Results for 'definability'

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  1. Stephen Finlay, University of Southern California.Defining Normativity - 2019 - In Toh Kevin, Plunkett David & Shapiro Scott (eds.), Dimensions of Normativity: New Essays on Metaethics and Jurisprudence. New York: Oxford University Press.
     
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  2.  45
    Carnap’s Problem, Definability and Compositionality.Pedro del Valle-Inclán - 2024 - Journal of Philosophical Logic 53 (5):1321-1346.
    In his Formalization of Logic (1943) Carnap pointed out that there are non-normal interpretations of classical logic: non-standard interpretations of the connectives and quantifiers that are consistent with the classical consequence relation of a language. Different ways around the problem have been proposed. In a recent paper, Bonnay and Westerståhl argue that the key to a solution is imposing restrictions on the type of interpretation we take into account. More precisely, they claim that if we restrict attention to interpretations that (...)
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  3.  25
    Frame definability in finitely valued modal logics.Guillermo Badia, Xavier Caicedo & Carles Noguera - 2023 - Annals of Pure and Applied Logic 174 (7):103273.
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    On definability of team relations with k-invariant atoms.Raine Rönnholm - 2022 - Annals of Pure and Applied Logic 173 (10):103136.
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  5. Definability in valued Ore modules.Françoise Point - forthcoming - Bulletin of Symbolic Logic.
  6.  43
    Undefinability vs. Definability of Satisfaction and Truth.Roman Murawski - 1999 - Vienna Circle Institute Yearbook 6:203-215.
    Among the main theorems obtained in mathematical logic in this century are the so called limitation theorems, i.e., the Löwenheim-Skolem theorem on the cardinality of models of first-order theories, Gödel’s incompleteness theorems and Tarski’s theorem on the undefinability of truth. Problems connected with the latter are the subject of this paper. In Section 1 we shall consider Tarski’s theorem. In particular the original formulation of it as well as some specifications will be provided. Next various meanings of the notion of (...)
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  7. Prolegomenon to Any Future Philosophy of History.Defining an Event - 1974 - Social Research: An International Quarterly 41:439-66.
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  8.  25
    Logic in Finite Structures: Definability, Complexity, and Randomness.Scott Weinstein - 2002 - In Dale Jacquette (ed.), A Companion to Philosophical Logic. Malden, MA, USA: Wiley-Blackwell. pp. 332–348.
    This chapter contains sections titled: Validity in the Finite Model Theory in the Finite? Definability and Complexity First‐Order Definability Second‐Order Definability Inductive Definability Infinitary Logics Random Graphs and 0–1 Laws.
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  9.  38
    On Definability of Connectives and Modal Logics over FDE.Sergei P. Odintsov, Daniel Skurt & Heinrich Wansing - forthcoming - Logic and Logical Philosophy:1.
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  10.  85
    Deduction and definability in infinite statistical systems.Benjamin H. Feintzeig - 2017 - Synthese 196 (5):1-31.
    Classical accounts of intertheoretic reduction involve two pieces: first, the new terms of the higher-level theory must be definable from the terms of the lower-level theory, and second, the claims of the higher-level theory must be deducible from the lower-level theory along with these definitions. The status of each of these pieces becomes controversial when the alleged reduction involves an infinite limit, as in statistical mechanics. Can one define features of or deduce the behavior of an infinite idealized system from (...)
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  11. " In vain have I Smitten your children".Augustine Defines Just War - 2006 - In R. Joseph Hoffmann (ed.), The Just War and Jihad. Prometheus Press.
     
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  12.  39
    Infinite combinatorics and definability.Arnold W. Miller - 1989 - Annals of Pure and Applied Logic 41 (2):179-203.
  13.  14
    On the definability of mad families of vector spaces.Haim Horowitz & Saharon Shelah - 2022 - Annals of Pure and Applied Logic 173 (4):103079.
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  14.  19
    Chapter 5. The Recursive Definability of Probability Functions.Peter Roeper & Hughes Leblanc - 1999 - In Peter Roeper & Hugues Leblanc (eds.), Probability Theory and Probability Semantics. University of Toronto Press. pp. 78-98.
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  15.  43
    Structure and definability in general bounded arithmetic theories.Chris Pollett - 1999 - Annals of Pure and Applied Logic 100 (1-3):189-245.
