Results for 'Recursion'

927 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.  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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  3.  60
    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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  4.  7
    Recursion: Complexity in Cognition.Tom Roeper & Margaret Speas (eds.) - 2014 - Cham: Imprint: Springer.
    This volume focuses on recursion and reveals a host of new theoretical arguments, philosophical perspectives, formal representations, and empirical evidence from parsing, acquisition, and computer models, highlighting its central role in modern science. Noam Chomsky, whose work introduced recursion to linguistics and cognitive science, and other leading researchers in the fields of philosophy, semantics, computer science, and psycholinguistics in showing the profound reach of this concept into modern science. Recursion has been at the heart of generative grammar (...)
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  5.  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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  6.  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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  7. Recursive Bayesian Nets for Prediction, Explanation and Control in Cancer Science.Jon Williamson - unknown
    this paper we argue that the formalism can also be applied to modelling the hierarchical structure of physical mechanisms. The resulting network contains quantitative information about probabilities, as well as qualitative information about mechanistic structure and causal relations. Since information about probabilities, mechanisms and causal relations are vital for prediction, explanation and control respectively, a recursive Bayesian net can be applied to all these tasks. We show how a Recursive Bayesian Net can be used to model mechanisms in cancer science. (...)
     
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  8.  42
    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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  9.  25
    Recursion-theoretic hierarchies.Peter G. Hinman - 1978 - New York: Springer Verlag.
  10.  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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  11.  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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  12.  41
    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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  13.  37
    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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  14.  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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  15.  41
    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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  16.  20
    Remarks on Recursive Definitions of Truth.Philippe de Rouilhan - unknown
    For the sake of simplicity, we adopt the same logical frame as Tarski's in his Wahrheitsbegriff (Wb). There, Tarski is mainly interested in the possibility of explicitely defining truth for an object-language, he does not pay much attention to recursive definitions of truth. We say why. However, recursive definitions have advantages of their own. In particular, we prove the positive theorem: if L is of finite order ≥ 4, then a recursive definition is possible for L in a metalanguage of (...)
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  17. (1 other version)Limiting recursion.E. Mark Gold - 1965 - Journal of Symbolic Logic 30 (1):28-48.
    A class of problems is called decidable if there is an algorithm which will give the answer to any problem of the class after a finite length of time. The purpose of this paper is to discuss the classes of problems that can be solved by infinitely long decision procedures in the following sense: An algorithm is given which, for any problem of the class, generates an infinitely long sequence of guesses. The problem will be said to be solved in (...)
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  18. Simple recursively-based pseudorecursive varieties of semigroups.B. Wells - 1995 - Bulletin of Symbolic Logic 1:371.
  19. Neoliberalism, recursivity, theatre.Patricia Ybarra - 2018 - In Stephannie S. Gearhart & Jonathan L. Chambers, Reversing the cult of speed in higher education: the slow movement in the arts and humanities. New York: Routledge.
     
