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  1. What is a Non-Truth-Functional Logic?João Marcos - 2009 - Studia Logica 92 (2):215-240.
    What is the fundamental insight behind truth-functionality ? When is a logic interpretable by way of a truth-functional semantics? To address such questions in a satisfactory way, a formal definition of truth-functionality from the point of view of abstract logics is clearly called for. As a matter of fact, such a definition has been available at least since the 70s, though to this day it still remains not very widely well-known. A clear distinction can be drawn between logics characterizable through: (...)
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  • The Harmony of Identity.Ansten Klev - 2019 - Journal of Philosophical Logic 48 (5):867-884.
    The standard natural deduction rules for the identity predicate have seemed to some not to be harmonious. Stephen Read has suggested an alternative introduction rule that restores harmony but presupposes second-order logic. Here it will be shown that the standard rules are in fact harmonious. To this end, natural deduction will be enriched with a theory of definitional identity. This leads to a novel conception of canonical derivation, on the basis of which the identity elimination rule can be justified in (...)
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  • Recovery Operators, Paraconsistency and Duality.Walter Carnielli, Marcelo E. Coniglio & Abilio Rodrigues - forthcoming - Logic Journal of the IGPL.
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  • Non-Deterministic Algebraization of Logics by Swap Structures.Marcelo E. Coniglio, Aldo Figallo-Orellano & Ana Claudia Golzio - forthcoming - Logic Journal of the IGPL.
    Multialgebras (or hyperalgebras or non-deterministic algebras) have been much studied in mathematics and in computer science. In 2016 Carnielli and Coniglio introduced a class of multialgebras called swap structures, as a semantic framework for dealing with several Logics of Formal Inconsistency (or LFIs) that cannot be semantically characterized by a single finite matrix. In particular, these LFIs are not algebraizable by the standard tools of abstract algebraic logic. In this paper, the first steps towards a theory of non-deterministic algebraization of (...)
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  • Existence Assumptions and Logical Principles: Choice Operators in Intuitionistic Logic.Corey Edward Mulvihill - 2015 - Dissertation, University of Waterloo
    Hilbert’s choice operators τ and ε, when added to intuitionistic logic, strengthen it. In the presence of certain extensionality axioms they produce classical logic, while in the presence of weaker decidability conditions for terms they produce various superintuitionistic intermediate logics. In this thesis, I argue that there are important philosophical lessons to be learned from these results. To make the case, I begin with a historical discussion situating the development of Hilbert’s operators in relation to his evolving program in the (...)
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  • „Kauza Afthonios“: Ilustrácia k otázke správneho riešenia antických paradoxov.Vladimir Marko - 2014 - Organon F: Medzinárodný Časopis Pre Analytickú Filozofiu 1 (20):88-103.
    The article deals with the question of correct reconstruction of and solutions to the ancient paradoxes. Analyzing one contemporary example of a reconstruction of the so-called Crocodile Paradox, taken from Sorensen’s A Brief History of Paradox, the author shows how the original pattern of paradox could have been incorrectly transformed in its meaning by overlooking its adequate historical background. Sorensen’s quoting of Aphthonius, as the author of a certain solution to the paradox, seems to be a systematic failure since the (...)
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  • Towards a Formal Ontology of Information. Selected Ideas of K. Turek.Roman Krzanowski - 2016 - Zagadnienia Filozoficzne W Nauce 61:23-52.
    There are many ontologies of the world or of specific phenomena such as time, matter, space, and quantum mechanics1. However, ontologies of information are rather rare. One of the reasons behind this is that information is most frequently associated with communication and computing, and not with ‘the furniture of the world’. But what would be the nature of an ontology of information? For it to be of significant import it should be amenable to formalization in a logico-grammatical formalism. A candidate (...)
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  • Sentence, Proposition and Identity.Jean-Yves Béziau - 2007 - Synthese 154 (3):371 - 382.
    In this paper we discuss the distinction between sentence and proposition from the perspective of identity. After criticizing Quine, we discuss how objects of logical languages are constructed, explaining what is Kleene’s congruence—used by Bourbaki with his square—and Paul Halmos’s view about the difference between formulas and objects of the factor structure, the corresponding boolean algebra, in case of classical logic. Finally we present Patrick Suppes’s congruence approach to the notion of proposition, according to which a whole hierarchy of congruences (...)
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  • Notes on the Art of Logic.Nuel Belnap - manuscript
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  • On Language Adequacy.Urszula Wybraniec-Skardowska - 2015 - Studies in Logic, Grammar and Rhetoric 40 (1):257-292.