    The bounded arithmetic theories R2i, S2i, and T2i are closely connected with complexity theory. This paper is motivated by the questions: what are the Σi+1b-definable multifunctions of R2i? and when is one theory conservative over another? To answer these questions we consider theories , and where induction is restricted to prenex formulas. We also define which has induction up to the 0 or 1-ary L2-terms in the set τ. We show and and for . We show that the -multifunctions of (...)
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  16. Definability of measures and ultrafilters.David Pincus & Robert M. Solovay - 1977 - Journal of Symbolic Logic 42 (2):179-190.
  17.  35
    Two-variable logic has weak, but not strong, Beth definability.Hajnal Andréka & István Németi - 2021 - Journal of Symbolic Logic 86 (2):785-800.
    We prove that the two-variable fragment of first-order logic has the weak Beth definability property. This makes the two-variable fragment a natural logic separating the weak and the strong Beth properties since it does not have the strong Beth definability property.
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  18. Definability and Invariance.A. A. M. Rodrigues & N. C. A. da Costa - 2007 - Studia Logica 86 (1):1-30.
    In his thesis 'Para uma Teoria Geral dos Homomorfismos' (1944) the Portuguese mathematician José Sebastião e Silva constructed an abstract or generalized Galois theory, that is intimately linked to F. Klein’s Erlangen Program and that foreshadows some notions and results of today’s model theory; an analogous theory was independently worked out by M. Krasner in 1938. In this paper, we present a version of the theory making use of tools which were not at Silva’s disposal. At the same time, we (...)
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  19.  69
    Note on Supervenience and Definability.Lloyd Humberstone - 1998 - Notre Dame Journal of Formal Logic 39 (2):243-252.
    The idea of a property's being supervenient on a class of properties is familiar from much philosophical literature. We give this idea a linguistic turn by converting it into the idea of a predicate symbol's being supervenient on a set of predicate symbols relative to a (first order) theory. What this means is that according to the theory, any individuals differing in respect to whether the given predicate applies to them also differ in respect to the application of at least (...)
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  20.  54
    First-Order Definability of Transition Structures.Antje Rumberg & Alberto Zanardo - 2019 - Journal of Logic, Language and Information 28 (3):459-488.
    The transition semantics presented in Rumberg (J Log Lang Inf 25(1):77–108, 2016a) constitutes a fine-grained framework for modeling the interrelation of modality and time in branching time structures. In that framework, sentences of the transition language L_t are evaluated on transition structures at pairs consisting of a moment and a set of transitions. In this paper, we provide a class of first-order definable Kripke structures that preserves L_t-validity w.r.t. transition structures. As a consequence, for a certain fragment of L_t, validity (...)
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  21.  14
    Completeness and Definability of a Modal Logic Interpreted over Iterated Strict Partial Orders.Philippe Baldiani & Levan Uridia - 1998 - In Marcus Kracht, Maarten de Rijke, Heinrich Wansing & Michael Zakharyaschev (eds.), Advances in Modal Logic. CSLI Publications. pp. 71-88.
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  22.  19
    κ‐Madness and definability.Haim Horowitz & Saharon Shelah - 2022 - Mathematical Logic Quarterly 68 (3):346-351.
    Assuming the existence of a supercompact cardinal, we construct a model where, for some uncountable regular cardinal κ, there are no κ‐mad families.
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  23.  8
    Interpolation and Beth Definability over the Minimal Logic.Larisa Maksimova - 1998 - In Marcus Kracht, Maarten de Rijke, Heinrich Wansing & Michael Zakharyaschev (eds.), Advances in Modal Logic. CSLI Publications. pp. 459-463.
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  24.  19
    Definability and commonsense reasoning.Gianni Amati, Luigia Carlucci Aiello & Fiora Pirri - 1997 - Artificial Intelligence 93 (1-2):169-199.
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  25.  39
    Definability Aspects of the Denjoy Integral.Walsh Sean - forthcoming - Fundamenta Mathematicae.
    The Denjoy integral is an integral that extends the Lebesgue integral and can integrate any derivative. In this paper, it is shown that the graph of the indefinite Denjoy integral f↦∫xaf is a coanalytic non-Borel relation on the product space M[a,b]×C[a,b], where M[a,b] is the Polish space of real-valued measurable functions on [a,b] and where C[a,b] is the Polish space of real-valued continuous functions on [a,b]. Using the same methods, it is also shown that the class of indefinite Denjoy integrals, (...)
