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  1. Natural Deduction for Three-Valued Regular Logics.Yaroslav Petrukhin - 2017 - Logic and Logical Philosophy 26 (2):197–206.
    In this paper, I consider a family of three-valued regular logics: the well-known strong and weak S.C. Kleene’s logics and two intermedi- ate logics, where one was discovered by M. Fitting and the other one by E. Komendantskaya. All these systems were originally presented in the semantical way and based on the theory of recursion. However, the proof theory of them still is not fully developed. Thus, natural deduction sys- tems are built only for strong Kleene’s logic both with one (...)
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  • 40 years of FDE: An Introductory Overview.Hitoshi Omori & Heinrich Wansing - 2017 - Studia Logica 105 (6):1021-1049.
    In this introduction to the special issue “40 years of FDE”, we offer an overview of the field and put the papers included in the special issue into perspective. More specifically, we first present various semantics and proof systems for FDE, and then survey some expansions of FDE by adding various operators starting with constants. We then turn to unary and binary connectives, which are classified in a systematic manner. First-order FDE is also briefly revisited, and we conclude by listing (...)
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  • Symposium: On What there is.P. T. Geach, A. J. Ayer & W. V. Quine - 1948 - Aristotelian Society Supplementary Volume 25 (1):125-160.
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  • Introduction to Mathematical Philosophy.Bertrand Russell - 1919 - Revue Philosophique de la France Et de l'Etranger 89:465-466.
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  • Two Dogmas of Empiricism.W. Quine - 1951 - [Longmans, Green].
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  • Theory of Logical Calculi, Basic Theory of Consequence Operations.Ryszard Wójcicki - 1991 - Studia Logica 50 (3):623-629.
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  • Paradox without Self-Reference.Stephen Yablo - 1993 - Analysis 53 (4):251-252.
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  • The Philosophy of Logical Atomism.Bertrand Russell - 1918 - In ¸ Iterussell1986. Open Court. pp. 193-210..
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  • The Philosophy of Logical Atomism.Bertrand Russell (ed.) - 1940 - Routledge.
    Logical Atomism is a philosophy that sought to account for the world in all its various aspects by relating it to the structure of the language in which we articulate information. In _The Philosophy of Logical Atomism,_ Bertrand Russell, with input from his young student Ludwig Wittgenstein, developed the concept and argues for a reformed language based on pure logic. Despite Russell’s own future doubts surrounding the concept, this founding and definitive work in analytical philosophy by one of the world’s (...)
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  • Truth and Paradox.Anil Gupta - 1981 - Journal of Philosophy 78 (11):735-736.
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  • Anti-exceptionalism about logic.Ole Thomassen Hjortland - 2017 - Philosophical Studies 174 (3):631-658.
    Logic isn’t special. Its theories are continuous with science; its method continuous with scientific method. Logic isn’t a priori, nor are its truths analytic truths. Logical theories are revisable, and if they are revised, they are revised on the same grounds as scientific theories. These are the tenets of anti-exceptionalism about logic. The position is most famously defended by Quine, but has more recent advocates in Maddy, Priest, Russell, and Williamson. Although these authors agree on many methodological issues about logic, (...)
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  • Connected components of definable groups, and o-minimality II.Annalisa Conversano & Anand Pillay - 2015 - Annals of Pure and Applied Logic 166 (7-8):836-849.
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  • Scientific method in philosophy.Bertrand Russell - 1914 - Oxford,: Clarendon press.
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  • Correspondence analysis for strong three-valued logic.Allard Tamminga - 2014 - Logical Investigations 20:255-268.
    I apply Kooi and Tamminga's (2012) idea of correspondence analysis for many-valued logics to strong three-valued logic (K3). First, I characterize each possible single entry in the truth-table of a unary or a binary truth-functional operator that could be added to K3 by a basic inference scheme. Second, I define a class of natural deduction systems on the basis of these characterizing basic inference schemes and a natural deduction system for K3. Third, I show that each of the resulting natural (...)
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  • Completeness via correspondence for extensions of the logic of paradox.Barteld Kooi & Allard Tamminga - 2012 - Review of Symbolic Logic 5 (4):720-730.