    The paper concentrates on the problem of adequate reflection of fragments of reality via expressions of language and inter-subjective knowledge about these fragments, called here, in brief, language adequacy. This problem is formulated in several aspects, the most being: the compatibility of language syntax with its bi-level semantics: intensional and extensional. In this paper, various aspects of language adequacy find their logical explication on the ground of the formal-logical theory T of any categorial language L generated by the so-called classical (...)
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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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  • Types in Logic and Mathematics Before 1940.Fairouz Kamareddine, Twan Laan & Rob Nederpelt - 2002 - Bulletin of Symbolic Logic 8 (2):185-245.
    In this article, we study the prehistory of type theory up to 1910 and its development between Russell and Whitehead's Principia Mathematica ([71], 1910-1912) and Church's simply typed λ-calculus of 1940. We first argue that the concept of types has always been present in mathematics, though nobody was incorporating them explicitly as such, before the end of the 19th century. Then we proceed by describing how the logical paradoxes entered the formal systems of Frege, Cantor and Peano concentrating on Frege's (...)
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  • Philosophy of Logic – Reexamining the Formalized Notion of Truth.Pete Olcott - manuscript
    Because formal systems of symbolic logic inherently express and represent the deductive inference model formal proofs to theorem consequences can be understood to represent sound deductive inference to true conclusions without any need for other representations such as model theory.
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  • Trees for E.Shawn Standefer - 2018 - Logic Journal of the IGPL 26 (3):300-315.
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  • A Brief History of Natural Deduction.Francis Jeffry Pelletier - 1999 - History and Philosophy of Logic 20 (1):1-31.
    Natural deduction is the type of logic most familiar to current philosophers, and indeed is all that many modern philosophers know about logic. Yet natural deduction is a fairly recent innovation in logic, dating from Gentzen and Ja?kowski in 1934. This article traces the development of natural deduction from the view that these founders embraced to the widespread acceptance of the method in the 1960s. I focus especially on the different choices made by writers of elementary textbooks?the standard conduits of (...)
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  • Subformula and Separation Properties in Natural Deduction Via Small Kripke Models: Subformula and Separation Properties.Peter Milne - 2010 - Review of Symbolic Logic 3 (2):175-227.
    Various natural deduction formulations of classical, minimal, intuitionist, and intermediate propositional and first-order logics are presented and investigated with respect to satisfaction of the separation and subformula properties. The technique employed is, for the most part, semantic, based on general versions of the Lindenbaum and Lindenbaum–Henkin constructions. Careful attention is paid to which properties of theories result in the presence of which rules of inference, and to restrictions on the sets of formulas to which the rules may be employed, restrictions (...)
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  • Some Calculi with Strong Negation Primitive.J. Jay Zeman - 1968 - Journal of Symbolic Logic 33 (1):97-100.
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  • Intensional Models for First Degree Formulas.Nuel D. Belnap - 1967 - Journal of Symbolic Logic 32 (1):1-22.
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  • A Reduction Theorem for Normal Algorithms.J. W. Swanson - 1966 - Journal of Symbolic Logic 31 (1):86-97.
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  • Independence of Two Nice Sets of Axioms for the Propositional Calculus.T. Thacher Robinson - 1968 - Journal of Symbolic Logic 33 (2):265-270.
    Kanger [4] gives a set of twelve axioms for the classical propositional Calculus which, together with modus ponens and substitution, have the following nice properties: (0.1) Each axiom contains $\supset$ , and no axiom contains more than two different connectives. (0.2) Deletions of certain of the axioms yield the intuitionistic, minimal, and classical refutability1 subsystems of propositional calculus. (0.3) Each of these four systems of axioms has the separation property: that if a theorem is provable in such a system, then (...)
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  • Prior’s OIC Nonconservativity Example Revisited.Lloyd Humberstone - 2014 - Journal of Applied Non-Classical Logics 24 (3):209-235.
    In his 1964 note, ‘Two Additions to Positive Implication’, A. N. Prior showed that standard axioms governing conjunction yield a nonconservative extension of the pure implicational intermediate logic OIC of R. A. Bull. Here, after reviewing the situation with the aid of an adapted form of the Kripke semantics for intuitionistic and intermediate logics, we proceed to illuminate this example by transposing it to the setting of modal logic, and then relate it to the propositional logic of what have been (...)
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  • A Sequent Calculus for Type Assignment.Jonathan P. Seldin - 1977 - Journal of Symbolic Logic 42 (1):11-28.
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  • Head or Tail? De Morgan on the Bounds of Traditional Logic.Víctor Sánchez Valencia - 1997 - History and Philosophy of Logic 18 (3):123-138.
    This paper is concerned with De Morgan?s explanation of the validity of arguments that involve relational notions. It discusses De Morgan?s expansion of traditional logic aimed at accommodating those inferences, and makes the point that his endeavour is not successful in that the rules that made up his new logic are not sound. Nevertheless, the most important scholarly work on De Morgan?s logic, and contrary to that De Morgan?s mistake is not beyond repair. The rules that determine his new logic (...)
