Search results for 'relevance logic' (try it on Scholar)

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  1. Vladimir L. Vasyukov (2011). Paraconsistency in Categories: Case of Relevance Logic. Studia Logica 98 (3):429-443.score: 180.0
    Categorical-theoretic semantics for the relevance logic is proposed which is based on the construction of the topos of functors from a relevant algebra (considered as a preorder category endowed with the special endofunctors) in the category of sets Set. The completeness of the relevant system R of entailment is proved in respect to the semantic considered.
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  2. Lisa Galminas & John G. Mersch (2012). A Pretabular Classical Relevance Logic. Studia Logica 100 (6):1211-1221.score: 180.0
    In this paper we construct an extension, ℒ, of Anderson and Belnap's relevance logic R that is classical in the sense that it contains p&p → q as a theorem, and we prove that ℒ is pretabular in the sense that while it does not have a finite characteristic matrix, every proper normal extension of it does. We end the paper by commenting on the possibility of finding other classical relevance logics that are also pretabular.
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  3. Jan Dejnožka (2010). The Concept of Relevance and the Logic Diagram Tradition. Logica Universalis 4 (1):67-135.score: 154.0
    What is logical relevance? Anderson and Belnap say that the “modern classical tradition [,] stemming from Frege and Whitehead-Russell, gave no consideration whatsoever to the classical notion of relevance.” But just what is this classical notion? I argue that the relevance tradition is implicitly most deeply concerned with the containment of truth-grounds, less deeply with the containment of classes, and least of all with variable sharing in the Anderson–Belnap manner. Thus modern classical logicians such as Peirce, Frege, (...)
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  4. Ryszard Mirek (2011). The Systems of Relevance Logic. ARGUMENT 1 (1):87-102.score: 148.0
    The system R, or more precisely the pure implicational fragment R›, is considered by the relevance logicians as the most important. The another central system of relevance logic has been the logic E of entailment that was supposed to capture strict relevant implication. The next system of relevance logic is RM or R-mingle. The question is whether adding mingle axiom to R› yields the pure implicational fragment RM› of the system? As concerns the weak (...)
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  5. Eunsuk Yang (2014). Algebraic Kripke-Style Semantics for Relevance Logics. Journal of Philosophical Logic 43 (4):803-826.score: 134.0
    This paper deals with one kind of Kripke-style semantics, which we shall call algebraic Kripke-style semantics, for relevance logics. We first recall the logic R of relevant implication and some closely related systems, their corresponding algebraic structures, and algebraic completeness results. We provide simpler algebraic completeness proofs. We then introduce various types of algebraic Kripke-style semantics for these systems and connect them with algebraic semantics.
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  6. Josep Maria Font & Gonzalo Rodríguez (1994). Algebraic Study of Two Deductive Systems of Relevance Logic. Notre Dame Journal of Formal Logic 35 (3):369-397.score: 126.0
    In this paper two deductive systems (i.e., two consequence relations) associated with relevance logic are studied from an algebraic point of view. One is defined by the familiar, Hilbert-style, formalization of R; the other one is a weak version of it, called WR, which appears as the semantic entailment of the Meyer-Routley-Fine semantics, and which has already been suggested by Wójcicki for other reasons. This weaker consequence is first defined indirectly, using R, but we prove that the first (...)
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  7. Robin Hirsch & Szabolcs Mikulás (2011). Positive Fragments of Relevance Logic and Algebras of Binary Relations. Review of Symbolic Logic 4 (1):81-105.score: 126.0
    We prove that algebras of binary relations whose similarity type includes intersection, union, and one of the residuals of relation composition form a nonfinitely axiomatizable quasivariety and that the equational theory is not finitely based. We apply this result to the problem of the completeness of the positive fragment of relevance logic with respect to binary relations.
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  8. C. Kenneth Waters (1987). Relevance Logic Brings Hope to Hypothetico-Deductivism. Philosophy of Science 54 (3):453-464.score: 120.0
    Clark Glymour has argued that hypothetico-deductivism, which many take to be an important method of scientific confirmation, is hopeless because it cannot be reconstructed in classical logic. Such reconstructions, as Glymour points out, fail to uphold the condition of relevance between theory and evidence. I argue that the source of the irrelevant confirmations licensed by these reconstructions lies not with hypothetico-deductivism itself, but with the classical logic in which it is typically reconstructed. I present a new reconstruction (...)