    Taking our inspiration from modal correspondence theory, we present the idea of correspondence analysis for many-valued logics. As a benchmark case, we study truth-functional extensions of the Logic of Paradox (LP). First, we characterize each of the possible truth table entries for unary and binary operators that could be added to LP by an inference scheme. Second, we define a class of natural deduction systems on the basis of these characterizing inference schemes and a natural deduction system for LP. Third, (...)
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  • Theory of Logical Calculi: Basic Theory of Consequence Operations.Ryszard Wójcicki - 1988 - Dordrecht, Boston and London: Kluwer Academic Publishers.
    The general aim of this book is to provide an elementary exposition of some basic concepts in terms of which both classical and non-dassicallogirs may be studied and appraised. Although quantificational logic is dealt with briefly in the last chapter, the discussion is chiefly concemed with propo gjtional cakuli. Still, the subject, as it stands today, cannot br covered in one book of reasonable length. Rather than to try to include in the volume as much as possible, I have put (...)
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  • Modal meinongianism and fiction: The best of three worlds.Francesco Berto - 2011 - Philosophical Studies 152 (3):313-35.
    We outline a neo-Meinongian framework labeled as Modal Meinongian Metaphysics (MMM) to account for the ontology and semantics of fictional discourse. Several competing accounts of fictional objects are originated by the fact that our talking of them mirrors incoherent intuitions: mainstream theories of fiction privilege some such intuitions, but are forced to account for others via complicated paraphrases of the relevant sentences. An ideal theory should resort to as few paraphrases as possible. In Sect. 1, we make this explicit via (...)
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  • Introduction to metamathematics.Stephen Cole Kleene - 1952 - Groningen: P. Noordhoff N.V..
    Stephen Cole Kleene was one of the greatest logicians of the twentieth century and this book is the influential textbook he wrote to teach the subject to the next generation. It was first published in 1952, some twenty years after the publication of Godel's paper on the incompleteness of arithmetic, which marked, if not the beginning of modern logic. The 1930s was a time of creativity and ferment in the subject, when the notion of computable moved from the realm of (...)
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  • Kleene's logic, generalized.Melvin Fitting - unknown
    Kleene’s well-known strong three-valued logic is shown to be one of a family of logics with similar mathematical properties. These logics are produced by an intuitively natural construction. The resulting logics have direct relationships with bilattices. In addition they possess mathematical features that lend themselves well to semantical constructions based on fixpoint procedures, as in logic programming.
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  • The concept of truth in formalized languages.Alfred Tarski - 1956 - In Logic, semantics, metamathematics. Oxford,: Clarendon Press. pp. 152--278.
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  • Demonstratives: An Essay on the Semantics, Logic, Metaphysics and Epistemology of Demonstratives and other Indexicals.David Kaplan - 1989 - In Joseph Almog, John Perry & Howard Wettstein (eds.), Themes From Kaplan. New York: Oxford University Press. pp. 481-563.
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  • On Denoting.Bertrand Russell - 2005 - Mind 114 (456):873 - 887.
    By a `denoting phrase' I mean a phrase such as any one of the following: a man, some man, any man, every man, all men, the present King of England, the present King of France, the center of mass of the solar system at the first instant of the twentieth century, the revolution of the earth round the sun, the revolution of the sun round the earth. Thus a phrase is denoting solely in virtue of its form. We may distinguish (...)
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  • Connexive logic.Heinrich Wansing - 2008 - Stanford Encyclopedia of Philosophy.
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  • Arthur prior.B. Jack Copeland - 2008 - Stanford Encyclopedia of Philosophy.
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  • How a computer should think.Nuel Belnap - 1977 - In Gilbert Ryle (ed.), Contemporary aspects of philosophy. Boston: Oriel Press.
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  • Intuitive semantics for first-degree entailments and 'coupled trees'.J. Michael Dunn - 1976 - Philosophical Studies 29 (3):149-168.
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  • Normalization theorems for full first order classical natural deduction.Gunnar Stålmarck - 1991 - Journal of Symbolic Logic 56 (1):129-149.
