Switch to: References

Citations of:

Multiple Conclusion Logic

Philosophical Quarterly 30 (121):379-382 (1980)

Add citations

You must login to add citations.
  1. Expanding the universe of universal logic.James Trafford - 2014 - Theoria: Revista de Teoría, Historia y Fundamentos de la Ciencia 29 (3):325-343.
    In [5], Béziau provides a means by which Gentzen’s sequent calculus can be combined with the general semantic theory of bivaluations. In doing so, according to Béziau, it is possible to construe the abstract “core” of logics in general, where logical syntax and semantics are “two sides of the same coin”. The central suggestion there is that, by way of a modification of the notion of maximal consistency, it is possible to prove the soundness and completeness for any normal logic. (...)
    Download  
     
    Export citation  
     
    Bookmark  
  • Aristotle on Circular Proof.Marko Malink - 2013 - Phronesis 58 (3):215-248.
    In Posterior Analytics 1.3, Aristotle advances three arguments against circular proof. The third argument relies on his discussion of circular proof in Prior Analytics 2.5. This is problematic because the two chapters seem to deal with two rather disparate conceptions of circular proof. In Posterior Analytics 1.3, Aristotle gives a purely propositional account of circular proof, whereas in Prior Analytics 2.5 he gives a more complex, syllogistic account. My aim is to show that these problems can be solved, and that (...)
    Download  
     
    Export citation  
     
    Bookmark   7 citations  
  • Some remarks on axiomatizing logical consequence operations.Jacek Malinowski - 2005 - Logic and Logical Philosophy 14 (1):103-117.
    In this paper we investigate the relation between the axiomatization of a given logical consequence operation and axiom systems defining the class of algebras related to that consequence operation. We show examples which prove that, in general there are no natural relation between both ways of axiomatization.
    Download  
     
    Export citation  
     
    Bookmark  
  • Framework for formal ontology.Barry Smith & Kevin Mulligan - 1983 - Topoi 2 (1):73-85.
    The discussions which follow rest on a distinction, first expounded by Husserl, between formal logic and formal ontology. The former concerns itself with (formal) meaning-structures; the latter with formal structures amongst objects and their parts. The paper attempts to show how, when formal ontological considerations are brought into play, contemporary extensionalist theories of part and whole, and above all the mereology of Leniewski, can be generalised to embrace not only relations between concrete objects and object-pieces, but also relations between what (...)
    Download  
     
    Export citation  
     
    Bookmark   56 citations  
  • Rejection.Timothy Smiley - 1996 - Analysis 56 (1):1–9.
    Download  
     
    Export citation  
     
    Bookmark   129 citations  
  • Semantics without Toil? Brady and Rush Meet Halldén.Lloyd Humberstone - 2019 - Organon F: Medzinárodný Časopis Pre Analytickú Filozofiu 26 (3):340–404.
    The present discussion takes up an issue raised in Section 5 of Ross Brady and Penelope Rush’s paper ‘Four Basic Logical Issues’ concerning the (claimed) triviality – in the sense of automatic availability – of soundness and completeness results for a logic in a metalanguage employing at least as much logical vocabulary as the object logic, where the metalogical behaviour of the common logical vocabulary is as in the object logic. We shall see – in Propositions 4.5–4.7 – that this (...)
    Download  
     
    Export citation  
     
    Bookmark  
  • Preface.Matteo Pascucci & Adam Tamas Tuboly - 2019 - Organon F: Medzinárodný Časopis Pre Analytickú Filozofiu 26 (3):318-322.
    Special issue: "Reflecting on the Legacy of C.I. Lewis: Contemporary and Historical Perspectives on Modal Logic".
    Download  
     
    Export citation  
     
    Bookmark  
  • Socratic Proofs and Paraconsistency: A Case Study.Andrzej Wiśniewski, Guido Vanackere & Dorota Leszczyńska - 2005 - Studia Logica 80 (2):431-466.
    This paper develops a new proof method for two propositional paraconsistent logics: the propositional part of Batens' weak paraconsistent logic CLuN and Schütte's maximally paraconsistent logic Φv. Proofs are de.ned as certain sequences of questions. The method is grounded in Inferential Erotetic Logic.
    Download  
     