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  9. James B. Freeman & Charles B. Daniels (1979). A Second-Order Relevance Logic with Modality. Studia Logica 38 (2):113 - 135.score: 120.0
    In this paper a system, RPF, of second-order relevance logic with S5 necessity is presented which contains a defined, notion of identity for propositions. A complete semantics is provided. It is shown that RPF allows for more than one necessary proposition. RPF contains primitive syntactic counterparts of the following semantic notions: (1) the reflexive, symmetrical, transitive binary alternativeness relation for S5 necessity, (2) the ternary Routley-Meyer alternativeness relation for implication, and (3) the Routley-Meyer notion of a prime intensional (...)
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  10. Edwin D. Mares (1992). Semantics for Relevance Logic with Identity. Studia Logica 51 (1):1 - 20.score: 120.0
    Models are constructed for a variety of systems of quantified relevance logic with identity. Models are given for systems with different principles governing the transitivity of identity and substitution, and the relative merits of these principles are discussed. The models in this paper are all extensions of the semantics of Fine's Semantics for Quantified Relevance Logic (Journal of Philosophical Logic 17 (1988)).
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  11. David C. Makinson, Relevance Logic as a Conservative Extension of Classical Logic.score: 120.0
    Relevance logic is ordinarily seen as a subsystem of classical logic under the translation that replaces arrows by horseshoes. If, however, we consider the arrow as an additional connective alongside the horseshoe, then another perspective emerges: the theses of relevance logic, specifically the system R, may also be seen as the output of a conservative extension of the relation of classical consequence. We describe two ways in which this may be done. One is by defining (...)
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  12. Luca Viganò (2000). An o(N Log N)-Space Decision Procedure for the Relevance Logic B+. Studia Logica 66 (3):385-407.score: 120.0
    In previous work we gave a new proof-theoretical method for establishing upper-bounds on the space complexity of the provability problem of modal and other propositional non-classical logics. Here we extend and refine these results to give an O(n log n)-space decision procedure for the basic positive relevance logic B+. We compute this upper-bound by first giving a sound and complete, cut-free, labelled sequent system for B+, and then establishing bounds on (...)
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  13. Mark Jago (2013). Recent Work in Relevant Logic. Analysis 73 (3):526-541.score: 116.0
    This paper surveys important work done in relevant logic in the past 10 years.
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  14. Edwin David Mares (2004). Relevant Logic: A Philosophical Interpretation. Cambridge Univeristy Press.score: 116.0
    This book introduces the reader to relevant logic and provides it with a philosophical interpretation. The defining feature of relevant logic is that it forces the premises of an argument to be really used ('relevant') in deriving its conclusion. The logic is placed in the context of possible world semantics and situation semantics, which are then applied to provide an understanding of the various logical particles (especially implication and negation) and natural language conditionals. The book ends by (...)
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  15. Lou Goble (2000). An Incomplete Relevant Modal Logic. Journal of Philosophical Logic 29 (1):103-119.score: 114.0
    The relevant modal logic G is a simple extension of the logic RT, the relevant counterpart of the familiar classically based system T. Using the Routley-Meyer semantics for relevant modal logics, this paper proves three main results regarding G: (i) G is semantically complete, but only with a non-standard interpretation of necessity. From this, however, other nice properties follow. (ii) With a standard interpretation of necessity, G is semantically incomplete; there is no class of frames that characterizes G. (...)
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  16. J. Michael Dunn & Katalin Bimb� (2001). Four-Valued Logic. Notre Dame Journal of Formal Logic 42 (3):171-192.score: 110.0
    Four-valued semantics proved useful in many contexts from relevance logics to reasoning about computers. We extend this approach further. A sequent calculus is defined with logical connectives conjunction and disjunction that do not distribute over each other. We give a sound and complete semantics for this system and formulate the same logic as a tableaux system. Intensional conjunction (fusion) and its residuals (implications) can be added to the sequent calculus straightforwardly. We extend a simplified version of the earlier (...)