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  26.  16
    Definitions and Definability: Philosophical Perspectives.J. H. Fetzer, D. Shatz & G. Schlesinger - 1991 - Springer.
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  27.  28
    On the Modal Definability of Simulability by Finite Transitive Models.David Fernández Duque - 2011 - Studia Logica 98 (3):347-373.
    We show that given a finite, transitive and reflexive Kripke model 〈 W , ≼, ⟦ ⋅ ⟧ 〉 and $${w \in W}$$ , the property of being simulated by w (i.e., lying on the image of a literalpreserving relation satisfying the ‘forth’ condition of bisimulation) is modally undefinable within the class of S4 Kripke models. Note the contrast to the fact that lying in the image of w under a bi simulation is definable in the standard modal language even (...)
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  28.  45
    Admissible sets and structures: an approach to definability theory.Jon Barwise - 1975 - New York: Springer Verlag.
  29.  26
    Correction to: Deduction and definability in infinite statistical systems.Benjamin H. Feintzeig - 2018 - Synthese 197 (12):5539-5540.
    Prop. 1 on p. 10 is false as stated. The proof implicitly assumes that all Cauchy sequences.
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  30.  41
    Robinson Raphael M.. Arithmetical definability of field elements.Rózsa Péter - 1952 - Journal of Symbolic Logic 17 (4):270-270.
  31.  25
    Game-theoretic inductive definability.Juha Oikkonen & Jouko Väänänen - 1993 - Annals of Pure and Applied Logic 65 (3):265-306.
    Oikkonen, J. and J. Väänänen, Game-theoretic inductive definability, Annals of Pure and Applied Logic 65 265-306. We use game-theoretic ideas to define a generalization of the notion of inductive definability. This approach allows induction along non-well-founded trees. Our definition depends on an underlying partial ordering of the objects. In this ordering every countable ascending sequence is assumed to have a unique supremum which enables us to go over limits. We establish basic properties of this induction and examine examples (...)
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  32.  59
    Definability problems for modules and rings.Gabriel Sabbagh & Paul Eklof - 1971 - Journal of Symbolic Logic 36 (4):623-649.
  33. Games and definability for FPC.Guy McCusker - 1997 - Bulletin of Symbolic Logic 3 (3):347-362.
    A new games model of the language FPC, a type theory with products, sums, function spaces and recursive types, is described. A definability result is proved, showing that every finite element of the model is the interpretation of some term of the language.
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  34.  56
    A critique of Suits’s (alleged) counterexample to Wittgenstein’s position on the definability of ‘game’.Ralph H. Johnson & Dennis Hudecki - 2019 - Journal of the Philosophy of Sport 47 (1):89-104.
    A central theme in the philosophy of sport literature is the definability of games. According to Thomas Hurka, and others, the argument presented by Bernard Suits in The Grasshopper refutes...
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  35.  72
    Interpolation and definability in guarded fragments.Eva Hoogland & Maarten Marx - 2002 - Studia Logica 70 (3):373 - 409.
    The guarded fragment (GF) was introduced by Andréka, van Benthem and Németi as a fragment of first order logic which combines a great expressive power with nice, modal behavior. It consists of relational first order formulas whose quantifiers are relativized by atoms in a certain way. Slightly generalizing the admissible relativizations yields the packed fragment (PF). In this paper we investigate interpolation and definability in these fragments. We first show that the interpolation property of first order logic fails in (...)
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  36.  59
    Interpolation and definability in abstract logics.Finn V. Jensen - 1974 - Synthese 27 (1-2):251 - 257.
    A semantical definition of abstract logics is given. It is shown that the Craig interpolation property implies the Beth definability property, and that the Souslin-Kleene interpolation property implies the weak Beth definability property. An example is given, showing that Beth does not imply Souslin-Kleene.
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  37.  54
    A paradox of definability: Richard's and poincaré's ways out.Keith Simmons - 1994 - History and Philosophy of Logic 15 (1):33-44.
    In 1905, Richard discovered his paradox of definability, and in a letter written that year he presented both the paradox and a solution to it.Soon afterwards, Poincaré endorsed a variant of Richard?s solution.In this paper, I critically examine Richard?s and Poincaré?s ways out.I draw on an objection of Peano?s, and argue that their stated solutions do not work.But I also claim that their writings suggest another way out, different from their stated solutions, and different from the orthodox Tarskian approach.I (...)
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  38.  30
    An application of invariant sets to global definability.Douglas E. Miller - 1979 - Journal of Symbolic Logic 44 (1):9-14.