    Export citation  
     
    Bookmark   11 citations  
  • Expressive Power and Incompleteness of Propositional Logics.James W. Garson - 2010 - Journal of Philosophical Logic 39 (2):159-171.
    Natural deduction systems were motivated by the desire to define the meaning of each connective by specifying how it is introduced and eliminated from inference. In one sense, this attempt fails, for it is well known that propositional logic rules underdetermine the classical truth tables. Natural deduction rules are too weak to enforce the intended readings of the connectives; they allow non-standard models. Two reactions to this phenomenon appear in the literature. One is to try to restore the standard readings, (...)
    Download  
     
    Export citation  
     
    Bookmark   6 citations  
  • The categoricity problem and truth-value gaps.Ian Rumfitt - 1997 - Analysis 57 (4):223-235.
    In his article 'Rejection' (1996), Timothy Smiley had shown how a logical system allowing rules of rejection could provide a categorical axiomatization of the classical propositional calculus. This paper shows how rules of rejection, when placed in a multiple conclusion setting, can also provide categorical axiomatizations of a range of non-classical calculi which permit truth-value gaps, among them the calculus in Smiley's own 'Sense without denotation' (1960).
    Download  
     
    Export citation  
     
    Bookmark   18 citations  
  • Why Conclusions Should Remain Single.Florian Steinberger - 2011 - Journal of Philosophical Logic 40 (3):333-355.
    This paper argues that logical inferentialists should reject multiple-conclusion logics. Logical inferentialism is the position that the meanings of the logical constants are determined by the rules of inference they obey. As such, logical inferentialism requires a proof-theoretic framework within which to operate. However, in order to fulfil its semantic duties, a deductive system has to be suitably connected to our inferential practices. I argue that, contrary to an established tradition, multiple-conclusion systems are ill-suited for this purpose because they fail (...)
    Download  
     
    Export citation  
     
    Bookmark   39 citations  
  • Theory and Reality : Metaphysics as Second Science.Staffan Angere - unknown
    Theory and Reality is about the connection between true theories and the world. A mathematical framefork for such connections is given, and it is shown how that framework can be used to infer facts about the structure of reality from facts about the structure of true theories, The book starts with an overview of various approaches to metaphysics. Beginning with Quine's programmatic "On what there is", the first chapter then discusses the perils involved in going from language to metaphysics. It (...)
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  • Remarks on the Scott–Lindenbaum Theorem.Gillman Payette & Peter K. Schotch - 2014 - Studia Logica 102 (5):1003-1020.
    In the late 1960s and early 1970s, Dana Scott introduced a kind of generalization (or perhaps simplification would be a better description) of the notion of inference, familiar from Gentzen, in which one may consider multiple conclusions rather than single formulas. Scott used this idea to good effect in a number of projects including the axiomatization of many-valued logics (of various kinds) and a reconsideration of the motivation of C.I. Lewis. Since he left the subject it has been vigorously prosecuted (...)
    Download  
     
    Export citation  
     
    Bookmark   4 citations  
  • False though partly true – an experiment in logic.Lloyd Humberstone - 2003 - Journal of Philosophical Logic 32 (6):613-665.
    We explore in an experimental spirit the prospects for extending classical propositional logic with a new operator P intended to be interpreted when prefixed to a formula as saying that formula in question is at least partly true. The paradigm case of something which is, in the sense envisaged, false though still "partly" true is a conjunction one of whose conjuncts is false while the other is true. Ideally, we should like such a logic to extend classical logic - or (...)
    Download  
     
    Export citation  
     
    Bookmark   3 citations  
  • Anything Goes.David Ripley - 2015 - Topoi 34 (1):25-36.
    This paper consider Prior's connective Tonk from a particular bilateralist perspective. I show that there is a natural perspective from which we can see Tonk and its ilk as perfectly well-defined pieces of vocabulary; there is no need for restrictions to bar things like Tonk.
    Download  
     
    Export citation  
     
    Bookmark   27 citations  
  • Erotetic implications.Andrzej Wiśniewski - 1994 - Journal of Philosophical Logic 23 (2):173 - 195.
    Three semantic relations are analyzed: the relation of implication of a question by a question and a set of declarative sentences, the relation of implication of a question by a question, and the relation of strong implication of a question by a question and a set of declarative sentences. The connections between these concepts and the concepts of relative soundness, partial answerhood and presupposition are examined. The principal results are theorems about, to speak generally, epistemic reducibility of well-posed questions to (...)
    Download  
     
