Search results for 'Implication' (try it on Scholar)

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  1. Gillian Russell (2011). Indexicals, Context-Sensitivity and the Failure of Implication. Synthese 183 (2):143 - 160.score: 24.0
    This paper investigates, formulates and proves an indexical barrier theorem, according to which sets of non-indexical sentences do not entail (except under specified special circumstances) indexical sentences. It surveys the usual difficulties for this kind of project, as well some that are specific to the case of indexicals, and adapts the strategy of Restall and Russell's "Barriers to Implication" to overcome these. At the end of the paper a reverse barrier theorem is also proved, according to which an indexical (...)
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  2. Robert Kirk (2001). Nonreductive Physicalism and Strict Implication. Australasian Journal of Philosophy 79 (4):544-552.score: 24.0
    I have argued that a strong kind of physicalism based on the strict implication thesis can consistently reject both eliminativism and reductionism (in any nontrivial sense). This piece defends that position against objections from Andrew Melnyk, who claims that either my formulation doesn't entail physicalism, or it must be interpreted in such a way that the mental is after all reducible to the physical. His alternatives depend on two interesting assumptions. I argue that both are mistaken, thereby, making this (...)
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  3. Liza Verhoeven (2007). The Relevance of a Relevantly Assertable Disjunction for Material Implication. Journal of Philosophical Logic 36 (3):339-366.score: 24.0
    In this paper Grice's requirements for assertability are imposed on the disjunction of Classical Logic. Defining material implication in terms of negation and disjunction supplemented by assertability conditions, results in the disappearance of the most important paradoxes of material implication. The resulting consequence relation displays a very strong resemblance to Schurz's conclusion-relevant consequence relation.
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  4. Jurgen Schroder (2006). Physicalism and Strict Implication. Synthese 151 (3):537-545.score: 24.0
    The aim of this paper is to determine the plausibility of Robert Kirk’s strict implication thesis as an explication of physicalism and its relation to Jackson and Chalmer’s notion of application conditionals, to the notion of global supervenience and to a posteriori identities. It is argued that the strict implication thesis is subject to the same objection that affects the notion of global supervenience. Furthermore, reference to an idealised physics in the formulation of strict implication threatens to (...)
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  5. Jonathan P. Seldin (2000). On the Role of Implication in Formal Logic. Journal of Symbolic Logic 65 (3):1076-1114.score: 24.0
    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. (...)
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  6. Diderik Batens (2001). A Dynamic Characterization of the Pure Logic of Relevant Implication. Journal of Philosophical Logic 30 (3):267-280.score: 24.0
    This paper spells out a dynamic proof format for the pure logic of relevant implication. (A proof is dynamic if a formula derived at some stage need not be derived at a later stage.) The paper illustrates three interesting points. (i) A set of properties that characterizes an inference relation on the (very natural) dynamic proof interpretation, need not characterize the same inference relation (or even any inference relation) on the usual settheoretical interpretation. (ii) A proof format may display (...)
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  7. Claudio Pizzi (2008). Aristotle's Cubes and Consequential Implication. Logica Universalis 2 (1):143-153.score: 24.0
    . It is shown that the properties of so-called consequential implication allow to construct more than one aristotelian square relating implicative sentences of the consequential kind. As a result, if an aristotelian cube is an object consisting of two distinct aristotelian squares and four distinct “semiaristotelian” squares sharing corner edges, it is shown that there is a plurality of such cubes, which may also result from the composition of cubes of lower complexity.
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  8. Fabrice Correia (2001). Priorean Strict Implication, Q and Related Systems. Studia Logica 69 (3):411-427.score: 24.0
    We introduce a system PSI for a strict implication operator called Priorean strict implication. The semantics for PSI is based on partial Kripke models without accessibility relations. PSI is proved sound and complete with respect to that semantics, and Prior's system Q and related systems are shown to be fragments of PSI or of a mild extension of it.
