Search results for 'Recursively defined function' (try it on Scholar)

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  1. Laureano Luna (2010). Ungrounded Causal Chains and Beginningless Time. Logic and Logical Philosophy 18 (3-4):297-307.score: 90.0
    We use two logical resources, namely, the notion of recursively defined function and the Benardete-Yablo paradox, together with some inherent features of causality and time, as usually conceived, to derive two results: that no ungrounded causal chain exists and that time has a beginning.
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  2. Laureano Luna (forthcoming). No Successful Infinite Regress. Logic and Logical Philosophy.score: 79.3
    We model infinite regress structures -not arguments- by means of ungrounded recursively defined functions in order to show that no such structure can perform the task of providing determination to the items composing it, that is, that no determination process containing an infinite regress structure is successful.
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  3. Damian Rössler (2013). Infinitely $P$-Divisible Points on Abelian Varieties Defined Over Function Fields of Characteristic $Pgt 0$. Notre Dame Journal of Formal Logic 54 (3-4):579-589.score: 54.0
    In this article we consider some questions raised by F. Benoist, E. Bouscaren, and A. Pillay. We prove that infinitely $p$-divisible points on abelian varieties defined over function fields of transcendence degree one over a finite field are necessarily torsion points. We also prove that when the endomorphism ring of the abelian variety is $\mathbb{Z}$, then there are no infinitely $p$-divisible points of order a power of $p$.
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  4. Oded Ghitza (2013). The Theta-Syllable: A Unit of Speech Information Defined by Cortical Function. Frontiers in Psychology 4.score: 48.0
    A recent commentary (Oscillators and syllables: a cautionary note. Cummins, 2012) questions the validity of a class of speech perception models inspired by the possible role of neuronal oscillations in decoding speech (e.g., Ghitza 2011, Giraud & Poeppel 2012). In arguing against the approach, Cummins raises a cautionary flag “from a phonetician’s point of view.” Here we respond to his arguments from an auditory processing viewpoint, referring to a phenomenological model of Ghitza (2011) taken as a representative of the criticized (...)
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  5. Karl-Heinz Niggl (1997). Non-Definability of the Ackermann Function with Type 1 Partial Primitive Recursion. Archive for Mathematical Logic 37 (1):1-13.score: 44.0
    The paper builds on a simply typed term system ${\cal PR}^\omega $ providing a notion of partial primitive recursive functional on arbitrary Scott domains $D_\sigma$ that includes a suitable concept of parallelism. Computability on the partial continuous functionals seems to entail that Kleene's schema of higher type simultaneous course-of-values recursion (SCVR) is not reducible to partial primitive recursion. So an extension ${\cal PR}^{\omega e}$ is studied that is closed under SCVR and yet stays within the realm of subrecursiveness. The twist (...)
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  6. Hugues Leblanc & Peter Roeper (1992). Probability Functions: The Matter of Their Recursive Definability. Philosophy of Science 59 (3):372-388.score: 38.7
    This paper studies the extent to which probability functions are recursively definable. It proves, in particular, that the (absolute) probability of a statement A is recursively definable from a certain point on, to wit: from the (absolute) probabilities of certain atomic components and conjunctions of atomic components of A on, but to no further extent. And it proves that, generally, the probability of a statement A relative to a statement B is recursively definable from a certain point (...)
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  7. Nigel Cutland (1980). Computability, an Introduction to Recursive Function Theory. Cambridge University Press.score: 38.0
    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). (...)
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  8. Jesse B. Wright (1972). Characterization of Recursively Enumerable Sets. Journal of Symbolic Logic 37 (3):507-511.score: 36.7
    Let N, O and S denote the set of nonnegative integers, the graph of the constant 0 function and the graph of the successor function respectively. For sets $P, Q, R \subseteq N^2$ operations of transposition, composition, and bracketing are defined as follows: $P^\cup = \{\langle x, y\rangle | \langle y, x\rangle \epsilon P\}, PQ = \{\langle x, z\rangle| \exists y\langle x, y\rangle \epsilon P & \langle y, z\rangle \epsilon Q\}$ , and [ P, Q, R] = (...)
