Results for 'Conservativity'

93 found
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  1.  39
    DEFLATIONARY TRUTH: CONSERVATIVITY OR LOGICALITY?Henri Galinon - 2015 - Philosophical Quarterly 65 (259):268-274.
    It has been argued in the literature that the deflationists’ thesis about the dispensability of truth as an explanatory notion forces them to adopt a conservative theory of truth. I suggest that the deflationists’ claim that the notion of truth is akin to a logical notion should be taken more seriously. This claim casts some doubts on the adequacy of the conservativity requirement, while it also calls for further investigation to assess its philosophical plausibility.
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  2.  28
    A Generalization of Conservativity Theorem for Classical Versus Intuitionistic Arithmetic.S. Berardi - 2004 - Mathematical Logic Quarterly 50 (1):41.
    A basic result in intuitionism is Π02-conservativity. Take any proof p in classical arithmetic of some Π02-statement , with P decidable). Then we may effectively turn p in some intuitionistic proof of the same statement. In a previous paper [1], we generalized this result: any classical proof p of an arithmetical statement ∀x.∃y.P, with P of degree k, may be effectively turned into some proof of the same statement, using Excluded Middle only over degree k formulas. When k = (...)
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  3.  10
    A Semantic Approach to Conservativity.Tomasz Połacik - 2016 - Studia Logica 104 (2):235-248.
    The aim of this paper is to describe from a semantic perspective the problem of conservativity of classical first-order theories over their intuitionistic counterparts. In particular, we describe a class of formulae for which such conservativity results can be proven in case of any intuitionistic theory T which is complete with respect to a class of T-normal Kripke models. We also prove conservativity results for intuitionistic theories which are closed under the Friedman translation and complete with respect (...)
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  4. Common Nouns as Variables: Evidence From Conservativity and the Temperature Paradox.Peter Nathan Lasersohn - 2018 - In Proceedings of Sinn und Bedeutung 21. pp. 731-746.
    Common nouns and noun phrases have usually been analyzed semantically as predicates. In quantified sentences, these predicates take variables as arguments. This paper develops and defends an analysis in which common nouns and noun phrases themselves are treated as variables, rather than as predicates taking variables as arguments. Several apparent challenges for this view will be addressed, including the modal non-rigidity of common nouns. Two major advantages to treating common nouns as variables will be presented: Such an analysis predicts that (...)
     
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  5.  15
    On the Conservativity of the Axiom of Choice Over Set Theory.Timothy J. Carlson - 2011 - Archive for Mathematical Logic 50 (7-8):777-790.
    We show that for various set theories T including ZF, T + AC is conservative over T for sentences of the form ${\forall x \exists ! y}$ A(x, y) where A(x, y) is a Δ0 formula.
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  6.  12
    The Conservativity of Many : Split Scope and Most.Maribel Romero - 2018 - Topoi 37 (3):393-404.
    Besides their cardinal and proportional readings, many and few have been argued to allow for a ‘reverse’ proportional reading that defies the conservativity universal. Recently, an analysis has been developed that derives the correct truth conditions for this reading while preserving conservativity. The present paper investigates two predictions of this analysis, based on two key ingredients. First, many is decomposed into a determiner stem many and the degree operator POS. This predicts that other elements may scopally intervene between (...)
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  7.  32
    Generics, Conservativity, and Kind-Subordination.Bernhard Nickel - 2018 - Philosophers' Imprint 18.
    Many approaches to the semantics of generic sentences posit an unpronounced quantifier gen. However, while overt quantifiers are conservative, gen does not seem to be. A quantifier Q is conservative iff instances of the following schemas are equivalent: Q As are F and Q As are As that are F. All ravens are black is obviously equivalent to All ravens are ravens that are black, yet ravens are black is not equivalent to ravens are ravens that are black. This may (...)
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  8.  25
    The Intensional Many - Conservativity Reclaimed.Harald Andreas Bastiaanse - 2014 - Journal of Philosophical Logic 43 (5):883-901.
    Following on Westerståhl’s argument that many is not Conservative [9], I propose an intensional account of Conservativity as well as intensional versions of EXT and Isomorphism closure. I show that an intensional reading of many can easily possess all three of these, and provide a formal statement and proof that they are indeed proper intensionalizations. It is then discussed to what extent these intensionalized properties apply to various existing readings of many.
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  9.  55
    Conservativity of Heyting Implication Over Relevant Quantification.Robert Goldblatt - 2009 - Review of Symbolic Logic 2 (2):310-341.