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  9. Diderik Batens (forthcoming). Propositional Logic Extended with a Pedagogically Useful Relevant Implication. Logic and Logical Philosophy.score: 24.0
    First and foremost, this paper concerns the combination of classical propositional logic with a relevant implication. The proposed combination is simple and transparent from a proof theoretic point of view and at the same time extremely useful for relating formal logic to natural language sentences. A specific system will be presented and studied, also from a semantic point of view. The last sections of the paper contain more general considerations on combining classical propositional logic with a relevant logic that (...)
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  10. Jürgen Schröder (2006). Physicalism and Strict Implication. Synthese 151 (3):537 - 545.score: 24.0
    The aim of this paper is to determine the plausibility of Robert Kirk's strict implication thesis as an explication of physicalism and its relation to Jackson and Chalmer's notion of application conditionals, to the notion of global supervenience and to a posteriori identities. It is argued that the strict implication thesis is subject to the same objection that affects the notion of global supervenience. Furthermore, reference to an idealised physics in the formulation of strict implication threatens to (...)
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  11. M. Campercholi, D. Castaño & J. P. Díaz Varela (2011). Quasivarieties and Congruence Permutability of Łukasiewicz Implication Algebras. Studia Logica 98 (1-2):267-283.score: 24.0
    In this paper we study some questions concerning Łukasiewicz implication algebras. In particular, we show that every subquasivariety of Łukasiewicz implication algebras is, in fact, a variety. We also derive some characterizations of congruence permutable algebras. The starting point for these results is a representation of finite Łukasiewicz implication algebras as upwardly-closed subsets in direct products of MV-chains.
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  12. Peter Schroeder-Heister (2011). Implications-as-Rules Vs. Implications-as-Links: An Alternative Implication-Left Schema for the Sequent Calculus. [REVIEW] Journal of Philosophical Logic 40 (1):95 - 101.score: 24.0
    The interpretation of implications as rules motivates a different left-introduction schema for implication in the sequent calculus, which is conceptually more basic than the implication-left schema proposed by Gentzen. Corresponding to results obtained for systems with higher-level rules, it enjoys the subformula property and cut elimination in a weak form.
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  13. José Patricio Díaz Varela (2008). Free Łukasiewicz Implication Algebras. Archive for Mathematical Logic 47 (1):25-33.score: 24.0
    Łukasiewicz implication algebras are the {→,1}-subreducts of MV- algebras. They are the algebraic counterpart of Super-Łukasiewicz Implicational Logics investigated in Komori (Nogoya Math J 72:127–133, 1978). In this paper we give a description of free Łukasiewicz implication algebras in the context of McNaughton functions. More precisely, we show that the |X|-free Łukasiewicz implication algebra is isomorphic to ${\bigcup_{x\in X} [x_\theta)}$ for a certain congruence θ over the |X|-free MV-algebra. As corollary we describe the free algebras in all (...)
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  14. E. Espéret, P. Coirier, D. Coquin & J. -M. Passerault (1987). L'Implication du Locuteur Dans Son Discours: Discours Argumentatifs Formel Et Naturel. [REVIEW] Argumentation 1 (2):155-174.score: 24.0
    Written argumentative discourses were produced by 7 to 14 year-old children in two debate situations: one concerning a scientific issue (“Discours Formel”: DF,) and another concerning an opinion issue (“Discours Naturel”: DN). We had made the following developmental hypothesis: a specific discourse representation would be gradually built up by children in each situation, and would enable them to produce two different discourses, particularly with regard to the implication marks used by the writer. The two debate situations had been set (...)
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  15. Jeffrey Barrett (2004). Computer Implication and the Curry Paradox. Journal of Philosophical Logic 33 (6):631 - 637.score: 21.0
    There are theoretical limitations to what can be implemented by a computer program. In this paper we are concerned with a limitation on the strength of computer implemented deduction. We use a version of the Curry paradox to arrive at this limitation.
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  16. Wayne Aitken & Jeffrey A. Barrett (2004). Computer Implication and the Curry Paradox. Journal of Philosophical Logic 33 (6):631-637.score: 21.0
    There are theoretical limitations to what can be implemented by a computer program. In this paper we are concerned with a limitation on the strength of computer implemented deduction. We use a version of the Curry paradox to arrive at this limitation.