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  9. Efrain C. Azmitia & Particia M. Whitaker-Azmitia (1986). Searching for an Ill-Defined Brain Function Results in an Uneasy Reconciliation. Behavioral and Brain Sciences 9 (2):335.score: 36.0
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  10. F. Bagemihl (1971). A Property of the Function Ψ(Α) Defined by 2ℵα = ℵα+Ψ(Α). Mathematical Logic Quarterly 17 (1):23-24.score: 36.0
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  11. Cristian Calude, Gabriel Istrate & Marius Zimand (1992). Recursive Baire Classification and Speedable Functions. Mathematical Logic Quarterly 38 (1):169-178.score: 36.0
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  12. Mary Jane Dinardo & Thomas C. Toppino (1984). Formation of Ill-Defined Concepts as a Function of Category Size and Category Exposure. Bulletin of the Psychonomic Society 22 (4):317-320.score: 36.0
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  13. Qing Zhou (1996). Computable Real‐Valued Functions on Recursive Open and Closed Subsets of Euclidean Space. Mathematical Logic Quarterly 42 (1):379-409.score: 36.0
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  14. Farzad Didehvar (1999). On a Class of Recursively Enumerable Sets. Mathematical Logic Quarterly 45 (4):467-470.score: 33.0
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  15. Charles Morgan, Local Connectedness and Distance Functions.score: 30.0
    Local connectedness functions for (κ, 1)-simplified morasses, localisations of the coupling function c studied in [M96, §1], are defined and their elementary properties discussed. Several different, useful, canonical ways of arriving at the functions are examined. This analysis is then used to give explicit formulae for generalisations of the local distance functions which were defined recursively in [K00], leading to simple proofs of the principal properties of those functions. It is then extended to the properties of (...)
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  16. Michael Rathjen (1994). Collapsing Functions Based on Recursively Large Ordinals: A Well-Ordering Proof for KPM. [REVIEW] Archive for Mathematical Logic 33 (1):35-55.score: 30.0
    It is shown how the strong ordinal notation systems that figure in proof theory and have been previously defined by employing large cardinals, can be developed directly on the basis of their recursively large counterparts. Thereby we provide a completely new approach to well-ordering proofs as will be exemplified by determining the proof-theoretic ordinal of the systemKPM of [R91].
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  17. Peter Smith, Expressing and Capturing the Primitive Recursive Functions.score: 29.0
    The last Episode wasn’t about logic or formal theories at all: it was about common-or-garden arithmetic and the informal notion of computability. We noted that addition can be defined in terms of repeated applications of the successor function. Multiplication can be defined in terms of repeated applications of addition. The exponential and factorial functions can be defined, in different ways, in terms of repeated applications of multiplication. There’s already a pattern emerging here! The main task in (...)
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  18. Vincent W. J. Van Gerven Oei (2012). Cumposition: Theses on Philosophy's Etymology. Continent 2 (1).score: 29.0
    continent. 2.1 (2012): 44–55. Philosophers are sperm, poetry erupts sperm and dribbles, philosopher recodes term, to terminate, —A. Staley Groves 1 There is, in the relation of human languages to that of things, something that can be approximately described as “overnaming”—the deepest linguistic reason for all melancholy and (from the point of view of the thing) for all deliberate muteness. Overnaming as the linguistic being of melancholy points to another curious relation of language: the overprecision that obtains in the tragic (...)
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  19. Vincent Astier (2008). Elementary Equivalence of Some Rings of Definable Functions. Archive for Mathematical Logic 47 (4):327-340.score: 28.0
    We characterize elementary equivalences and inclusions between von Neumann regular real closed rings in terms of their boolean algebras of idempotents, and prove that their theories are always decidable. We then show that, under some hypotheses, the map sending an L-structure R to the L-structure of definable functions from R n to R preserves elementary inclusions and equivalences and gives a structure with a decidable theory whenever R is decidable. We briefly consider structures of definable functions satisfying an extra condition (...)
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  20. 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.score: 28.0
    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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  21. Bence Nanay (2010). A Modal Theory of Function. Journal of Philosophy 107 (8):412-431.score: 27.0
    The function of a trait token is usually defined in terms of some properties of other (past, present, future) tokens of the same trait type. I argue that this strategy is problematic, as trait types are (at least partly) individuated by their functional properties, which would lead to circularity. In order to avoid this problem, I suggest a way to define the function of a trait token in terms of the properties of the very same trait token. (...)
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  22. Ron Amundson & George V. Lauder (1994). Function Without Purpose. Biology and Philosophy 9 (4):443-469.score: 27.0
    Philosophers of evolutionary biology favor the so-called etiological concept of function according to which the function of a trait is its evolutionary purpose, defined as the effect for which that trait was favored by natural selection. We term this the selected effect (SE) analysis of function. An alternative account of function was introduced by Robert Cummins in a non-evolutionary and non-purposive context. Cummins''s account has received attention but little support from philosophers of biology. This paper (...)
