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  1. Model-theoretic semantics and revenge paradoxes.Lorenzo Rossi - 2019 - Philosophical Studies 176 (4):1035-1054.
    Revenge arguments purport to show that any proposed solution to the semantic paradoxes generates new paradoxes that prove that solution to be inadequate. In this paper, I focus on revenge arguments that employ the model-theoretic semantics of a target theory and I argue, contra the current revenge-theoretic wisdom, that they can constitute genuine expressive limitations. I consider the anti-revenge strategy elaborated by Field and argue that it does not offer a way out of the revenge problem. More generally, I argue (...)
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  • Defining LFIs and LFUs in extensions of infectious logics.Szmuc Damian Enrique - 2016 - Journal of Applied Non-Classical Logics 26 (4):286-314.
    The aim of this paper is to explore the peculiar case of infectious logics, a group of systems obtained generalizing the semantic behavior characteristic of the -fragment of the logics of nonsense, such as the ones due to Bochvar and Halldén, among others. Here, we extend these logics with classical negations, and we furthermore show that some of these extended systems can be properly regarded as logics of formal inconsistency and logics of formal undeterminedness.
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  • (1 other version)Classes of Recursively Enumerable Sets and Degrees of Unsolvability.Donald A. Martin - 1966 - Mathematical Logic Quarterly 12 (1):295-310.
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  • (1 other version)Forms of Luminosity: Epistemic Modality and Hyperintensionality in Mathematics.David Elohim - 2017 - Dissertation, Arché, University of St Andrews
    This book concerns the foundations of epistemic modality and hyperintensionality and their applications to the philosophy of mathematics. David Elohim examines the nature of epistemic modality, when the modal operator is interpreted as concerning both apriority and conceivability, as well as states of knowledge and belief. The book demonstrates how epistemic modality and hyperintensionality relate to the computational theory of mind; metaphysical modality and hyperintensionality; the types of mathematical modality and hyperintensionality; to the epistemic status of large cardinal axioms, undecidable (...)
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  • LP, K3, and FDE as Substructural Logics.Lionel Shapiro - 2017 - In Arazim Pavel & Lávička Tomáš (eds.), The Logica Yearbook 2016. College Publications.
    Building on recent work, I present sequent systems for the non-classical logics LP, K3, and FDE with two main virtues. First, derivations closely resemble those in standard Gentzen-style systems. Second, the systems can be obtained by reformulating a classical system using nonstandard sequent structure and simply removing certain structural rules (relatives of exchange and contraction). I clarify two senses in which these logics count as “substructural.”.
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  • What is morphological computation? On how the body contributes to cognition and control.Vincent Müller & Matej Hoffmann - 2017 - Artificial Life 23 (1):1-24.
    The contribution of the body to cognition and control in natural and artificial agents is increasingly described as “off-loading computation from the brain to the body”, where the body is said to perform “morphological computation”. Our investigation of four characteristic cases of morphological computation in animals and robots shows that the ‘off-loading’ perspective is misleading. Actually, the contribution of body morphology to cognition and control is rarely computational, in any useful sense of the word. We thus distinguish (1) morphology that (...)
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  • Theological Underpinnings of the Modern Philosophy of Mathematics.Vladislav Shaposhnikov - 2016 - Studies in Logic, Grammar and Rhetoric 44 (1):147-168.
    The study is focused on the relation between theology and mathematics in the situation of increasing secularization. My main concern in the second part of this paper is the early-twentieth-century foundational crisis of mathematics. The hypothesis that pure mathematics partially fulfilled the functions of theology at that time is tested on the views of the leading figures of the three main foundationalist programs: Russell, Hilbert and Brouwer.
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  • (1 other version)Some Remarks on Uniform Halting Problems.Stephen L. Bloom - 1971 - Mathematical Logic Quarterly 17 (1):281-284.
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  • (2 other versions)Some Notions of Reducibility and Productiveness.A. H. Lachlan - 1965 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 11 (1):17-44.
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  • Supervaluationism and Its Logics.Achille C. Varzi - 2007 - Mind 116 (463):633-676.
    What sort of logic do we get if we adopt a supervaluational semantics for vagueness? As it turns out, the answer depends crucially on how the standard notion of validity as truth preservation is recasted. There are several ways of doing that within a supervaluational framework, the main alternative being between “global” construals (e.g., an argument is valid iff it preserves truth-under-all-precisifications) and “local” construals (an argument is valid iff, under all precisifications, it preserves truth). The former alternative is by (...)