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  17. Barry Smith (1991). Relevance, Relatedness and Restricted Set Theory. In Georg Schurz (ed.), Advances in Scientific Philosophy. 45--56.score: 108.0
    Relevance logic has become ontologically fertile. No longer is the idea of relevance restricted in its application to purely logical relations among propositions, for as Dunn has shown in his (1987), it is possible to extend the idea in such a way that we can distinguish also between relevant and irrelevant predications, as for example between “Reagan is tall” and “Reagan is such that Socrates is wise”. Dunn shows that we can exploit certain special properties of identity (...)
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  18. Eunsuk Yang (2013). R and Relevance Principle Revisited. Journal of Philosophical Logic 42 (5):767-782.score: 108.0
    This paper first shows that some versions of the logic R of Relevance do not satisfy the relevance principle introduced by Anderson and Belnap, the principle of which is generally accepted as the principle for relevance. After considering several possible (but defective) improvements of the relevance principle, this paper presents a new relevance principle for (three versions of) R, and explains why this principle is better than the original and others.
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  19. Ahti-Veikko Pietarinen (2005). Compositionality, Relevance, and Peirce's Logic of Existential Graphs. Axiomathes 15 (4):513-540.score: 108.0
    Charles S. Peirce’s pragmatist theory of logic teaches us to take the context of utterances as an indispensable logical notion without which there is no meaning. This is not a spat against compositionality per se , since it is possible to posit extra arguments to the meaning function that composes complex meaning. However, that method would be inappropriate for a realistic notion of the meaning of assertions. To accomplish a realistic notion of meaning (as opposed e.g. to algebraic meaning), (...)
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  20. Andreas Schöter (1996). Evidential Bilattice Logic and Lexical Inference. Journal of Logic, Language and Information 5 (1):65-105.score: 108.0
    This paper presents an information-based logic that is applied to the analysis of entailment, implicature and presupposition in natural language. The logic is very fine-grained and is able to make distinctions that are outside the scope of classical logic. It is independently motivated by certain properties of natural human reasoning, namely partiality, paraconsistency, relevance, and defeasibility: once these are accounted for, the data on implicature and presupposition comes quite naturally.The logic is based on the family (...)
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  21. Roger D. Maddux (2010). Relevance Logic and the Calculus of Relations. Review of Symbolic Logic 3 (1):41-70.score: 102.0
    Sound and complete semantics for classical propositional logic can be obtained by interpreting sentences as sets. Replacing sets with commuting dense binary relations produces an interpretation that turns out to be sound but not complete for R. Adding transitivity yields sound and complete semantics for RM, because all normal Sugihara matrices are representable as algebras of binary relations.
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  22. Stephen Read (1988). Relevant Logic: A Philosophical Examination of Inference. B. Blackwell.score: 102.0
  23. Kit Fine (1988). Semantics for Quantified Relevance Logic. Journal of Philosophical Logic 17 (1):27 - 59.score: 96.0
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  24. B. J. Copeland (1979). On When a Semantics is Not a Semantics: Some Reasons for Disliking the Routley-Meyer Semantics for Relevance Logic. [REVIEW] Journal of Philosophical Logic 8 (1):399 - 413.score: 96.0
  25. Yingjin Xu & Pei Wang (2012). The Frame Problem, the Relevance Problem, and a Package Solution to Both. Synthese 187 (S1):43-72.score: 96.0
    As many philosophers agree, the frame problem is concerned with how an agent may efficiently filter out irrelevant information in the process of problem-solving. Hence, how to solve this problem hinges on how to properly handle semantic relevance in cognitive modeling, which is an area of cognitive science that deals with simulating human's cognitive processes in a computerized model. By "semantic relevance", we mean certain inferential relations among acquired beliefs which may facilitate information retrieval and practical reasoning under (...)