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  23. Shan Gao, The Wave Function and Particle Ontology.score: 27.0
    In quantum mechanics, the wave function of a N-body system is a mathematical function defined in a 3N-dimensional configuration space. We argue that wave function realism implies particle ontology when assuming: (1) the wave function of a N-body system describes N physical entities; (2) each triple of the 3N coordinates of a point in configuration space that relates to one physical entity represents a point in ordinary three-dimensional space. Moreover, the motion of particles is random (...)
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  24. Richard Martin Pagni (2009). The Origin and Development of the Acidity Function. Foundations of Chemistry 11 (1):43-50.score: 27.0
    The acidity function is a thermodynamic quantitative measure of acid strength for non-aqueous and concentrated aqueous Brønsted acids, with acid strength being defined as the extent to which the acid protonates a base of known basicity. The acidity function, which was developed, both theoretically and experimentally, by Louis P. Hammett of Columbia University during the 1930s, has proven useful in the area of physical organic chemistry where it has been used to correlate rates of acid-catalyzed reactions and (...)
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  25. M. Revzen (2006). The Wigner Function as Distribution Function. Foundations of Physics 36 (4):546-562.score: 27.0
    Some entangled states have nonnegative Wigner representative function. The latter allow being viewed as a distribution function of local hidden variables. It is argued herewith that the interpretation of expectation values using such distribution functions as local hidden variable theory requires restrictions pertaining to the observables under study. The reasoning lead to support the view that violation of Bell’s inequalities that is always possible for entangled states hinges not only on the states involved but also whether the dynamical (...)
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  26. Véronique Izard, Pierre Pica, Elizabeth S. Spelke & Stanislas Dehaene (2008). Exact Equality and Successor Function: Two Key Concepts on the Path Towards Understanding Exact Numbers. Philosophical Psychology 21 (4):491 – 505.score: 27.0
    Humans possess two nonverbal systems capable of representing numbers, both limited in their representational power: the first one represents numbers in an approximate fashion, and the second one conveys information about small numbers only. Conception of exact large numbers has therefore been thought to arise from the manipulation of exact numerical symbols. Here, we focus on two fundamental properties of the exact numbers as prerequisites to the concept of EXACT NUMBERS : the fact that all numbers can be generated by (...)
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  27. W. W. Tait (1965). Functionals Defined by Transfinite Recursion. Journal of Symbolic Logic 30 (2):155-174.score: 27.0
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  28. J. W. Addison (2004). Tarski's Theory of Definability: Common Themes in Descriptive Set Theory, Recursive Function Theory, Classical Pure Logic, and Finite-Universe Logic. Annals of Pure and Applied Logic 126 (1-3):77-92.score: 27.0
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  29. Richard Beigel, William Gasarch, Martin Kummer, Georgia Martin, Timothy McNicholl & Frank Stephan (2000). The Complexity of Oddan. Journal of Symbolic Logic 65 (1):1 - 18.score: 27.0
    For a fixed set A, the number of queries to A needed in order to decide a set S is a measure of S's complexity. We consider the complexity of certain sets defined in terms of A: $ODD^A_n = \{(x_1, \dots ,x_n): {\tt\#}^A_n(x_1, \dots, x_n) \text{is odd}\}$ and, for m ≥ 2, $\text{MOD}m^A_n = \{(x_1, \dots ,x_n):{\tt\#}^A_n(x_1, \dots ,x_n) \not\equiv 0 (\text{mod} m)\},$ where ${\tt\#}^A_n(x_1, \dots ,x_n) = A(x_1)+\cdots+A(x_n)$ . (We identify A(x) with χ A (x), where χ A (...)
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  30. J. C. E. Dekker (1990). An Isolic Generalization of Cauchy's Theorem for Finite Groups. Archive for Mathematical Logic 29 (4):231-236.score: 27.0
    In his note [5] Hausner states a simple combinatorial principle, namely: $$(H)\left\{ {\begin{array}{*{20}c} {if f is a function a non - empty finite set \sigma into itself, p a} \\ {prime, f^p = i_\sigma and \sigma _0 the set of fixed points of f, then } \\ {\left| \sigma \right| \equiv \left| {\sigma _0 } \right|(mod p).} \\\end{array}} \right.$$ .He then shows how this principle can be used to prove:Fermat's little theorem,Cauchy's theorem for finite groups,Lucas' theorem for binomial numbers.Letε=(0,1, (...)