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  • Neo-Logicism and Its Logic.Panu Raatikainen - 2020 - History and Philosophy of Logic 41 (1):82-95.
    The rather unrestrained use of second-order logic in the neo-logicist program is critically examined. It is argued in some detail that it brings with it genuine set-theoretical existence assumptions and that the mathematical power that Hume’s Principle seems to provide, in the derivation of Frege’s Theorem, comes largely from the ‘logic’ assumed rather than from Hume’s Principle. It is shown that Hume’s Principle is in reality not stronger than the very weak Robinson Arithmetic Q. Consequently, only a few rudimentary facts (...)
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  • Translations of Logical Formulas and the Equiconsistency Problem.Andrei A. Kuzichev - 1994 - Mathematical Logic Quarterly 40 (1):44-50.
    A translation of formulas in a language L1 to formulas in a language L2 is a mapping which preserves the parameters and commutes with the substitution prefix, the propositional connectives and the quantifiers. Every translation generates a corresponding transformation of theories in L1 to theories in L2. We formulate the equiconsistency problem for such transformations and propose a variant of its solution. First, for a transformation F we find the least theory A in L1 such that its inclusion in a (...)
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  • Modal sequents for normal modal logics.Claudio Cerrato - 1993 - Mathematical Logic Quarterly 39 (1):231-240.
    We present sequent calculi for normal modal logics where modal and propositional behaviours are separated, and we prove a cut elimination theorem for the basic system K, so as completeness theorems both for K itself and for its most popular enrichments. MSC: 03B45, 03F05.
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  • On the connection between Nonstandard Analysis and Constructive Analysis.Sam Sanders - forthcoming - Logique Et Analyse.
    Constructive Analysis and Nonstandard Analysis are often characterized as completely antipodal approaches to analysis. We discuss the possibility of capturing the central notion of Constructive Analysis (i.e. algorithm, finite procedure or explicit construction) by a simple concept inside Nonstandard Analysis. To this end, we introduce Omega-invariance and argue that it partially satisfies our goal. Our results provide a dual approach to Erik Palmgren's development of Nonstandard Analysis inside constructive mathematics.
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  • The Paraconsistent Logic of Quantum Superpositions.Newton C. A. da Costa & Christian de Ronde - 2013 - Foundations of Physics 43 (7):845-858.
    Physical superpositions exist both in classical and in quantum physics. However, what is exactly meant by ‘superposition’ in each case is extremely different. In this paper we discuss some of the multiple interpretations which exist in the literature regarding superpositions in quantum mechanics. We argue that all these interpretations have something in common: they all attempt to avoid ‘contradiction’. We argue in this paper, in favor of the importance of developing a new interpretation of superpositions which takes into account contradiction, (...)
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  • (1 other version)Non-Alethic Meinongian Logic.Nicola Grana - 2010 - Principia: An International Journal of Epistemology 14 (1):99-110.
    O propósito deste trabalho é fornecer uma resposta a duas questões fundamentais: 1) pode uma lógica não alética ser uma lógica meinongiana? E consequentemente 2) pode uma lógica não alética ser uma lógica adequada a uma teoria meinongiana dos objetos? Usando os resultados de da Costa (1989) e da Costa & Marconi (1986) e além disso de da Costa (1986 e 1993), proponho uma lógica minimal não alética de primeira ordem com identidade e o símblo " de Hilbert (da Costa (...)
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  • Axioms in Mathematical Practice.Dirk Schlimm - 2013 - Philosophia Mathematica 21 (1):37-92.
    On the basis of a wide range of historical examples various features of axioms are discussed in relation to their use in mathematical practice. A very general framework for this discussion is provided, and it is argued that axioms can play many roles in mathematics and that viewing them as self-evident truths does not do justice to the ways in which mathematicians employ axioms. Possible origins of axioms and criteria for choosing axioms are also examined. The distinctions introduced aim at (...)
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  • A survey of Mučnik and Medvedev degrees.Peter G. Hinman - 2012 - Bulletin of Symbolic Logic 18 (2):161-229.
    We survey the theory of Mucnik and Medvedev degrees of subsets of $^{\omega}{\omega}$with particular attention to the degrees of $\Pi_{1}^{0}$ subsets of $^{\omega}2$. Sections 1-6 present the major definitions and results in a uniform notation. Sections 7-6 present proofs, some more complete than others, of the major results of the subject together with much of the required background material.