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  • On the Proof Theory of the Modal Logic for Arithmetic Provability.Daniel Leivant - 1981 - Journal of Symbolic Logic 46 (3):531-538.
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  • Sequent-Systems for Modal Logic.Kosta Došen - 1985 - Journal of Symbolic Logic 50 (1):149-168.
    The purpose of this work is to present Gentzen-style formulations of S5 and S4 based on sequents of higher levels. Sequents of level 1 are like ordinary sequents, sequents of level 1 have collections of sequents of level 1 on the left and right of the turnstile, etc. Rules for modal constants involve sequents of level 2, whereas rules for customary logical constants of first-order logic with identity involve only sequents of level 1. A restriction on Thinning on the right (...)
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  • On the Proof Theory of the Intermediate Logic MH.Jonathan P. Seldin - 1986 - Journal of Symbolic Logic 51 (3):626-647.
    A natural deduction formulation is given for the intermediate logic called MH by Gabbay in [4]. Proof-theoretic methods are used to show that every deduction can be normalized, that MH is the weakest intermediate logic for which the Glivenko theorem holds, and that the Craig-Lyndon interpolation theorem holds for it.
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  • On Communication and Computation.Paul Bohan Broderick - 2004 - Minds and Machines 14 (1):1-19.
    Comparing technical notions of communication and computation leads to a surprising result, these notions are often not conceptually distinguishable. This paper will show how the two notions may fail to be clearly distinguished from each other. The most famous models of computation and communication, Turing Machines and (Shannon-style) information sources, are considered. The most significant difference lies in the types of state-transitions allowed in each sort of model. This difference does not correspond to the difference that would be expected after (...)
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  • Extending the Curry-Howard Interpretation to Linear, Relevant and Other Resource Logics.Dov M. Gabbay & Ruy J. G. B. de Queiroz - 1992 - Journal of Symbolic Logic 57 (4):1319-1365.
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  • A Modal View of Linear Logic.Simone Martini & Andrea Masini - 1994 - Journal of Symbolic Logic 59 (3):888-899.
    We present a sequent calculus for the modal logic S4, and building on some relevant features of this system we show how S4 can easily be translated into full propositional linear logic, extending the Grishin-Ono translation of classical logic into linear logic. The translation introduces linear modalities only in correspondence with S4 modalities. We discuss the complexity of the decision problem for several classes of linear formulas naturally arising from the proposed translations.
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  • Gentzenizations of Relevant Logics Without Distribution. I.Ross T. Brady - 1996 - Journal of Symbolic Logic 61 (2):353-378.
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  • On the Role of Implication in Formal Logic.Jonathan P. Seldin - 2000 - Journal of Symbolic Logic 65 (3):1076-1114.
    Evidence is given that implication (and its special case, negation) carry the logical strength of a system of formal logic. This is done by proving normalization and cut elimination for a system based on combinatory logic or λ-calculus with logical constants for and, or, all, and exists, but with none for either implication or negation. The proof is strictly finitary, showing that this system is very weak. The results can be extended to a "classical" version of the system. They can (...)
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  • Logical Consecutions in Discrete Linear Temporal Logic.V. V. Rybakov - 2005 - Journal of Symbolic Logic 70 (4):1137 - 1149.
    We investigate logical consequence in temporal logics in terms of logical consecutions. i.e., inference rules. First, we discuss the question: what does it mean for a logical consecution to be 'correct' in a propositional logic. We consider both valid and admissible consecutions in linear temporal logics and discuss the distinction between these two notions. The linear temporal logic LDTL, consisting of all formulas valid in the frame 〈L, ≤, ≥〉 of all integer numbers, is the prime object of our investigation. (...)
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  • On the Decidability of Implicational Ticket Entailment.Katalin Bimbó & J. Michael Dunn - 2013 - Journal of Symbolic Logic 78 (1):214-236.
    The implicational fragment of the logic of relevant implication, $R_\to$ is known to be decidable. We show that the implicational fragment of the logic of ticket entailment, $T_\to$ is decidable. Our proof is based on the consecution calculus that we introduced specifically to solve this 50-year old open problem. We reduce the decidability problem of $T_\to$ to the decidability problem of $R_\to$. The decidability of $T_\to$ is equivalent to the decidability of the inhabitation problem of implicational types by combinators over (...)
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  • A Modal Translation for Dual-Intuitionistic Logic.Yaroslav Shramko - 2016 - Review of Symbolic Logic 9 (2):251-265.