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  • Solution of a problem of Leon Henkin.M. H. Löb - 1955 - Journal of Symbolic Logic 20 (2):115-118.
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  • Outline of a theory of truth.Saul Kripke - 1975 - Journal of Philosophy 72 (19):690-716.
    A formal theory of truth, alternative to tarski's 'orthodox' theory, based on truth-value gaps, is presented. the theory is proposed as a fairly plausible model for natural language and as one which allows rigorous definitions to be given for various intuitive concepts, such as those of 'grounded' and 'paradoxical' sentences.
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  • Partiality and its dual.J. Michael Dunn - 2000 - Studia Logica 66 (1):5-40.
    This paper explores allowing truth value assignments to be undetermined or "partial" and overdetermined or "inconsistent", thus returning to an investigation of the four-valued semantics that I initiated in the sixties. I examine some natural consequence relations and show how they are related to existing logics, including ukasiewicz's three-valued logic, Kleene's three-valued logic, Anderson and Belnap's relevant entailments, Priest's "Logic of Paradox", and the first-degree fragment of the Dunn-McCall system "R-mingle". None of these systems have nested implications, and I investigate (...)
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  • Impossible Worlds.Francesco Berto & Mark Jago - 2019 - Oxford: Oxford University Press. Edited by Mark Jago.
    Impossible Worlds focuses on an exciting new theory in philosophy, with applications in metaphysics, logic, and the theory of meaning. Its central topic is: how do we meaningfully talk and reason about situations which, unbeknownst to us, are impossible? This issue emerges as a central problem in contemporary philosophical accounts of meaning, information, knowledge, belief, fiction, conditionality, and counterfactual supposition. The book is written bytwo of the leading philosophers in the area and contains original research of relevance to professional philosophers (...)
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  • A Causal-Mentalist View of Propositions.Jeremiah Joven Joaquin & James Franklin - 2022 - Organon F: Medzinárodný Časopis Pre Analytickú Filozofiu 29 (1):47-77.
    In order to fulfil their essential roles as the bearers of truth and the relata of logical relations, propositions must be public and shareable. That requirement has favoured Platonist and other nonmental views of them, despite the well-known problems of Platonism in general. Views that propositions are mental entities have correspondingly fallen out of favour, as they have difficulty in explaining how propositions could have shareable, objective properties. We revive a mentalist view of propositions, inspired by Artificial Intelligence work on (...)
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  • Normalisation for Bilateral Classical Logic with some Philosophical Remarks.Nils Kürbis - 2021 - Journal of Applied Logics 2 (8):531-556.
    Bilateralists hold that the meanings of the connectives are determined by rules of inference for their use in deductive reasoning with asserted and denied formulas. This paper presents two bilateral connectives comparable to Prior's tonk, for which, unlike for tonk, there are reduction steps for the removal of maximal formulas arising from introducing and eliminating formulas with those connectives as main operators. Adding either of them to bilateral classical logic results in an incoherent system. One way around this problem is (...)
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  • A remark on functional completeness of binary expansions of Kleene’s strong 3-valued logic.Gemma Robles & José M. Méndez - 2022 - Logic Journal of the IGPL 30 (1):21-33.
    A classical result by Słupecki states that a logic L is functionally complete for the 3-element set of truth-values THREE if, in addition to functionally including Łukasiewicz’s 3-valued logic Ł3, what he names the ‘$T$-function’ is definable in L. By leaning upon this classical result, we prove a general theorem for defining binary expansions of Kleene’s strong logic that are functionally complete for THREE.
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  • Two Dogmas of Empiricism.W. V. O. Quine - 2011 - In Robert B. Talisse & Scott F. Aikin (eds.), The Pragmatism Reader: From Peirce Through the Present. Princeton University Press. pp. 202-220.
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  • Anti-Exceptionalism about Logic.Ole Thomassen Hjortland - 2019 - Australasian Journal of Logic 16 (7):186.
    Introduction to this special issue of The Australasian Journal of Logic.