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  17. Thomas A. Long (1965). The Problem of Pain and Contextual Implication. Philosophy and Phenomenological Research 26 (September):106-111.score: 21.0
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  18. Andrea Cantini (1992). Levels of Implication and Type Free Theories of Classifications with Approximation Operator. Mathematical Logic Quarterly 38 (1):107-141.score: 21.0
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  19. K. Kikuchi (2002). Dual-Context Sequent Calculus and Strict Implication. Mathematical Logic Quarterly 48 (1):87-92.score: 21.0
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  20. Manuel Abad, Diego Castaño & José P. Díaz Varela (2010). Zariski‐Type Topology for Implication Algebras. Mathematical Logic Quarterly 56 (3):299-309.score: 21.0
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  21. Robert Kirk (1982). Physicalism, Identity, and Strict Implication. Ratio 24 (December):131-41.score: 21.0
     
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  22. Jose Patricio Díaz Varela & Antoni Torrens Torrell (2006). Decomposability of Free Łukasiewicz Implication Algebras. Archive for Mathematical Logic 45 (8):1011-1020.score: 20.0
    Łukasiewicz implication algebras are {→,1}-subreducts of Wajsberg algebras (MV-algebras). They are the algebraic counterpart of Super-Łukasiewicz Implicational logics investigated in Komori, Nogoya Math J 72:127–133, 1978. The aim of this paper is to study the direct decomposability of free Łukasiewicz implication algebras. We show that freely generated algebras are directly indecomposable. We also study the direct decomposability in free algebras of all its proper subvarieties and show that infinitely freely generated algebras are indecomposable, while finitely free generated algebras (...)
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  23. Robert Kirk (2006). Physicalism and Strict Implication. Synthese 151 (3):523-536.score: 18.0
    Suppose P is the conjunction of all truths statable in the austere vocabulary of an ideal physics. Then phsicalists are likely to accept that any truths not included in P are different ways of talking about the reality specified by P. This ‘redescription thesis’ can be made clearer by means of the ‘strict implication thesis’, according to which inconsistency or incoherence are involved in denying the implication from P to interesting truths not included in it, such as truths (...)
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  24. Jacob Blair (2011). Honor in the Military and the Possible Implication for the Traditional Separation of Jus Ad Bellum and Jus in Bello. In Applied Ethics Series (Center for Applied Ethics and Philosophy). 94-102.score: 18.0
    Traditional just war theory maintains that the two types of rules that govern justice in times of war, jus ad bellum (justice of war) and jus in bello (justice in war), are logically independent of one another. Call this the independence thesis. According to this thesis, a war that satisfies the ad bellum rules does not guarantee that the in bello rules will be satisfied; and a war that violates the ad bellum rules does not guarantee that the in bello (...)
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  25. C. Pizzi & T. Williamson (2005). Conditional Excluded Middle in Systems of Consequential Implication. Journal of Philosophical Logic 34 (4):333 - 362.score: 18.0
    It is natural to ask under what conditions negating a conditional is equivalent to negating its consequent. Given a bivalent background logic, this is equivalent to asking about the conjunction of Conditional Excluded Middle (CEM, opposite conditionals are not both false) and Weak Boethius' Thesis (WBT, opposite conditionals are not both true). In the system CI.0 of consequential implication, which is intertranslatable with the modal logic KT, WBT is a theorem, so it is natural to ask which instances of (...)
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  26. Chuansheng He (2013). E-Type Interpretation Without E-Type Pronoun: How Peirce's Graphs Capture the Uniqueness Implication of Donkey Pronouns in Discourse Anaphora. Synthese:1-20.score: 18.0
    In this essay, we propose that Peirce’s Existential Graphs can derive the desired uniqueness implication (or in a weaker claim, the definite description readings) of donkey pronouns in conjunctive discourse (A man walks in the park. He whistles), without postulating a separate category of E-type pronouns.