    It is known that propositional relevant logics can be conservatively extended by the addition of a Heyting (intuitionistic) implication connective. We show that this same conservativity holds for a range of first-order relevant logics with strong identity axioms, using an adaptation of Fine’s stratified model theory. For systems without identity, the question of conservatively adding Heyting implication is thereby reduced to the question of conservatively adding the axioms for identity. Some results in this direction are also obtained. The conservative (...)
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  10.  25
    On the Status of Reflection and Conservativity in Replacement Theories of Truth.Jeffrey R. Schatz - 2018 - Notre Dame Journal of Formal Logic 59 (3):437-454.
    This article examines Kevin Scharp’s formal solution to the alethic paradoxes, ADT, which stands for ascending and descending truth. One of the main supposed benefits of ADT over its competitors is that it alone can validate the uses of truth concepts in theoretical contexts, such as truth-theoretic semantics. The appendixes contain a new consistency proof for ADT, and additionally show that it is conservative. As a result of its conservativity, the article argues that ADT faces a problem in accounting (...)
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  11.  9
    The Logic of Π1-Conservativity.Petr Hájek & Franco Montagna - 1990 - Archive for Mathematical Logic 30 (2):113-123.
    We show that the modal prepositional logicILM (interpretability logic with Montagna's principle), which has been shown sound and complete as the interpretability logic of Peano arithmetic PA (by Berarducci and Savrukov), is sound and complete as the logic ofπ 1-conservativity over eachbE 1-sound axiomatized theory containingI⌆ 1 (PA with induction restricted tobE 1-formulas). Furthermore, we extend this result to a systemILMR obtained fromILM by adding witness comparisons in the style of Guaspari's and Solovay's logicR (this will be done in (...)
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  12.  21
    A Simple Proof of Arithmetical Completeness for $\Pi_1$ -Conservativity Logic.Giorgi Japaridze - 1994 - Notre Dame Journal of Formal Logic 35 (3):346-354.
    Hájek and Montagna proved that the modal propositional logic ILM is the logic of -conservativity over sound theories containing I (PA with induction restricted to formulas). I give a simpler proof of the same fact.
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  13.  9
    The Logic ofII 1-Conservativity Continued.Petr Hájek & Franco Montagna - 1992 - Archive for Mathematical Logic 32 (1):57-63.
    It is shown that the propositional modal logic IRM (interpretability logic with Montagna's principle and with witness comparisons in the style of Guaspari's and Solovay's logicR) is sound and complete as the logic ofII 1-conservativity over each∑ 1-sound axiomatized theory containingI∑ 1. The exact statement of the result uses the notion of standard proof predicate. This paper is an immediate continuation of our paper [HM]. Knowledge of [HM] is presupposed. We define a modal logic, called IRM, which includes both (...)
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  14.  33
    Coercion Completion and Conservativity in Coercive Subtyping.Sergei Soloviev & Zhaohui Luo - 2001 - Annals of Pure and Applied Logic 113 (1-3):297-322.
    Coercive subtyping offers a general approach to subtyping and inheritance by introducing a simple abbreviational mechanism to constructive type theories. In this paper, we study coercion completion in coercive subtyping and prove that the formal extension with coercive subtyping of a type theory such as Martin–Löf's type theory and UTT is a conservative extension. The importance of coherence conditions for the conservativity result is also discussed.
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  15.  8
    Notes on II-Conservativity, W-Submodels, and the Collection Schema.Jeremy Avigad - unknown
    Jeremy Avigad. Notes on II-conservativity, w-submodels, and the Collection Schema.
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  16.  6
    A Phase Semantics for Polarized Linear Logic and Second Order Conservativity.Masahiro Hamano & Ryo Takemura - 2010 - Journal of Symbolic Logic 75 (1):77-102.
    This paper presents a polarized phase semantics, with respect to which the linear fragment of second order polarized linear logic of Laurent [15] is complete. This is done by adding a topological structure to Girard's phase semantics [9]. The topological structure results naturally from the categorical construction developed by Hamano—Scott [12]. The polarity shifting operator ↓ (resp. ↑) is interpreted as an interior (resp. closure) operator in such a manner that positive (resp. negative) formulas correspond to open (resp. closed) facts. (...)
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  17. Epistemic Conservativity and Imprecise Credence.Jason Konek - forthcoming - Philosophy and Phenomenological Research.