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  • Belnap-Dunn semantics for natural implicative expansions of Kleene's strong three-valued matrix with two designated values.Gemma Robles & José M. Méndez - 2019 - Journal of Applied Non-Classical Logics 29 (1):37-63.
    ABSTRACTA conditional is natural if it fulfils the three following conditions. It coincides with the classical conditional when restricted to the classical values T and F; it satisfies the Modus Ponens; and it is assigned a designated value whenever the value assigned to its antecedent is less than or equal to the value assigned to its consequent. The aim of this paper is to provide a ‘bivalent’ Belnap-Dunn semantics for all natural implicative expansions of Kleene's strong 3-valued matrix with two (...)
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  • Strong Types for Direct Logic.Carl Hewitt - unknown
    This article follows on the introductory article “Direct Logic for Intelligent Applications” [Hewitt 2017a]. Strong Types enable new mathematical theorems to be proved including the Formal Consistency of Mathematics. Also, Strong Types are extremely important in Direct Logic because they block all known paradoxes[Cantini and Bruni 2017]. Blocking known paradoxes makes Direct Logic safer for use in Intelligent Applications by preventing security holes. Inconsistency Robustness is performance of information systems with pervasively inconsistent information. Inconsistency Robustness of the community of professional (...)
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  • Les paradoxes de la logique.B. Russell - 1906 - Revue de Métaphysique et de Morale 14 (5):627-650.
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  • What is Strict Implication?Ian Hacking - 1972 - Journal of Symbolic Logic 37 (2):417-417.
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  • Nominalism and Realism.David Armstrong - unknown
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  • Classifying torsion free groups in o-minimal expansions of real closed fields.Eliana Barriga & Alf Onshuus - 2016 - Annals of Pure and Applied Logic 167 (12):1267-1297.
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  • Does changing the subject from A to B really provide an enlarged understanding of A?John Woods - 2016 - Logic Journal of the IGPL 24 (4).
    There are various ways of achieving an enlarged understanding of a concept of interest. One way is by giving its proper definition. Another is by giving something else a proper definition and then using it to model or formally represent the original concept. Between the two we find varying shades of grey. We might open up a concept by a direct lexical definition of the predicate that expresses it, or by a theory whose theorems define it implicitly. At the other (...)
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  • A companion to Brady's 4-valued relevant logic BN4: The 4-valued logic of entailment E4.Gemma Robles & José M. Méndez - 2016 - Logic Journal of the IGPL 24 (5).
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  • S7.Andrew David Irvine - 2013 - Journal of Applied Logic 11 (4):523-529.
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  • Frege on Number Properties.Andrew D. Irvine - 2010 - Studia Logica 96 (2):239-260.
    In the Grundlagen , Frege offers eight main arguments, together with a series of more minor supporting arguments, against Mill’s view that numbers are “properties of external things”. This paper reviews all eight of these arguments, arguing that none are conclusive.
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  • A Strong and Rich 4-Valued Modal Logic Without Łukasiewicz-Type Paradoxes.José M. Méndez & Gemma Robles - 2015 - Logica Universalis 9 (4):501-522.
    The aim of this paper is to introduce an alternative to Łukasiewicz’s 4-valued modal logic Ł. As it is known, Ł is afflicted by “Łukasiewicz type paradoxes”. The logic we define, PŁ4, is a strong paraconsistent and paracomplete 4-valued modal logic free from this type of paradoxes. PŁ4 is determined by the degree of truth-preserving consequence relation defined on the ordered set of values of a modification of the matrix MŁ characteristic for the logic Ł. On the other hand, PŁ4 (...)
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  • A useful four-valued logic.N. D. Belnap - 1977 - In J. M. Dunn & G. Epstein (eds.), Modern Uses of Multiple-Valued Logic. D. Reidel.
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  • Completeness proofs for the systems RM3 and BN4.Ross T. Brady - 1982 - Logique Et Analyse 25 (97):9.
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  • C. I. Lewis. Emch's calculus and strict implication. The journal of symbolic logic, vol. 1 (1936), pp. 77–86.Jerzy Slupecki - 1937 - Journal of Symbolic Logic 2 (1):46-46.
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