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  27. Greg Restall, Barriers to Implication.score: 18.0
    Implication barrier theses deny that one can derive sentences of one type from sentences of another. Hume’s Law is an implication barrier thesis; it denies that one can derive an ‘ought’ (a normative sentence) from an ‘is’ (a descriptive sentence). Though Hume’s Law is controversial, some barrier theses are philosophical platitudes; in his Lectures on Logical Atomism, Bertrand Russell claims: You can never arrive at a general proposition by inference particular propositions alone. You will always have to have (...)
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  28. Ross T. Brady (1996). Relevant Implication and the Case for a Weaker Logic. Journal of Philosophical Logic 25 (2):151 - 183.score: 18.0
    We collect together some misgivings about the logic R of relevant inplication, and then give support to a weak entailment logic $DJ^{d}$ . The misgivings centre on some recent negative results concerning R, the conceptual vacuousness of relevant implication, and the treatment of classical logic. We then rectify this situation by introducing an entailment logic based on meaning containment, rather than meaning connection, which has a better relationship with classical logic. Soundness and completeness results are proved for $DJ^{d}$ with (...)
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  29. B. G. Sundholm (1998). Inference, Consequence, Implication: A Constructivist's Perspective. Philosophia Mathematica 6 (2):178-194.score: 18.0
    An implication is a proposition, a consequence is a relation between propositions, and an inference is act of passage from certain premise-judgements to another conclusion-judgement: a proposition is true, a consequence holds, whereas an inference is valid. The paper examines interrelations, differences, refinements and linguistic renderings of these notions, as well as their history. The truth of propositions, respectively the holding of consequences, are treated constructively in terms of verification-objects. The validity of an inference is elucidated in terms of (...)
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  30. Stephen Barker (1997). Material Implication and General Indicative Conditionals. Philosophical Quarterly 47 (187):195-211.score: 18.0
    This paper falls into two parts. In the first part, I argue that consideration of general indicative conditionals, e.g., sentences like If a donkey brays it is beaten, provides a powerful argument that a pure material implication analysis of indicative if p, q is correct. In the second part I argue, opposing writers like Jackson, that a Gricean style theory of pragmatics can explain the manifest assertability conditions of if p, q in terms of its conventional content – assumed (...)
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  31. Claudio Pizzi & Timothy Williamson (1997). Strong Boethius' Thesis and Consequential Implication. Journal of Philosophical Logic 26 (5):569-588.score: 18.0
    The paper studies the relation between systems of modal logic and systems of consequential implication, a non-material form of implication satisfying "Aristotle's Thesis" (p does not imply not p) and "Weak Boethius' Thesis" (if p implies q, then p does not imply not q). Definitions are given of consequential implication in terms of modal operators and of modal operators in terms of consequential implication. The modal equivalent of "Strong Boethius' Thesis" (that p implies q implies that (...)
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  32. Peter B. M. Vranas, “Barriers to Implication”.score: 18.0
    I was quite excited when I first read Restall and Russell’s (2010) paper. For two reasons. First, because the paper provides rigorous formulations and formal proofs of implication barrier theses, namely “theses [which] deny that one can derive sentences of one type from sentences of another”. Second (and primarily), because the paper proves a general theorem, the Barrier Construction Theorem, which unifies implication barrier theses concerning four topics: generality, necessity, time, and normativity. After thinking about the paper, I (...)
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  33. Jean-Yves Beziau, Introduction of Implication and Generalization in Axiomatic Calculi.score: 18.0
    of implication and generalization rules have a close relationship, for which there is a key idea for clarifying how they are connected: varying objects. Varying objects trace how generalization rules are used along a demonstration in an axiomatic calculus. Some ways for introducing implication and for generalization are presented here, taking into account some basic properties that calculi can have.
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  34. Arthur Buchsbaum & Jean-Yves Beziau, Introduction of Implication and Generalization in Axiomatic Calculi.score: 18.0
    of implication and generalization rules have a close relationship, for which there is a key idea for clarifying how they are connected: varying objects. Varying objects trace how generalization rules are used along a demonstration in an axiomatic calculus. Some ways for introducing implication and for generalization are presented here, taking into account some basic properties that calculi can have.