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  26. Arnon Avron (1992). Whither Relevance Logic? Journal of Philosophical Logic 21 (3):243 - 281.score: 96.0
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  27. Garrel Pottinger (1979). A New Classical Relevance Logic. Journal of Philosophical Logic 8 (1):135 - 147.score: 96.0
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  28. William Max Knorpp (1997). The Relevance of Logic to Reasoning and Beleif Revision: Harman on 'Change in View'. Pacific Philosophical Quarterly 78 (1):78–92.score: 96.0
    In Change of View: Principles of Reasoning, Gilbert Harman argues that (i) all genuine reasoning is a matter of belief revision, and that, since (ii) logic is not "specially relevant" to belief revision, (iii) logic is not specially relevant to reasoning, either. Thus, Harman suggests, what is needed is a "theory of reasoning"-which, incidentally, will be psychologistic, telling us both how we do and how we should reason. I argue that Harman fails to establish the need for such (...)
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  29. J. B. Paris & P. Waterhouse (2009). Atom Exchangeability and Instantial Relevance. Journal of Philosophical Logic 38 (3):313 - 332.score: 96.0
    We give an account of some relationships between the principles of Constant and Atom Exchangeability and various generalizations of the Principle of Instantial Relevance within the framework of Inductive Logic. In particular we demonstrate some surprising and somewhat counterintuitive dependencies of these relationships on ostensibly unimportant parameters, such as the number of predicates in the overlying language.
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  30. Philip Kremer (1993). Quantifying Over Propositions in Relevance Logic: Nonaxiomatisability of Primary Interpretations of ∀P and ∃P. Journal of Symbolic Logic 58 (1):334-349.score: 96.0
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  31. Alasdair Urquhart (1999). The Complexity of Decision Procedures in Relevance Logic II. Journal of Symbolic Logic 64 (4):1774-1802.score: 96.0
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  32. G. Charlwood (1981). An Axiomatic Version of Positive Semilattice Relevance Logic. Journal of Symbolic Logic 46 (2):233-239.score: 96.0
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  33. Marvin J. Croy (2010). Teaching the Practical Relevance of Propositional Logic. Teaching Philosophy 33 (3):253-270.score: 96.0
    This article advances the view that propositional logic can and should be taught within general education logic courses in ways that emphasizes its practical usefulness, much beyond what commonly occurs in logic textbooks. Discussion and examples of this relevance include database searching, understanding structured documents, and integrating concepts of proof construction with argument analysis. The underlying rationale for this approach is shown to have import for questions concerning the design of logic courses, textbooks, and the (...)
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  34. David Hitchcock (2000). The Significance of Informal Logic for Philosophy. Informal Logic 20 (2).score: 96.0
    Informal logic is a new sub-discipline of philosophy, roughly definable as the philosophy of argument. Contributors have challenged the traditional concept of an argument as a premiss-conclusion complex, in favour of speech-act, functional and dialogical conceptions; they have identified as additional components warrants, modal qualifiers, rebuttals, and a dialectical tier. They have objected that "soundness" is neither necessary nor sufficient for a good argument. Alternative proposals include acceptability, relevance and sufficiency of the premisses; conformity to a valid argument (...)
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  35. Arnon Avron (2014). The Classical Constraint on Relevance. Logica Universalis 8 (1):1-15.score: 96.0
    We show that as long as the propositional constants t and f are not included in the language, any language-preserving extension of any important fragment of the relevance logics R and RMI can have only classical tautologies as theorems (this includes intuitionistic logic and its extensions). This property is not preserved, though, if either t or f is added to the language, or if the contraction axiom is deleted.
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  36. M. W. Bunder (1979). A More Relevant Relevance Logic. Notre Dame Journal of Formal Logic 20 (3):701-704.score: 96.0
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  37. Arnon Avron (2014). What is Relevance Logic? Annals of Pure and Applied Logic 165 (1):26-48.score: 96.0
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  38. Johan van Benthem (1984). Review: B. J. Copeland, On When a Semantics is Not a Semantics: Some Reasons for Disliking the Routley-Meyer Semantics for Relevance Logic. [REVIEW] Journal of Symbolic Logic 49 (3):994-995.score: 96.0
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  39. Derek Allen (1993). Relevance, Conduction and Canada's Rape-Shield Decision. Informal Logic 15 (2).score: 96.0
    I examine a Canadian Supreme Court decision concerning the constitutionality of Canada's 1982 rape-shield legislation, and suggest how material from the decision might profitably be used in an informal-logic class in connection with the topics of relevance and conductive argument. I also consider theoretical matters related to the decision: first I develop two analyses of what I call an argument from 'unchasteness' and connect them to George Bowles's theory of propositional relevance; then I present Trudy Govier with (...)