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  • Quantifier probability logic and the confirmation paradox.Theodore Hailperin - 2007 - History and Philosophy of Logic 28 (1):83-100.
    Exhumation and study of the 1945 paradox of confirmation brings out the defect of its formulation. In the context of quantifier conditional-probability logic it is shown that a repair can be accomplished if the truth-functional conditional used in the statement of the paradox is replaced with a connective that is appropriate to the probabilistic context. Description of the quantifier probability logic involved in the resolution of the paradox is presented in stages. Careful distinction is maintained between a formal logic language (...)
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  • Formalizations après la lettre: Studies in Medieval Logic and Semantics.Catarina Dutilh Novaes - 2006 - Dissertation, Leiden University
    This thesis is on the history and philosophy of logic and semantics. Logic can be described as the ‘science of reasoning’, as it deals primarily with correct patterns of reasoning. However, logic as a discipline has undergone dramatic changes in the last two centuries: while for ancient and medieval philosophers it belonged essentially to the realm of language studies, it has currently become a sub-branch of mathematics. This thesis attempts to establish a dialogue between the modern and the medieval traditions (...)
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  • Proceedings of Sinn und Bedeutung 9.Emar Maier, Corien Bary & Janneke Huitink (eds.) - 2005 - Nijmegen Centre for Semantics.
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  • On understanding understanding.Roger Penrose - 1997 - International Studies in the Philosophy of Science 11 (1):7 – 20.
    It is argued, by use of specific examples, that mathematical understanding is something which cannot be modelled in terms of entirely computational procedures. Our conception of a natural number (a non-negative integer: 0, 1, 2, 3,…) is something which goes beyond any formulation in terms of computational rules. Our ability to perceive the properties of natural numbers depends upon our awareness, and represents just one of the many ways in which awareness provides an essential ingredient to our ability to understand. (...)
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  • (1 other version)Valuation Semantics for Intuitionic Propositional Calculus and some of its Subcalculi.Andréa Loparić - 2010 - Principia: An International Journal of Epistemology 14 (1):125-133.
    In this paper, we present valuation semantics for the Propositional Intuitionistic Calculus (also called Heyting Calculus) and three important subcalculi: the Implicative, the Positive and the Minimal Calculus (also known as Kolmogoroff or Johansson Calculus). Algorithms based in our definitions yields decision methods for these calculi.
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  • Descriptions in Mathematical Logic.Gerard R. Renardel - 1984 - Studia Logica 43 (3):281-294.
    After a discussion of the different treatments in the literature of vacuous descriptions, the notion of descriptor is slightly generalized to function descriptor Ⅎ $\overset \rightarrow \to{y}$, so as to form partial functions φ = Ⅎ $y.A$ which satisfy $\forall \overset \rightarrow \to{x}z\leftrightarrow y=z))$. We use logic with existence predicate, as introduced by D. S. Scott, to handle partial functions, and prove that adding function descriptors to a theory based on such a logic is conservative. For theories with quantification over (...)
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  • Schemata: The concept of schema in the history of logic.John Corcoran - 2006 - Bulletin of Symbolic Logic 12 (2):219-240.
    The syllogistic figures and moods can be taken to be argument schemata as can the rules of the Stoic propositional logic. Sentence schemata have been used in axiomatizations of logic only since the landmark 1927 von Neumann paper [31]. Modern philosophers know the role of schemata in explications of the semantic conception of truth through Tarski’s 1933 Convention T [42]. Mathematical logicians recognize the role of schemata in first-order number theory where Peano’s second-order Induction Axiom is approximated by Herbrand’s Induction-Axiom (...)
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  • Intensionality and the gödel theorems.David D. Auerbach - 1985 - Philosophical Studies 48 (3):337--51.
    Philosophers of language have drawn on metamathematical results in varied ways. Extensionalist philosophers have been particularly impressed with two, not unrelated, facts: the existence, due to Frege/Tarski, of a certain sort of semantics, and the seeming absence of intensional contexts from mathematical discourse. The philosophical import of these facts is at best murky. Extensionalists will emphasize the success and clarity of the model theoretic semantics; others will emphasize the relative poverty of the mathematical idiom; still others will question the aptness (...)
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  • (1 other version)On the recursion theorem in iterative operative spaces.J. Zashev - 2001 - Journal of Symbolic Logic 66 (4):1727-1748.