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  35. Dov M. Gabbay & Nicola Olivetti (1998). Algorithmic Proof Methods and Cut Elimination for Implicational Logics Part I: Modal Implication. Studia Logica 61 (2):237-280.score: 18.0
    In this work we develop goal-directed deduction methods for the implicational fragment of several modal logics. We give sound and complete procedures for strict implication of K, T, K4, S4, K5, K45, KB, KTB, S5, G and for some intuitionistic variants. In order to achieve a uniform and concise presentation, we first develop our methods in the framework of Labelled Deductive Systems [Gabbay 96]. The proof systems we present are strongly analytical and satisfy a basic property of cut admissibility. (...)
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  36. Jan Heylen (forthcoming). Closure of A Priori Knowability Under A Priori Knowable Material Implication. Erkenntnis:1-22.score: 18.0
    The topic of this article is the closure of a priori knowability under a priori knowable material implication: if a material conditional is a priori knowable and if the antecedent is a priori knowable, then the consequent is a priori knowable as well. This principle is arguably correct under certain conditions, but there is at least one counterexample when completely unrestricted. To deal with this, Anderson proposes to restrict the closure principle to necessary truths and Horsten suggests to restrict (...)
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  37. Peter B. M. Vranas, Comments on Greg Restall & Gillian Russell's “Barriers to Implication”.score: 18.0
    I was quite excited when I first read Restall and Russell’s (2010) paper. For two reasons. First, because the paper provides rigorous formulations and formal proofs of implication barrier the- ses, namely “theses [which] deny that one can derive sentences of one type from sentences of another”. Second (and primarily), because the paper proves a general theorem, the Barrier Con- struction Theorem, which unifies implication barrier theses concerning four topics: generality, necessity, time, and normativity. After thinking about the (...)
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  38. Isabel C. Hungerland (1960). Contextual Implication. Inquiry 3 (1-4):211 – 258.score: 18.0
    In this essay, I have rejected the inductive interpretation of the paradigm of contextual implication (to say “p”; is to imply that one believes that ) and proposed in its stead an explicatory model according to which a speaker in making a statement contextually implies whatever one is entitled to infer on the basis of the presumption that his act of stating is normal. In developing this model, I show how contextual implication depends on three distinct matters: a (...)
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  39. Richard Sylvan & Newton Costa (1988). Cause as an Implication. Studia Logica 47 (4):413 - 428.score: 18.0
    An appropriately unprejudiced logical investigation of causation as a type of implication relation is undertaken. The implication delineated is bounded syntactically. The developing argument then leads to a very natural process analysis, which demonstrably captures the established syntactical features. Next relevantly-based semantics for the resulting logical theory are adduced, and requisite adequacy results delivered. At the end of the tour, further improvements are pointed out, and the attractive terrain beyond present developments is glimpsed.
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  40. Marcello D'agostino, Dov M. Gabbay & Alessandra Russo (1997). Grafting Modalities Onto Substructural Implication Systems. Studia Logica 59 (1):65-102.score: 18.0
    We investigate the semantics of the logical systems obtained by introducing the modalities and into the family of substructural implication logics (including relevant, linear and intuitionistic implication). Then, in the spirit of the LDS (Labelled Deductive Systems) methodology, we "import" this semantics into the classical proof system KE. This leads to the formulation of a uniform labelled refutation system for the new logics which is a natural extension of a system for substructural implication developed by the first (...)
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  41. Claudio Cerrato (1994). Natural Deduction Based Upon Strict Implication for Normal Modal Logics. Notre Dame Journal of Formal Logic 35 (4):471-495.score: 18.0
    We present systems of Natural Deduction based on Strict Implication for the main normal modal logics between K and S5. In this work we consider Strict Implication as the main modal operator, and establish a natural correspondence between Strict Implication and strict subproofs.
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  42. Branden Fitelson, MaGIC: Matrix Generator for Implication Connectives.score: 18.0
    The program MaGIC (Matrix Generator for Implication Connectives) is intended as a tool for logical research. It computes small algebras (normally with up to 14 elements) suitable for modelling certain non-classical logics. Along the way, it eliminates from the output any algebra isomorphic to one already generated, thus returning only one from each isomorphism class. Optionally, the user may specify a formula which is to be..