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  • The Theory of Relations, Complex Terms, and a Connection Between Λ and Ε Calculi.Edward N. Zalta - manuscript
    This paper introduces a new method of interpreting complex relation terms in a second-order quantified modal language. We develop a completely general second-order modal language with two kinds of complex terms: one kind for denoting individuals and one kind for denoting n-place relations. Several issues arise in connection with previous, algebraic methods for interpreting the relation terms. The new method of interpreting these terms described here addresses those issues while establishing an interesting connection between λ and ε calculi. The resulting (...)
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  • Negation in the Language of Theology – Some Issues.Adam Olszewski - 2018 - Philosophical Problems in Science 65:87-107.
    The paper consists of two parts. In the first one I present some general remarks regarding the history of negation and attempt to answer the philosophical question concerning the essence of negation. In the second part I resume the theological teaching on the degrees of certainty and point to five forms of negation – known from other areas of research -- as applied in the framework of theological investigations.
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  • Logical Constants.John MacFarlane - 2008 - Mind.
    Logic is usually thought to concern itself only with features that sentences and arguments possess in virtue of their logical structures or forms. The logical form of a sentence or argument is determined by its syntactic or semantic structure and by the placement of certain expressions called “logical constants.”[1] Thus, for example, the sentences Every boy loves some girl. and Some boy loves every girl. are thought to differ in logical form, even though they share a common syntactic and semantic (...)
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  • Logique mathématique et philosophie des mathématiques.Yvon Gauthier - 1971 - Dialogue 10 (2):243-275.
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  • What is a Logical Theory? On Theories Containing Assertions and Denials.Carolina Blasio, Carlos Caleiro & João Marcos - forthcoming - Synthese:1-24.
    The standard notion of formal theory, in logic, is in general biased exclusively towards assertion: it commonly refers only to collections of assertions that any agent who accepts the generating axioms of the theory should also be committed to accept. In reviewing the main abstract approaches to the study of logical consequence, we point out why this notion of theory is unsatisfactory at multiple levels, and introduce a novel notion of theory that attacks the shortcomings of the received notion by (...)
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  • Reply to Belot, Elgin, and Horsten. [REVIEW]Bas C. van Fraassen - 2010 - Philosophical Studies 150 (3):461 - 472.
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  • On Kalman’s Functor for Bounded Hemi-Implicative Semilattices and Hemi-Implicative Lattices.Ramon Jansana & Hernán Javier San Martín - 2018 - Logic Journal of the IGPL 26 (1):47-82.
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  • Proof Theory for Functional Modal Logic.Shawn Standefer - 2018 - Studia Logica 106 (1):49-84.
    We present some proof-theoretic results for the normal modal logic whose characteristic axiom is \. We present a sequent system for this logic and a hypersequent system for its first-order form and show that these are equivalent to Hilbert-style axiomatizations. We show that the question of validity for these logics reduces to that of classical tautologyhood and first-order logical truth, respectively. We close by proving equivalences with a Fitch-style proof system for revision theory.
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  • Definition in Mathematics.Carlo Cellucci - 2018 - European Journal for Philosophy of Science 8 (3):605-629.
    In the past century the received view of definition in mathematics has been the stipulative conception, according to which a definition merely stipulates the meaning of a term in other terms which are supposed to be already well known. The stipulative conception has been so absolutely dominant and accepted as unproblematic that the nature of definition has not been much discussed, yet it is inadequate. This paper examines its shortcomings and proposes an alternative, the heuristic conception.
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  • An Alternative Gentzenisation of RW+∘.Mirjana Ilić - 2016 - Mathematical Logic Quarterly 62 (6):465-480.
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  • L -Hemi-Implicative Semilattices.José Luis Castiglioni & Hernán Javier San Martín - 2018 - Studia Logica 106 (4):675-690.
    An l-hemi-implicative semilattice is an algebra \\) such that \\) is a semilattice with a greatest element 1 and satisfies: for every \, \ implies \ and \. An l-hemi-implicative semilattice is commutative if if it satisfies that \ for every \. It is shown that the class of l-hemi-implicative semilattices is a variety. These algebras provide a general framework for the study of different algebras of interest in algebraic logic. In any l-hemi-implicative semilattice it is possible to define an (...)
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  • Quantification as an Act of Mind.Bas C. Van Fraassen - 1982 - Journal of Philosophical Logic 11 (3):343-369.
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  • E, R, and Γ.Robert K. Meyer & J. Michael Dunn - 1969 - Journal of Symbolic Logic 34 (3):460-474.
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  • On Subsystems of the System J1 of Arruda and Da Costa.Igor Urbas - 1990 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 36 (2):95-106.
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  • Ein entscheidungsverfahren für den lewisschen modalkalkül S 4.Rainer Krauskope - 1969 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 15 (13-15):193-210.
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