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  20.  44
    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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  21.  54
    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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  22.  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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  23.  55
    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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  24. Recursive techniques in programming, de DW Barron.Enric Casaban Moya - 1972 - Teorema: International Journal of Philosophy 2 (5):136-138.
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  25.  28
    (1 other version)On Recursive Definitions in Empirical Sciences.Yehoshua Bar-Hillel - 1953 - Proceedings of the XIth International Congress of Philosophy 5:160-165.
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  26.  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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  27. Recursion Hypothesis Considered as a Research Program for Cognitive Science.Pauli Brattico - 2010 - Minds and Machines 20 (2):213-241.
    Humans grasp discrete infinities within several cognitive domains, such as in language, thought, social cognition and tool-making. It is sometimes suggested that any such generative ability is based on a computational system processing hierarchical and recursive mental representations. One view concerning such generativity has been that each of the mind’s modules defining a cognitive domain implements its own recursive computational system. In this paper recent evidence to the contrary is reviewed and it is proposed that there is only one supramodal (...)
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  28. Recursively enumerable generic sets.Wolfgang Maass - 1982 - Journal of Symbolic Logic 47 (4):809-823.
    We show that one can solve Post's Problem by constructing generic sets in the usual set theoretic framework applied to tiny universes. This method leads to a new class of recursively enumerable sets: r.e. generic sets. All r.e. generic sets are low and simple and therefore of Turing degree strictly between 0 and 0'. Further they supply the first example of a class of low recursively enumerable sets which are automorphic in the lattice E of recursively enumerable sets with inclusion. (...)
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  29.  40
    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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  30.  72
    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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  31. Theory of recursive functions and effective computability.Hartley Rogers - 1987 - Cambridge: MIT Press.
  32. 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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  33. Recursión.José Pedro Ubeda Rives - 2011 - In Luis Vega and Paula Olmos, Compendio de Lógica, Argumentación y Retórica. [Madrid]: Editorial Trotta.
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  34.  39
    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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  35.  45
    Primitive recursive real numbers.Qingliang Chen, Kaile Su & Xizhong Zheng - 2007 - Mathematical Logic Quarterly 53 (4‐5):365-380.
    In mathematics, various representations of real numbers have been investigated. All these representations are mathematically equivalent because they lead to the same real structure – Dedekind-complete ordered field. Even the effective versions of these representations are equivalent in the sense that they define the same notion of computable real numbers. Although the computable real numbers can be defined in various equivalent ways, if “computable” is replaced by “primitive recursive” , these definitions lead to a number of different concepts, which we (...)
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  36.  53
    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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  37. 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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  38.  16
    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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  39. Puzzles for Recursive Reliabilism.Shun Iizuka - 2022 - Review of Analytic Philosophy 2 (1):55-73.
    The recursive aspect of process reliabilism has rarely been examined. The regress puzzle, which illustrates infinite regress arising from the combination of the recursive structure and the no-defeater condition incorporated into it, is a valuable exception. However, this puzzle can be dealt with in the framework of process reliabilism by reconsidering the relationship between the recursion and the no-defeater condition based on the distinction between prima facie and ultima facie justification. Thus, the regress puzzle is not a basis for (...)
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  40.  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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  41.  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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  42.  38
    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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  43.  33
    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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  44.  75
    Induction–recursion and initial algebras.Peter Dybjer & Anton Setzer - 2003 - Annals of Pure and Applied Logic 124 (1-3):1-47.
    Induction–recursion is a powerful definition method in intuitionistic type theory. It extends inductive definitions and allows us to define all standard sets of Martin-Löf type theory as well as a large collection of commonly occurring inductive data structures. It also includes a variety of universes which are constructive analogues of inaccessibles and other large cardinals below the first Mahlo cardinal. In this article we give a new compact formalization of inductive–recursive definitions by modeling them as initial algebras in slice (...)
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  45. Sets, models and recursion theory.John N. Crossley (ed.) - 1967 - Amsterdam,: North-Holland Pub. Co..
     
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  46.  54
    Recursive and r.e. quotient Boolean algebras.John J. Thurber - 1994 - Archive for Mathematical Logic 33 (2):121-129.
    We prove a converse to one of the theorems from [F], giving a description in terms of Turing complexity of sets which can be coded into recursive and r.e. quotient Boolean algebras.
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  47.  99
    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 (...)
  48.  80
    Recursive expected utility and the separation of attitudes towards risk and ambiguity: an experimental study. [REVIEW]Sujoy Chakravarty & Jaideep Roy - 2008 - Theory and Decision 66 (3):199-228.
    We use the multiple price list method and a recursive expected utility theory of smooth ambiguity to separate out attitude towards risk from that towards ambiguity. Based on this separation, we investigate if there are differences in agent behaviour under uncertainty over gain amounts vis-a-vis uncertainty over loss amounts. On an aggregate level, we find that (i) subjects are risk averse over gains and risk seeking over losses, displaying a “reflection effect” and (ii) they are ambiguity neutral over gains and (...)
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  49. Recursive filtering of a rate modulated stochastic process.A. V. Cameron - 1968 - In Peter Koestenbaum, Proceedings. [San Jose? Calif.,: [San Jose? Calif.. pp. 456.
     
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  50. 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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