    Unspecific evidence calls for imprecise credence. My aim is to vindicate this thought. First, I will pin down what it is that makes one's imprecise credences more or less epistemically valuable. Then I will use this account of epistemic value to delineate a class of reasonable epistemic scoring rules for imprecise credences. Finally, I will show that if we plump for one of these scoring rules as our measure of epistemic value or utility, then a popular family of decision rules (...)
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  18.  20
    Conservativity for Theories of Compositional Truth Via Cut Elimination.Graham E. Leigh - 2015 - Journal of Symbolic Logic 80 (3):845-865.
  19.  40
    Conservativity and Learnability of Determiners.T. Hunter & J. Lidz - 2013 - Journal of Semantics 30 (3):315-334.
    A striking cross-linguistic generalisation about the semantics of determiners is that they never express non-conservative relations. To account for this one might hypothesise that the mechanisms underlying human language acquisition are unsuited to non-conservative determiner meanings. We present experimental evidence that 4- and 5-year-olds fail to learn a novel non-conservative determiner but succeed in learning a comparable conservative determiner, consistent with the learnability hypothesis.
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  20.  15
    A Note on Conservativity.Richard Zuber & Edward L. Keenan - forthcoming - Journal of Semantics.
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  21.  22
    Determiners, Conservativity, Witnesses.Kai von Fintel & Edward L. Keenan - 2018 - Journal of Semantics 35 (1):207-217.
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  22.  81
    Justification Logics, Logics of Knowledge, and Conservativity.Melvin Fitting - unknown
    Several justification logics have been created, starting with the logic LP, [1]. These can be thought of as explicit versions of modal logics, or of logics of knowledge or belief, in which the unanalyzed necessity (knowledge, belief) operator has been replaced with a family of explicit justification terms. We begin by sketching the basics of justification logics and their relations with modal logics. Then we move to new material. Modal logics come in various strengths. For their corresponding justification logics, differing (...)
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  23.  22
    Conservativity for Logics of Justified Belief: Two Approaches.Robert S. Milnikel - 2012 - Annals of Pure and Applied Logic 163 (7):809-819.
  24.  17
    A Note on Conservativity Relations Among Bounded Arithmetic Theories.Russell Impagliazzo & Jan Krajíček - 2002 - Mathematical Logic Quarterly 48 (3):375-377.
    For all i ≥ 1, Ti+11 is not ∀Σb2-conservative over Ti1.
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  25.  31
    Explicit Logics of Knowledge and Conservativity.Melvin Fitting - unknown
    Several justification logics have evolved, starting with the logicLP, (Artemov 2001). These can be thought of as explicit versions of modal logics, or logics of knowledge or belief, in which the unanalyzed necessity (knowledge, belief) operator has been replaced with a family of explicit justification terms. Modal logics come in various strengths. For their corresponding justification logics, differing strength is reflected in different vocabularies. What we show here is that for justification logics corresponding to modal logics extending T, various familiar (...)
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  26. Degree Quantifiers, Position of Merger Effects with Their Restrictors, and Conservativity.Rajesh Bhatt & Roumyana Pancheva - 2007 - In Chris Barker & Pauline I. Jacobson (eds.), Direct Compositionality. Oxford University Press. pp. 14--306.
     
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  27.  7
    A Theorem on Partial Conservativity in Arithmetic.Per Lindström - 2011 - Journal of Symbolic Logic 76 (1):341 - 347.
    Improving on a result of Arana, we construct an effective family (φ r | r ∈ ℚ ⋂ [0, 1]) of Σ n -conservative Π n sentences, increasing in strength as r decreases, with the property that ¬φ p is Π n -conservative over PA + φ q whenever p < q. We also construct a family of Σ n sentences with properties as above except that the roles of Σ n and Π n are reversed. The latter result allows (...)
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  28.  2
    Conservativity of Transitive Closure Over Weak Operational Set Theory.Laura Crosilla & Andrea Cantini - 2012 - In Ulrich Berger, Hannes Diener, Peter Schuster & Monika Seisenberger (eds.), Logic, Construction, Computation. De Gruyter.
    Constructive set theory a' la Myhill-Aczel has been extended in (Cantini and Crosilla 2008, Cantini and Crosilla 2010) to incorporate a notion of (partial, non--extensional) operation. Constructive operational set theory is a constructive and predicative analogue of Beeson's Inuitionistic set theory with rules and of Feferman's Operational set theory (Beeson 1988, Feferman 2006, Jaeger 2007, Jaeger 2009, Jaeger 1009b). This paper is concerned with an extension of constructive operational set theory (Cantini and Crosilla 2010) by a uniform operation of Transitive (...)