    Vaught's " * -transform method" is applied to derive a global definability theorem of M. Makkai from a classical theorem of Lusin.
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  39.  28
    (1 other version)On definability of ordinals in logic with infinitely long expressions.Akiko Kino - 1966 - Journal of Symbolic Logic 31 (3):365-375.
  40.  24
    (1 other version)Second‐order and Inductive Definability on Finite Structures.Michel De Rougemont - 1987 - Mathematical Logic Quarterly 33 (1):47-63.
  41.  20
    (1 other version)Decidability and Definability Results Concerning Well‐Orderings and Some Extensions of First Order Logic.Bogdan Stanislaw Chlebus - 1980 - Mathematical Logic Quarterly 26 (34‐35):529-536.
  42.  35
    Some local definability results on countable topological structures.Holger Eisenmenger - 1983 - Journal of Symbolic Logic 48 (3):683-692.
  43.  27
    On the definability of join by means of polynomials in implicative algebras.Antoni Torrens - 1985 - Bulletin of the Section of Logic 14 (4):158-162.
    In this paper we see that the answer of this question is affirmative. We prove this for Dco-algebras and as special case we obtain the result for Positive Implication algebras. First we give, without proof, the properties of Dco-algebras and S-algebras and their connection with Positive Implication algebras and Implication algebras. These results can be found in [T] and [IT].
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  44.  82
    Universal First‐Order Definability in Modal Logic.R. E. Jennings, D. K. Johnston & P. K. Schotch - 1980 - Mathematical Logic Quarterly 26 (19-21):327-330.
  45. Definability and undefinability with real order at the background.Yuri Gurevich & Alexander Rabinovich - 2000 - Journal of Symbolic Logic 65 (2):946-958.
  46.  20
    Definability in self-referential systems.J. Zimbarg Sobrinho - 1988 - Notre Dame Journal of Formal Logic 29 (4):574-578.
  47.  41
    Intuitionistic logic and implicit definability.Larisa Maksimova - 2000 - Annals of Pure and Applied Logic 105 (1-3):83-102.
    It is proved that there are exactly 16 superintuitionistic propositional logics with the projective Beth property. These logics are finitely axiomatizable and have the finite model property. Simultaneously, all varieties of Heyting algebras with strong epimorphisms surjectivity are found.
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  48.  18
    Forcing Axioms and the Definability of the Nonstationary Ideal on the First Uncountable.Stefan Hoffelner, Paul Larson, Ralf Schindler & W. U. Liuzhen - 2024 - Journal of Symbolic Logic 89 (4):1641-1658.
    We show that under $\mathsf {BMM}$ and “there exists a Woodin cardinal, $"$ the nonstationary ideal on $\omega _1$ cannot be defined by a $\Pi _1$ formula with parameter $A \subset \omega _1$. We show that the same conclusion holds under the assumption of Woodin’s $(\ast )$ -axiom. We further show that there are universes where $\mathsf {BPFA}$ holds and $\text {NS}_{\omega _1}$ is $\Pi _1(\{\omega _1\})$ -definable. Lastly we show that if the canonical inner model with one Woodin cardinal (...)
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  49. On the Mutual Definability of the Notions of Entailment, Rejection, and Inconsistency.Urszula Wybraniec-Skardowska - 2016 - Axioms 5 (15).
    In this paper, two axiomatic theories T− and T′ are constructed, which are dual to Tarski’s theory T+ (1930) of deductive systems based on classical propositional calculus. While in Tarski’s theory T+ the primitive notion is the classical consequence function (entailment) Cn+, in the dual theory T− it is replaced by the notion of Słupecki’s rejection consequence Cn− and in the dual theory T′ it is replaced by the notion of the family Incons of inconsistent sets. The author has proved (...)
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  50. From Linear to Branching-Time Temporal Logics: Transfer of Semantics and Definability.Valentin Goranko & Alberto Zanardo - 2007 - Logic Journal of the IGPL 15 (1):53-76.
    This paper investigates logical aspects of combining linear orders as semantics for modal and temporal logics, with modalities for possible paths, resulting in a variety of branching time logics over classes of trees. Here we adopt a unified approach to the Priorean, Peircean and Ockhamist semantics for branching time logics, by considering them all as fragments of the latter, obtained as combinations, in various degrees, of languages and semantics for linear time with a modality for possible paths. We then consider (...)
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