    The recursion theorem in abstract partially ordered algebras, such as operative spaces and others, is the most fundamental result of algebraic recursion theory. The primary aim of the present paper is to prove this theorem for iterative operative spaces in full generality. As an intermediate result, a new and rather large class of models of the combinatory logic is obtained.
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  • On logics intermediate between intuitionistic and classical predicate logic.Toshio Umezawa - 1959 - Journal of Symbolic Logic 24 (2):141-153.
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  • Computability and recursion.Robert I. Soare - 1996 - Bulletin of Symbolic Logic 2 (3):284-321.
    We consider the informal concept of "computability" or "effective calculability" and two of the formalisms commonly used to define it, "(Turing) computability" and "(general) recursiveness". We consider their origin, exact technical definition, concepts, history, general English meanings, how they became fixed in their present roles, how they were first and are now used, their impact on nonspecialists, how their use will affect the future content of the subject of computability theory, and its connection to other related areas. After a careful (...)
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  • A note on finite axiomatization of partial propositional calculi.W. E. Singletary - 1967 - Journal of Symbolic Logic 32 (3):352-354.
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  • (2 other versions)Step by recursive step: Church's analysis of effective calculability.Wilfried Sieg - 1997 - Bulletin of Symbolic Logic 3 (2):154-180.
    Alonzo Church's mathematical work on computability and undecidability is well-known indeed, and we seem to have an excellent understanding of the context in which it arose. The approach Church took to the underlying conceptual issues, by contrast, is less well understood. Why, for example, was "Church's Thesis" put forward publicly only in April 1935, when it had been formulated already in February/March 1934? Why did Church choose to formulate it then in terms of Gödel's general recursiveness, not his own λ (...)
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  • Constructively accessible ordinal numbers.Wayne Richter - 1968 - Journal of Symbolic Logic 33 (1):43-55.
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  • Trial and error predicates and the solution to a problem of Mostowski.Hilary Putnam - 1965 - Journal of Symbolic Logic 30 (1):49-57.
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  • Plural descriptions and many-valued functions.Alex Oliver & Timothy Smiley - 2005 - Mind 114 (456):1039-1068.
    Russell had two theories of definite descriptions: one for singular descriptions, another for plural descriptions. We chart its development, in which ‘On Denoting’ plays a part but not the part one might expect, before explaining why it eventually fails. We go on to consider many-valued functions, since they too bring in plural terms—terms such as ‘4’ or the descriptive ‘the inhabitants of London’ which, like plain plural descriptions, stand for more than one thing. Logicians need to take plural reference seriously (...)
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  • Classical and constructive hierarchies in extended intuitionistic analysis.Joan Rand Moschovakis - 2003 - Journal of Symbolic Logic 68 (3):1015-1043.
    This paper introduces an extension A of Kleene's axiomatization of Brouwer's intuitionistic analysis, in which the classical arithmetical and analytical hierarchies are faithfully represented as hierarchies of the domains of continuity. A domain of continuity is a relation R(α) on Baire space with the property that every constructive partial functional defined on {α : R(α)} is continuous there. The domains of continuity for A coincide with the stable relations (those equivalent in A to their double negations), while every relation R(α) (...)
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  • Proof theory in the USSR 1925–1969.Grigori Mints - 1991 - Journal of Symbolic Logic 56 (2):385-424.
    We present a survey of proof theory in the USSR beginning with the paper by Kolmogorov [1925] and ending (mostly) in 1969; the last two sections deal with work done by A. A. Markov and N. A. Shanin in the early seventies, providing a kind of effective interpretation of negative arithmetic formulas. The material is arranged in chronological order and subdivided according to topics of investigation. The exposition is more detailed when the work is little known in the West or (...)
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  • Universally free logic and standard quantification theory.Robert K. Meyer & Karel Lambert - 1968 - Journal of Symbolic Logic 33 (1):8-26.
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  • Programs, grammars and arguments: A personal view of some connections between computation, language and logic.J. Lambek - 1997 - Bulletin of Symbolic Logic 3 (3):312-328.
    As an undergraduate I was taught to multiply two numbers with the help of log tables, using the formulaHaving graduated to teach calculus to Engineers, I learned that log tables were to be replaced by slide rules. It was then that Imade the fateful decision that there was no need for me to learn how to use this tedious device, as I could always rely on the students to perform the necessary computations. In the course of time, slide rules were (...)