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  31. László Á Kóczy (2007). A Recursive Core for Partition Function Form Games. Theory and Decision 63 (1):41-51.score: 27.0
    We present a well-defined generalisation of the core to coalitional games with externalities, where the value of a deviation is given by an endogenous response, the solution (if nonempty: the core) of the residual game.
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  32. Bruno Kopp (2012). A Simple Hypothesis of Executive Function. Frontiers in Human Neuroscience 6.score: 27.0
    Executive function is traditionally conceptualized as a set of abilities required to guide behavior toward goals. Here, an integrated theoretical framework for executive function is developed which has its roots in the notion of hierarchical mental models. Further following Duncan (2010a,b), executive function is construed as a hierarchical recursive system of test-operation-test-exit units (Miller, Galanter, and Pribram, 1960). Importantly, it is shown that this framework can be used to model the main regional prefrontal syndromes, which are characterized (...)
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  33. Luis Elpidio Sanchis (1967). Functionals Defined by Recursion. Notre Dame Journal of Formal Logic 8 (3):161-174.score: 27.0
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  34. R. E. Vesley (1966). Review: W. W. Tait, Functionals Defined by Transfinite Recursion. [REVIEW] Journal of Symbolic Logic 31 (3):509-510.score: 27.0
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  35. R. E. Vesley (1996). Tait WW. Functionals Defined by Transfinite Recursion. Journal of Symbolic Logic 31 (3):509-510.score: 27.0
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  36. William R. Stirton (2013). A Decidable Theory of Type Assignment. Archive for Mathematical Logic 52 (5-6):631-658.score: 25.0
    This article investigates a theory of type assignment (assigning types to lambda terms) called ETA which is intermediate in strength between the simple theory of type assignment and strong polymorphic theories like Girard’s F (Proofs and types. Cambridge University Press, Cambridge, 1989). It is like the simple theory and unlike F in that the typability and type-checking problems are solvable with respect to ETA. This is proved in the article along with three other main results: (1) all primitive recursive functionals (...)
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  37. William R. Stirton (2012). How to Assign Ordinal Numbers to Combinatory Terms with Polymorphic Types. Archive for Mathematical Logic 51 (5-6):475-501.score: 25.0
    The article investigates a system of polymorphically typed combinatory logic which is equivalent to Gödel’s T. A notion of (strong) reduction is defined over terms of this system and it is proved that the class of well-formed terms is closed under both bracket abstraction and reduction. The main new result is that the number of contractions needed to reduce a term to normal form is computed by an ε 0-recursive function. The ordinal assignments used to obtain this result (...)
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  38. Somogy Varga (2011). Defining Mental Disorder. Exploring the 'Natural Function' Approach. Philosophy, Ethics, and Humanities in Medicine 6 (1):1-.score: 24.0
    Due to several socio-political factors, to many psychiatrists only a strictly objective definition of mental disorder, free of value components, seems really acceptable. In this paper, I will explore a variant of such an objectivist approach to defining metal disorder, natural function objectivism. Proponents of this approach make recourse to the notion of natural function in order to reach a value-free definition of mental disorder. The exploration of Christopher Boorse's 'biostatistical' account of natural function (1) will be (...)
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  39. Jochen Koenigsmann (2002). Defining Transcendentals in Function Fields. Journal of Symbolic Logic 67 (3):947-956.score: 24.0
    Given any field K, there is a function field F/K in one variable containing definable transcendentals over K, i.e., elements in F \ K first-order definable in the language of fields with parameters from K. Hence, the model-theoretic and the field-theoretic relative algebraic closure of K in F do not coincide. E.g., if K is finite, the model-theoretic algebraic closure of K in the rational function field K(t) is K(t). For the proof, diophantine $\emptyset-definability$ of K in F (...)
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  40. Victor Yelverton Haines (2004). Recursive Chaos in Defining Art Recursively. British Journal of Aesthetics 44 (1):73-83.score: 24.0
    Art history cannot be sealed off in cultural isolation: given our innate forms of life, language, and human nature, cultural diversity is only skin deep. The identification of art by historical recursion could not be restricted to the fixed art history of one hermetically sealed cultural tradition because there is no such thing. Attempts to define artworks recursively thus lead to the absurdity that everything in the present might be art because of unknown art antecedents in earlier human cultures (...)
