerode & Richard A. Shore (eds.) - 1985 - Providence, R.I.: American Mathematical Society.
    iterations of REA operators, as well as extensions, generalizations and other applications are given in [6] while those for the ...
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  43.  35
    Recursive functions and existentially closed structures.Emil Jeřábek - 2019 - Journal of Mathematical Logic 20 (1):2050002.
    The purpose of this paper is to clarify the relationship between various conditions implying essential undecidability: our main result is that there exists a theory T in which all partially recursive functions are representable, yet T does not interpret Robinson’s theory R. To this end, we borrow tools from model theory — specifically, we investigate model-theoretic properties of the model completion of the empty theory in a language with function symbols. We obtain a certain characterization of ∃∀ theories interpretable in (...)
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  44.  14
    Recursion: A Computational Investigation Into the Representation and Processing of Language.David J. Lobina - 2017 - Oxford University Press.
    The book examines one of the most contested topics in linguistics and cognitive science: the role of recursion in language. It offers a precise account of what recursion is, what role it should play in cognitive theories of human knowledge, and how it manifests itself in the mental representations of language and other cognitive domains.
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  45.  50
    Four Problems Concerning Recursively Saturated Models of Arithmetic.Roman Kossak - 1995 - Notre Dame Journal of Formal Logic 36 (4):519-530.
    The paper presents four open problems concerning recursively saturated models of Peano Arithmetic. One problems concerns a possible converse to Tarski's undefinability of truth theorem. The other concern elementary cuts in countable recursively saturated models, extending automorphisms of countable recursively saturated models, and Jonsson models of PA. Some partial answers are given.
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  46.  56
    On recursive solutions to simple allocation problems.Özgür Kıbrıs - 2013 - Theory and Decision 75 (3):449-463.
    We propose and axiomatically analyze a class of rational solutions to simple allocation problems where a policy-maker allocates an endowment $E$ among $n$ agents described by a characteristic vector c. We propose a class of recursive rules which mimic a decision process where the policy-maker initially starts with a reference allocation of $E$ in mind and then uses the data of the problem to recursively adjust his previous allocation decisions. We show that recursive rules uniquely satisfy rationality, c-continuity, and other-c (...)
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  47.  35
    Recursivity and Contingency.Daniel Neumann - 2021 - Philosophical Quarterly 71 (2):451-453.
    Recursivity and Contingency. By Hui Yuk.
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  48.  41
    Recursive properties of relations on models.Geoffrey R. Hird - 1993 - Annals of Pure and Applied Logic 63 (3):241-269.
    Hird, G.R., Recursive properties of relations on models, Annals of Pure and Applied Logic 63 241–269. We prove general existence theorems for recursive models on which various relations have specified recursive properties. These capture common features of results in the literature for particular algebraic structures. For a useful class of models with new relations R, S, where S is r.e., we characterize those for which there is a recursive model isomorphic to on which the relation corresponding to S remains r.e., (...)
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  49.  9
    Critique de la raison récursive.Michaël Crevoisier - 2020 - Philosophique 23.
    À propos de : Yuk Hui, Recursivity and Contingency, Londres, Rowman & Littlefield, coll. « Media Philosophy », 2019, 320 p. Le mouvement du livre suit un triple questionnement : 1) la réflexion grâce à laquelle la philosophie a cherché à systématiser la pensée peut-elle se réduire à une opération de récursivité? 2) Si oui, la notion cybernétique de feedback (rétroaction) signifie-t-elle que la machine informatique automatise ce type de réflexion et, par conséquent, réalise et achève le proje...
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    Sheaf recursion and a separation theorem.Nathanael Leedom Ackerman - 2014 - Journal of Symbolic Logic 79 (3):882-907.
    Define a second order tree to be a map between trees. We show that many properties of ordinary trees have analogs for second order trees. In particular, we show that there is a notion of “definition by recursion on a well-founded second order tree” which generalizes “definition by transfinite recursion”. We then use this new notion of definition by recursion to prove an analog of Lusin’s Separation theorem for closure spaces of global sections of a second order (...)
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