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  43. Davis Baird (1984). Tests of Significance Violate the Rule of Implication. PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1984:81 - 92.score: 18.0
    The rule of implication, (+) If hypothesis H implies hypothesis I, then evidence sufficient to warrant the rejection of I, in turn warrants the rejection of H, is a very plausible principle of inductive inference. It is shown that significance tests violate this principle. Two ways to account for this violation are considered; neither account is fully satisfactory. First, a distinction might be made between the absolute degree of confirmation and the change in the degree of confirmation due to (...)
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  44. Mitsuhiro Okada (1987). A Weak Intuitionistic Propositional Logic with Purely Constructive Implication. Studia Logica 46 (4):371 - 382.score: 18.0
    We introduce subsystems WLJ and SI of the intuitionistic propositional logic LJ, by weakening the intuitionistic implication. These systems are justifiable by purely constructive semantics. Then the intuitionistic implication with full strength is definable in the second order versions of these systems. We give a relationship between SI and a weak modal system WM. In Appendix the Kripke-type model theory for WM is given.
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  45. Yoad Winter (1994). Contrast and Implication in Natural Language. Journal of Semantics 11 (4):365-406.score: 18.0
    In this paper we introduce a theoretical framework and a logical application for analysing the semantics and pragmatics of contrastive conjunctions in natural language. It is shown how expressions like although, nevertheless, yet, and but are semantically definable as connectives using an operator for implication in natural language and how similar pragmatic principles affect the behaviour of both contrastive conjunctions and indicative conditionals. Following previous proposals, conditions on contrast in a conjunction are analysed as presuppositions of die conjunction. Further (...)
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  46. Joseph S. Fulda (1989). Material Implication Revisited. American Mathematical Monthly 96 (3):247-250.score: 18.0
    Demonstrates that the "paradoxes of material implication" are only apparent, sticking entirely within the confines of classical logic.
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  47. Robert Goldblatt (2009). Conservativity of Heyting Implication Over Relevant Quantification. Review of Symbolic Logic 2 (2):310-341.score: 18.0
    It is known that propositional relevant logics can be conservatively extended by the addition of a Heyting (intuitionistic) implication connective. We show that this same conservativity holds for a range of first-order relevant logics with strong identity axioms, using an adaptation of Fine’s stratified model theory. For systems without identity, the question of conservatively adding Heyting implication is thereby reduced to the question of conservatively adding the axioms for identity. Some results in this direction are also obtained. The (...)
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  48. Herman Jurjus & Harrie de Swart (2001). Implication with Possible Exceptions. Journal of Symbolic Logic 66 (2):517-535.score: 18.0
    We introduce an implication-with-possible-exceptions and define validity of rules-with-possible-exceptions by means of the topological notion of a full subset. Our implication-with-possible-exceptions characterises the preferential consequence relation as axiomatized by Kraus, Lehmann and Magidor [Kraus, Lehmann, and Magidor, 1990]. The resulting inference relation is non-monotonic. On the other hand, modus ponens and the rule of monotony, as well as all other laws of classical propositional logic, are valid-up-to-possible exceptions. As a consequence, the rules of classical propositional logic do not (...)
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  49. Matthew Lockard (2013). Implication and Reasoning in Mental State Attribution: Comments on Jane Heal's Theory of Co-Cognition. Philosophical Psychology (5):1-16.score: 18.0
    Implication and reasoning in mental state attribution: Comments on Jane Heal's theory of co-cognition. . ???aop.label???. doi: 10.1080/09515089.2012.730040.
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  50. John L. Pollock (1967). Non-Analytic Implication. Inquiry 10 (1-4):196 – 203.score: 18.0
    Some ordinary language philosophers, including Stanley Cavell, have attacked certain tendencies of traditional philosophers as follows. E.g., when we say that something looks red to us, we imply that we think it isn't really red. Thus we arc breaking a rule of language when we say that something looks red to us when we know it is red. And thus there is something logically wrong with the traditional attempt, to say that what justifies us in thinking that something is red (...)
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