    Export citation  
     
    Bookmark   21 citations  
  • Investigations into a left-structural right-substructural sequent calculus.Lloyd Humberstone - 2007 - Journal of Logic, Language and Information 16 (2):141-171.
    We study a multiple-succedent sequent calculus with both of the structural rules Left Weakening and Left Contraction but neither of their counterparts on the right, for possible application to the treatment of multiplicative disjunction against the background of intuitionistic logic. We find that, as Hirokawa dramatically showed in a 1996 paper with respect to the rules for implication, the rules for this connective render derivable some new structural rules, even though, unlike the rules for implication, these rules are what we (...)
    Download  
     
    Export citation  
     
    Bookmark   4 citations  
  • An Inferentialist Approach to Paraconsistency.James Trafford - 2014 - Abstracta 8 (1):55-73.
    This paper develops and motivates a paraconsistent approach to semantic paradox from within a modest inferentialist framework. I begin from the bilateralist theory developed by Greg Restall, which uses constraints on assertions and denials to motivate a multiple-conclusion sequent calculus for classical logic, and, via which, classical semantics can be determined. I then use the addition of a transparent truth-predicate to motivate an intermediate speech-act. On this approach, a liar-like sentence should be “weakly asserted”, involving a commitment to the sentence (...)
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  • Invitation to Autoepistemology.Lloyd Humberstone - 2002 - Theoria 68 (1):13-51.
    The phrase ‘autoepistemic logic’ was introduced in Moore [1985] to refer to a study inspired in large part by criticisms in Stalnaker [1980] of a particular nonmonotonic logic proposed by McDermott and Doyle.1 Very informative discussions for those who have not encountered this area are provided by Moore [1988] and the wide-ranging survey article Konolige [1994], and the scant remarks in the present introductory section do not pretend to serve in place of those treatments as summaries of the field. A (...)
    Download  
     
    Export citation  
     
    Bookmark  
  • A meta-logic of inference rules: Syntax.Alex Citkin - 2015 - Logic and Logical Philosophy 24 (3).
    Download  
     
    Export citation  
     
    Bookmark   5 citations  
  • Valuations: Bi, Tri, and Tetra.Rohan French & David Ripley - 2019 - Studia Logica 107 (6):1313-1346.
    This paper considers some issues to do with valuational presentations of consequence relations, and the Galois connections between spaces of valuations and spaces of consequence relations. Some of what we present is known, and some even well-known; but much is new. The aim is a systematic overview of a range of results applicable to nonreflexive and nontransitive logics, as well as more familiar logics. We conclude by considering some connectives suggested by this approach.
    Download  
     
    Export citation  
     
    Bookmark   10 citations  
  • Cut elimination for entailment relations.Davide Rinaldi & Daniel Wessel - 2019 - Archive for Mathematical Logic 58 (5):605-625.
    Entailment relations, introduced by Scott in the early 1970s, provide an abstract generalisation of Gentzen’s multi-conclusion logical inference. Originally applied to the study of multi-valued logics, this notion has then found plenty of applications, ranging from computer science to abstract algebra. In particular, an entailment relation can be regarded as a constructive presentation of a distributive lattice and in this guise it has proven to be a useful tool for the constructive reformulation of several classical theorems in commutative algebra. In (...)
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  • Reasoned use of expertise in argumentation.Douglas N. Walton - 1989 - Argumentation 3 (1):59-73.
    This article evaluates the strengths and weaknesses of arguments based on appeals to expertise. The intersection of two areas is explored: (i) the traditional argumentum ad verecundiam (literally, “appeal to modesty,” but characteristically the appeal to the authority of expert judgment) in informal logic, and (ii) the uses of expert systems in artificial intelligence. The article identifies a model of practical reasoning that underlies the logic of expert systems and the model of argument appropriate for the informal logic of the (...)
    Download  
     
    Export citation  
     
    Bookmark   11 citations  
  • On sequence-conclusion natural deduction systems.Branislav R. Boričić - 1985 - Journal of Philosophical Logic 14 (4):359 - 377.
    Download  
     
    Export citation  
     
    Bookmark   14 citations  
  • Arbitrary truth-value functions and natural deduction.Krister Segerberg - 1983 - Mathematical Logic Quarterly 29 (11):557-564.
    Download  
     
    Export citation  
     
    Bookmark   6 citations  
  • (1 other version)Premiss tree proofs and logic of contradiction.Zvonimir Šikić - 1990 - Mathematical Logic Quarterly 36 (3):273-280.
    Download  
     
    Export citation  
     
    Bookmark