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Logical discrimination

In Jean-Yves Béziau (ed.), Logica Universalis: Towards a General Theory of Logic. Boston: Birkhäuser Verlog. pp. 225–246 (2005)

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  1. Algebraizable Logics.W. J. Blok & Don Pigozzi - 2022 - Advanced Reasoning Forum.
    W. J. Blok and Don Pigozzi set out to try to answer the question of what it means for a logic to have algebraic semantics. In this seminal book they transformed the study of algebraic logic by giving a general framework for the study of logics by algebraic means. The Dutch mathematician W. J. Blok (1947-2003) received his doctorate from the University of Amsterdam in 1979 and was Professor of Mathematics at the University of Illinois, Chicago until his death in (...)
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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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  • (2 other versions)Entailment: The Logic of Relevance and Necessity.[author unknown] - 1975 - Studia Logica 54 (2):261-266.
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  • Substructural Logics: A Primer.Francesco Paoli - 2002 - Dordrecht, Netherland: Springer.
    The aim of the present book is to give a comprehensive account of the ‘state of the art’ of substructural logics, focusing both on their proof theory and on their semantics (both algebraic and relational. It is for graduate students in either philosophy, mathematics, theoretical computer science or theoretical linguistics as well as specialists and researchers.
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  • A survey of abstract algebraic logic.J. M. Font, R. Jansana & D. Pigozzi - 2003 - Studia Logica 74 (1-2):13 - 97.
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  • A Structuralist Theory of Logic.Arnold Koslow - 1992 - New York: Cambridge University Press.
    In this 1992 book, Professor Koslow advances an account of the basic concepts of logic. A central feature of the theory is that it does not require the elements of logic to be based on a formal language. Rather, it uses a general notion of implication as a way of organizing the formal results of various systems of logic in a simple, but insightful way. The study has four parts. In the first two parts the various sources of the general (...)
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  • Grades of discriminability.W. V. Quine - 1976 - Journal of Philosophy 73 (5):113-116.
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  • Semantical Investigations in Heyting's Intuitionistic Logic.Dov M. Gabbay - 1981 - Dordrecht, Netherland: Reidel.
    From the point of view of non-classical logics, Heyting's implication is the smallest implication for which the deduction theorem holds. This book studies properties of logical systems having some of the classical connectives and implication in the neighbourhood of Heyt ing's implication. I have not included anything on entailment, al though it belongs to this neighbourhood, mainly because of the appearance of the Anderson-Belnap book on entailment. In the later chapters of this book, I have included material that might be (...)
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  • Contra-classical logics.Lloyd Humberstone - 2000 - Australasian Journal of Philosophy 78 (4):438 – 474.
    Only propositional logics are at issue here. Such a logic is contra-classical in a superficial sense if it is not a sublogic of classical logic, and in a deeper sense, if there is no way of translating its connectives, the result of which translation gives a sublogic of classical logic. After some motivating examples, we investigate the incidence of contra-classicality (in the deeper sense) in various logical frameworks. In Sections 3 and 4 we will encounter, originally as an example of (...)
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  • (1 other version)The independence of connectives.Timothy Smiley - 1962 - Journal of Symbolic Logic 27 (4):426-436.
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  • Solution to the P − W problem.E. P. Martin & R. K. Meyer - 1982 - Journal of Symbolic Logic 47 (4):869-887.
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  • Dual counterparts of consequence operations.Ryszard Wójcicki - 1973 - Bulletin of the Section of Logic 2 (1):54-57.
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  • A Treatise on Time and Space.J. R. Lucas - 1973 - Revue Philosophique de la France Et de l'Etranger 164 (4):486-487.
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  • Deductive versus Expressive Power: A Pre-Godelian Predicament.Neil Tennant - 2000 - Journal of Philosophy 97 (5):257.
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  • (1 other version)The Independence of Connectives.Timothy Smiley - 1975 - Journal of Symbolic Logic 40 (2):250-251.
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  • Classical negation can be expressed by one of its halves.Jean-Yves Beziau - 1999 - Logic Journal of the IGPL 7 (2):145-151.
    We present the logic K/2 which is a logic with classical implication and only the left part of classical negation.We show that it is possible to define a classical negation into K/2 and that the classical proposition logic K can be translated into this apparently weaker logic.We use concepts from model-theory in order to characterized rigorously this translation and to understand this paradox. Finally we point out that K/2 appears, following Haack's distinction, both as a deviation and an extension of (...)
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  • A study of logics.John P. Cleave - 1991 - New York: Oxford University Press.
    It is a fact of modern scientific thought that there is an enormous variety of logical systems - such as classical logic, intuitionist logic, temporal logic, and Hoare logic, to name but a few - which have originated in the areas of mathematical logic and computer science. In this book the author presents a systematic study of this rich harvest of logics via Tarski's well-known axiomatization of the notion of logical consequence. New and sometimes unorthodox treatments are given of the (...)
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  • Variations on a Theme of Curry.Lloyd Humberstone - 2006 - Notre Dame Journal of Formal Logic 47 (1):101-131.
    After an introduction to set the stage, we consider some variations on the reasoning behind Curry's Paradox arising against the background of classical propositional logic and of BCI logic and one of its extensions, in the latter case treating the "paradoxicality" as a matter of nonconservative extension rather than outright inconsistency. A question about the relation of this extension and a differently described (though possibly identical) logic intermediate between BCI and BCK is raised in a final section, which closes with (...)
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  • BCI-algebras from the point of view of logic.Jacek K. Kabzinski - 1983 - Bulletin of the Section of Logic 12 (3):126-128.
    The following logics are the most noteworthy from the perspective of the calculus of combinators: the Hilbert’s positive implicational logic , the Church’s weak theory of implication , the BCK-logic, and the BCI-logic. Their significance is due to a certain correspondence between combinators and implicational formulas . The first three logics mentioned have been immensely investigated but it was not so in case of the remaining one. The BCI-logics was mentioned by A. N. Prior in the second edition of his (...)
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  • (1 other version)Identical Twins, Deduction Theorems, and Pattern Functions: Exploring the Implicative BCSK Fragment of S5.Lloyd Humberstone - 2006 - Journal of Philosophical Logic 35 (5):435-487.
    We recapitulate (Section 1) some basic details of the system of implicative BCSK logic, which has two primitive binary implicational connectives, and which can be viewed as a certain fragment of the modal logic S5. From this modal perspective we review (Section 2) some results according to which the pure sublogic in either of these connectives (i.e., each considered without the other) is an exact replica of the material implication fragment of classical propositional logic. In Sections 3 and 5 we (...)
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  • On Logical Strength and Weakness.Chris Mortensen & Tim Burgess - 1989 - History and Philosophy of Logic 10 (1):47-51.
    First, we consider an argument due to Popper for maximal strength in choice of logic. We dispute this argument, taking a lead from some remarks by Susan Haack; but we defend a set of contrary considerations for minimal strength in logic. Finally, we consider the objection that Popper presupposes the distinctness of logic from science. We conclude from this that all claims to logical truth may be in equal epistemological trouble.
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  • (2 other versions)Classical Propositional Operators. An Exercise in the Foundations of Logic.Richard Fleming - 1984 - Journal of Symbolic Logic 49 (3):993-994.
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  • BCK and BCI logics, condensed detachment and the $2$-property. [REVIEW]J. Roger Hindley - 1993 - Notre Dame Journal of Formal Logic 34 (2):231-250.
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