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  29.  18
    On the $\Sigma^01$-Conservativity of $\Sigma^01$-Completeness.Albert Visser - 1991 - Notre Dame Journal of Formal Logic 32 (4):554-561.
  30.  47
    Deflationism and Conservativity: Who Changed the Subject ?Henri Galinon - unknown
    Deflationists about truth hold that truth is not a substantial property. But what counts as a substantial property? We shall be interested in the thesis that the following is a necessary and sufficient condition for the non-substantiality of truth.
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  31.  3
    Conservativity of Ultrafilters Over Subsystems of Second Order Arithmetic.Antonio Montalbán & Richard A. Shore - 2018 - Journal of Symbolic Logic 83 (2):740-765.
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  32.  13
    Events and Conservativity: Clues Towards Language Evolution.Massimo Piattelli Palmarini - 2008 - In M. Cristina Amoretti & Nicla Vassallo (eds.), Knowledge, Language, and Interpretation: On the Philosophy of Donald Davidson. Ontos Verlag. pp. 81.
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  33.  4
    Conservativity: A Necessary Property for the Maximization of Witness Sets.L. Robaldo - 2013 - Logic Journal of the IGPL 21 (5):853-878.
  34.  6
    Notes on Pi^1_1 Conservativity, Omega-Submodels, and the Collection Schema.Jeremy Avigad - unknown
    These are some minor notes and observations related to a paper by Cholak, Jockusch, and Slaman [3].
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  35. The Logic of 77,-Conservativity.Petr Hajek & Franco Montagna - 1988 - Archive for Mathematical Logic 30:113-123.
     
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  36. Making Sense of Deflationism From a Formal Perspective: Conservativity and Relative Interpretability.Andrea Strollo - 2018 - In Gabriele Pulcini & Mario Piazza (eds.), Truth, Existence and Explanation. Springer Verlag.
     
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  37. The Innocence of Truth.Cezary Cieśliński - 2015 - Dialectica 69 (1):61-85.
    One of the popular explications of the deflationary tenet of ‘thinness’ of truth is the conservativeness demand: the declaration that a deflationary truth theory should be conservative over its base. This paper contains a critical discussion and assessment of this demand. We ask and answer the question of whether conservativity forms a part of deflationary doctrines.
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  38.  62
    One Connection Between Standard Invariance Conditions on Modal Formulas and Generalized Quantifiers.Dorit Ben Shalom - 2003 - Journal of Logic, Language and Information 12 (1):47-52.
    The language of standard propositional modal logic has one operator (? or ?), that can be thought of as being determined by the quantifiers ? or ?, respectively: for example, a formula of the form ?F is true at a point s just in case all the immediate successors of s verify F.This paper uses a propositional modal language with one operator determined by a generalized quantifier to discuss a simple connection between standard invariance conditions on modal formulas and generalized (...)
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  39.  18
    Complete Additivity and Modal Incompleteness.Wesley H. Holliday & Tadeusz Litak - 2019 - Review of Symbolic Logic 12 (3):487-535.
    In this article, we tell a story about incompleteness in modal logic. The story weaves together an article of van Benthem, “Syntactic aspects of modal incompleteness theorems,” and a longstanding open question: whether every normal modal logic can be characterized by a class of completely additive modal algebras, or as we call them, ${\cal V}$-baos. Using a first-order reformulation of the property of complete additivity, we prove that the modal logic that starred in van Benthem’s article resolves the open question (...)
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  40. Subtle Truths. A Formal Investigation Into Deflationism and Conservativeness.Andrea Strollo - 2010 - Dissertation, University of Torino - Italy
    At the end of the nineties some authors (Leon Horsten, Stewart Shapiro and Jeffrey Ketland) worked out a fairly technical argument against deflationary theories of truth. In a nutshell, deflationism, it was argued, is committed to conservativeness by the the claim that truth is not a substantial notion, a conservative theory (under the light of certain logico-mathematical facts) can not be an adequate theory of truth, therefore deflationism is an inadequate theory of truth. Beside the apparent simplicity of this argument, (...)
     
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  41.  15
    Ficcionalismo matemático y si-entoncismo russelliano¿ dos caras de la misma moneda?Wilfredo Quezada Pulido - 2004 - Revista de Filosofía (Madrid) 29 (2):73-97.
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  42.  32
    Consistency Statements and Iterations of Computable Functions in IΣ1 and PRA.Joost J. Joosten - 2010 - Archive for Mathematical Logic 49 (7-8):773-798.