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  40. Katalin Bimbó (2005). Types of I -Free Hereditary Right Maximal Terms. Journal of Philosophical Logic 34 (5/6):607 - 620.score: 96.0
    The implicational fragment of the relevance logic "ticket entailment" is closely related to the so-called hereditary right maximal terms. I prove that the terms that need to be considered as inhabitants of the types which are theorems of $T_\rightarrow$ are in normal form and built in all but one casefrom B, B' and W only. As a tool in the proof ordered term rewriting systems are introduced. Based on the main theorem I define $FIT_\rightarrow$ - a Fitch-style calculus (...)
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  41. Brian Skyrms (1992). Review: Clark Glymour, Discussion: Hypothetico-Deductivism is Hopeless; C. Kenneth Waters, Relevance Logic Brings Hope to Hypothetico-Deductivism; Thomas R. Grimes, Discussion: Truth, Content, and the Hypothetico-Deductive Method. [REVIEW] Journal of Symbolic Logic 57 (2):756-758.score: 96.0
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  42. Harry Deutsch (1992). Review: J. Michael Dunn, Relevance Logic and Entailment. [REVIEW] Journal of Symbolic Logic 57 (2):752-753.score: 96.0
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  43. Josep M. Font & Gonzalo Rodríguez (1990). Note on Algebraic Models for Relevance Logic. Mathematical Logic Quarterly 36 (6):535-540.score: 96.0
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  44. Brian Skyrms (1992). Glymour Clark. Discussion: Hypothetico-Deductivism is Hopeless. Philosophy of Science, Vol. 47 (1980), Pp. 322–325. Waters C. Kenneth. Relevance Logic Brings Hope to Hypothetico-Deductivism. Philosophy of Science, Vol. 54 (1987), Pp. 453–464. Grimes Thomas R.. Discussion: Truth, Content, and the Hypothetico-Deductive Method. Philosophy of Science, Vol. 57 (1990), Pp. 514–522. [REVIEW] Journal of Symbolic Logic 57 (2):756-758.score: 96.0
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  45. Michael Dunn & Greg Restall (2002). Relevance Logic. In D. Gabbay & F. Guenthner (eds.), Handbook of Philosophical Logic. Kluwer.score: 96.0
     
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  46. Aleksandar Kron (1985). A Constructive Proof of a Theorem in Relevance Logic. Mathematical Logic Quarterly 31 (25‐28):423-430.score: 96.0
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  47. Edwin D. Mares (1993). Classically Complete Modal Relevant Logics. Mathematical Logic Quarterly 39 (1):165-177.score: 96.0
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  48. Brian Skyrms (1992). Review of “Hypothetico-Deductivism is Hopeless” by Clark Glymour,“Relevance Logic Brings Hope for Hypothetico-Deductivism” by C. Kenneth Waters, and “Truth, Content and Hypothetico-Deductive Method” by Thomas Grimes. [REVIEW] Journal of Symbolic Logic 57:756-758.score: 96.0
     
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  49. John A. Barker (1975). Relevance Logic, Classical Logic, and Disjunctive Syllogism. Philosophical Studies 27 (6):361 - 376.score: 90.0
  50. J. Landes, J. B. Paris & A. Vencovská (2011). A Survey of Some Recent Results on Spectrum Exchangeability in Polyadic Inductive Logic. Synthese 181 (1):19 - 47.score: 90.0
    We give a unified account of some results in the development of Polyadic Inductive Logic in the last decade with particular reference to the Principle of Spectrum Exchangeability, its consequences for Instantial Relevance, Language Invariance and Johnson's Sufficientness Principle, and the corresponding de Finetti style representation theorems.
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