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  41. José Iovino (1997). Definability in Functional Analysis. Journal of Symbolic Logic 62 (2):493-505.score: 24.0
    The role played by real-valued functions in functional analysis is fundamental. One often considers metrics, or seminorms, or linear functionals, to mention some important examples. We introduce the notion of definable real-valued function in functional analysis: a real-valued function f defined on a structure of functional analysis is definable if it can be "approximated" by formulas which do not involve f. We characterize definability of real-valued functions in terms of a purely topological condition which does not involve (...)
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  42. Luis E. Sanchis (1992). Recursive Functionals. North-Holland.score: 24.0
    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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  43. E. Herrmann (1984). Definable Structures in the Lattice of Recursively Enumerable Sets. Journal of Symbolic Logic 49 (4):1190-1197.score: 24.0
    It will be shown that in the lattice of recursively enumerable sets one can define elementarily with parameters a structure isomorphic to (∑ 0 4 , ∑ 0 3 ), i.e. isomorphic to the lattice of ∑ 0 4 sets together with a unary predicate selecting out exactly the ∑ 0 3 sets.
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  44. H. R. Strong (1970). Construction of Models for Algebraically Generalized Recursive Function Theory. Journal of Symbolic Logic 35 (3):401-409.score: 24.0
    The Uniformly Reflexive Structure was introduced by E. G. Wagner who showed that the theory of such structures generalized much of recursive function theory. In this paper Uniformly Reflexive Structures are constructed as factor algebras of Free nonassociative algebras. Wagner's question about the existence of a model with no computable splinter ("successor set") is answered in the affirmative by the construction of a model whose only computable sets are the finite sets and their complements. Finally, for each countable Boolean (...)
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  45. Arno Fehm & Wulf-Dieter Geyer (2009). A Note on Defining Transcendentals in Function Fields. Journal of Symbolic Logic 74 (4):1206 - 1210.score: 24.0
    The work [11] deals with questions of first-order definability in algebraic function fields. In particular, it exhibits new cases in which the field of constant functions is definable, and it investigates the phenomenon of definable transcendental elements. We fix some of its proofs and make additional observations concerning definable closure in these fields.
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  46. Alexander Kreuzer & Ulrich Kohlenbach (2009). Ramsey's Theorem for Pairs and Provably Recursive Functions. Notre Dame Journal of Formal Logic 50 (4):427-444.score: 24.0
    This paper addresses the strength of Ramsey's theorem for pairs ($RT^2_2$) over a weak base theory from the perspective of 'proof mining'. Let $RT^{2-}_2$ denote Ramsey's theorem for pairs where the coloring is given by an explicit term involving only numeric variables. We add this principle to a weak base theory that includes weak König's Lemma and a substantial amount of $\Sigma^0_1$-induction (enough to prove the totality of all primitive recursive functions but not of all primitive recursive functionals). In the (...)
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  47. Teresa Bigorajska (1995). On Σ1‐Definable Functions Provably Total in I ∏ 1−. Mathematical Logic Quarterly 41 (1):135-137.score: 23.3
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  48. Isaac Goldbring (2012). An Approximate Herbrand's Theorem and Definable Functions in Metric Structures. Mathematical Logic Quarterly 58 (3):208-216.score: 23.3
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  49. Frances Egan (forthcoming). Function-Theoretic Explanation and Neural Mechanisms. In David M. Kaplan (ed.), Integrating Mind and Brain Science: Mechanistic Perspectives and Beyond. Oxford University Press.score: 23.0
    A common kind of explanation in cognitive neuroscience might be called function-theoretic: with some target cognitive capacity in view, the theorist hypothesizes that the system computes a well-defined function (in the mathematical sense) and explains how computing this function contributes to the exercise of the cognitive capacity. Recently, proponents of the so-called ‘new mechanist’ approach in philosophy of science have argued that a model of a cognitive capacity is explanatory only to the extent that it reveals (...)
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  50. Richard Heersmink (2013). A Taxonomy of Cognitive Artifacts: Function, Information, and Categories. Review of Philosophy and Psychology 4 (3):1-17.score: 23.0
    The goal of this paper is to develop a systematic taxonomy of cognitive artifacts, i.e., human-made, physical objects that functionally contribute to performing a cognitive task. First, I identify the target domain by conceptualizing the category of cognitive artifacts as a functional kind: a kind of artifact that is defined purely by its function. Next, on the basis of their informational properties, I develop a set of related subcategories in which cognitive artifacts with similar properties can be grouped. (...)
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