    In this paper we will state and prove some comparative theorems concerning PRA and IΣ1. We shall provide a characterization of IΣ1 in terms of PRA and iterations of a class of functions. In particular, we prove that for this class of functions the difference between IΣ1 and PRA is exactly that, where PRA is closed under iterations of these functions, IΣ1 is moreover provably closed under iteration. We will formulate a sufficient condition for a model of PRA to be (...)
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  43.  9
    On the Fiction of the Retroaction of the Condition in Contracts.Giuliano Bacigalupo - 2016 - Philosophia Scientae 20:167-183.
    In this paper, I focus on the fiction of the retroaction of the condition in contracts, a very old tool of law which may be traced back to Roman antiquity. In the first part, I introduce the notion of a contract with a suspensive condition, i.e. a contract whose efficacy is subordinated to a future uncertain event. As will be addressed in the second part, this kind of contracts is often linked to the fiction of the retroaction of the condition (...)
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  44.  14
    Not Only Barbara.Paul J. E. Dekker - 2015 - Journal of Logic, Language and Information 24 (2):95-129.
    With this paper I aim to demonstrate that a look beyond the Aristotelian square of opposition, and a related non-conservative view on logical determiners, contributes to both the understanding of Aristotelian syllogistics as well as to the study of quantificational structures in natural language.
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  45.  14
    Harrington’s Conservation Theorem Redone.Fernando Ferreira & Gilda Ferreira - 2008 - Archive for Mathematical Logic 47 (2):91-100.
    Leo Harrington showed that the second-order theory of arithmetic WKL 0 is ${\Pi^1_1}$ -conservative over the theory RCA 0. Harrington’s proof is model-theoretic, making use of a forcing argument. A purely proof-theoretic proof, avoiding forcing, has been eluding the efforts of researchers. In this short paper, we present a proof of Harrington’s result using a cut-elimination argument.
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  46.  9
    Set Partitions and the Meaning of the Same.R. Zuber - 2017 - Journal of Logic, Language and Information 26 (1):1-20.
    It is shown that the notion of the partition of a set can be used to describe in a uniform way the meaning of the expression the same, in its basic uses in transitive and ditransitive sentences. Some formal properties of the function denoted by the same, which follow from such a description are indicated. These properties indicate similarities and differences between functions denoted by the same and generalised quantifiers.
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  47.  92
    Proof Analysis in Modal Logic.Sara Negri - 2005 - Journal of Philosophical Logic 34 (5-6):507-544.
    A general method for generating contraction- and cut-free sequent calculi for a large family of normal modal logics is presented. The method covers all modal logics characterized by Kripke frames determined by universal or geometric properties and it can be extended to treat also Gödel-Löb provability logic. The calculi provide direct decision methods through terminating proof search. Syntactic proofs of modal undefinability results are obtained in the form of conservativity theorems.
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  48.  15
    Learnability and Semantic Universals.Shane Steinert-Threlkeld & Jakub Szymanik - forthcoming - Semantics and Pragmatics.
    One of the great successes of the application of generalized quantifiers to natural language has been the ability to formulate robust semantic universals. When such a universal is attested, the question arises as to the source of the universal. In this paper, we explore the hypothesis that many semantic universals arise because expressions satisfying the universal are easier to learn than those that do not. While the idea that learnability explains universals is not new, explicit accounts of learning that can (...)
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  49.  56
    Classes and Truths in Set Theory.Kentaro Fujimoto - 2012 - Annals of Pure and Applied Logic 163 (11):1484-1523.
    This article studies three most basic systems of truth as well as their subsystems over set theory ZF possibly with AC or the axiom of global choice GC, and then correlates them with subsystems of Morse–Kelley class theory MK. The article aims at making an initial step towards the axiomatic study of truth in set theory in connection with class theory. Some new results on the side of class theory, such as conservativity, forcing and some forms of the reflection (...)
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  50.  22
    Learning From Conditionals.Benjamin Eva, Stephan Hartmann & Soroush Rafiee Rad - forthcoming - Mind:fzz025.
    In this article, we address a major outstanding question of probabilistic Bayesian epistemology: how should a rational Bayesian agent update their beliefs upon learning an indicative conditional? A number of authors have recently contended that this question is fundamentally underdetermined by Bayesian norms, and hence that there is no single update procedure that rational agents are obliged to follow upon learning an indicative conditional. Here we resist this trend and argue that a core set of widely accepted Bayesian norms is (...)
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