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  • A renaissance of empiricism in the recent philosophy of mathematics.Imre Lakatos - 1976 - British Journal for the Philosophy of Science 27 (3):201-223.
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  • (1 other version)Mathematical significance of consistency proofs.G. Kreisel - 1958 - Journal of Symbolic Logic 23 (2):155-182.
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  • (1 other version)A completeness theorem in modal logic.Saul Kripke - 1959 - Journal of Symbolic Logic 24 (1):1-14.
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  • (1 other version)Elementary completeness properties of intuitionistic logic with a note on negations of prenex formulae.G. Kreisel - 1958 - Journal of Symbolic Logic 23 (3):317-330.
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  • Effective Bounds from ineffective proofs in analysis: An application of functional interpretation and majorization.Ulrich Kohlenbach - 1992 - Journal of Symbolic Logic 57 (4):1239-1273.
    We show how to extract effective bounds Φ for $\bigwedge u^1 \bigwedge v \leq_\gamma tu \bigvee w^\eta G_0$ -sentences which depend on u only (i.e. $\bigwedge u \bigwedge v \leq_\gamma tu \bigvee w \leq_\eta \Phi uG_0$ ) from arithmetical proofs which use analytical assumptions of the form \begin{equation*}\tag{*}\bigwedge x^\delta\bigvee y \leq_\rho sx \bigwedge z^\tau F_0\end{equation*} (γ, δ, ρ, and τ are arbitrary finite types, η ≤ 2, G0 and F0 are quantifier-free, and s and t are closed terms). If τ (...)
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  • (1 other version)Gödel numberings of partial recursive functions.Hartley Rogers - 1958 - Journal of Symbolic Logic 23 (3):331-341.
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  • (1 other version)A reduction of the recursion scheme.M. D. Gladstone - 1967 - Journal of Symbolic Logic 32 (4):505-508.
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  • Whither relevant arithmetic?Harvey Friedman & Robert K. Meyer - 1992 - Journal of Symbolic Logic 57 (3):824-831.
    Based on the relevant logic R, the system R# was proposed as a relevant Peano arithmetic. R# has many nice properties: the most conspicuous theorems of classical Peano arithmetic PA are readily provable therein; it is readily and effectively shown to be nontrivial; it incorporates both intuitionist and classical proof methods. But it is shown here that R# is properly weaker than PA, in the sense that there is a strictly positive theorem QRF of PA which is unprovable in R#. (...)
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  • Three uses of the herbrand-Gentzen theorem in relating model theory and proof theory.William Craig - 1957 - Journal of Symbolic Logic 22 (3):269-285.
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  • String theory.John Corcoran, William Frank & Michael Maloney - 1974 - Journal of Symbolic Logic 39 (4):625-637.
    For each positive n , two alternative axiomatizations of the theory of strings over n alphabetic characters are presented. One class of axiomatizations derives from Tarski's system of the Wahrheitsbegriff and uses the n characters and concatenation as primitives. The other class involves using n character-prefixing operators as primitives and derives from Hermes' Semiotik. All underlying logics are second order. It is shown that, for each n, the two theories are definitionally equivalent [or synonymous in the sense of deBouvere]. It (...)
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  • The deduction rule and linear and near-linear proof simulations.Maria Luisa Bonet & Samuel R. Buss - 1993 - Journal of Symbolic Logic 58 (2):688-709.
    We introduce new proof systems for propositional logic, simple deduction Frege systems, general deduction Frege systems, and nested deduction Frege systems, which augment Frege systems with variants of the deduction rule. We give upper bounds on the lengths of proofs in Frege proof systems compared to lengths in these new systems. As applications we give near-linear simulations of the propositional Gentzen sequent calculus and the natural deduction calculus by Frege proofs. The length of a proof is the number of lines (...)
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  • Reconstructor: a computer program that uses three-valued logics to represent lack of information in empirical scientific contexts.Ariel Jonathan Roffé - 2020 - Journal of Applied Non-Classical Logics 30 (1):68-91.
    In this article, I develop three conceptual innovations within the area of formal metatheory, and present a computer program, called Reconstructor, that implements those developments. The first development consists in a methodology for testing formal reconstructions of scientific theories, which involves checking both whether translations of paradigmatically successful applications into models satisfy the formalisation of the laws, and also whether unsuccessful applications do not. I show how Reconstructor can help carry this out, since it allows the end-user to specify a (...)
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