Results for 'consequence relations'

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  1. Simple Consequence Relations.Arnon Avron - unknown
    We provide a general investigation of Logic in which the notion of a simple consequence relation is taken to be fundamental. Our notion is more general than the usual one since we give up monotonicity and use multisets rather than sets. We use our notion for characterizing several known logics (including Linear Logic and non-monotonic logics) and for a general, semantics-independent classi cation of standard connectives via equations on consequence relations (these include Girard's \multiplicatives" and \additives"). We (...)
     
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  2.  33
    Consequence Relations and Admissible Rules.Rosalie Iemhoff - 2016 - Journal of Philosophical Logic 45 (3):327-348.
    This paper contains a detailed account of the notion of admissibility in the setting of consequence relations. It is proved that the two notions of admissibility used in the literature coincide, and it provides an extension to multi–conclusion consequence relations that is more general than the one usually encountered in the literature on admissibility. The notion of a rule scheme is introduced to capture rules with side conditions, and it is shown that what is generally understood (...)
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  3.  25
    Modal Consequence Relations Extending $Mathbf{S4.3}$: An Application of Projective Unification.Wojciech Dzik & Piotr Wojtylak - 2016 - Notre Dame Journal of Formal Logic 57 (4):523-549.
    We characterize all finitary consequence relations over S4.3, both syntactically, by exhibiting so-called passive rules that extend the given logic, and semantically, by providing suitable strongly adequate classes of algebras. This is achieved by applying an earlier result stating that a modal logic L extending S4 has projective unification if and only if L contains S4.3. In particular, we show that these consequence relations enjoy the strong finite model property, and are finitely based. In this way, (...)
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  4.  52
    Equivalence of Consequence Relations: An Order-Theoretic and Categorical Perspective.Nikolaos Galatos & Constantine Tsinakis - 2009 - Journal of Symbolic Logic 74 (3):780-810.
    Equivalences and translations between consequence relations abound in logic. The notion of equivalence can be defined syntactically, in terms of translations of formulas, and order-theoretically, in terms of the associated lattices of theories. W. Blok and D. Pigozzi proved in [4] that the two definitions coincide in the case of an algebraizable sentential deductive system. A refined treatment of this equivalence was provided by W. Blok and B. Jónsson in [3]. Other authors have extended this result to the (...)
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  5.  84
    Consequence Mining: Constans Versus Consequence Relations.Denis Bonnay & Dag Westerståhl - 2012 - Journal of Philosophical Logic 41 (4):671-709.
    The standard semantic definition of consequence with respect to a selected set X of symbols, in terms of truth preservation under replacement (Bolzano) or reinterpretation (Tarski) of symbols outside X, yields a function mapping X to a consequence relation ⇒x. We investigate a function going in the other direction, thus extracting the constants of a given consequence relation, and we show that this function (a) retrieves the usual logical constants from the usual logical consequence relations, (...)
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  6.  14
    Tarskian Consequence Relations Bilaterally: Some Familiar Notions.Sergey Drobyshevich - 2019 - Synthese 198 (S22):5213-5240.
    This paper is dedicated to developing a formalism that takes rejection seriously. Bilateral notation of signed formulas with force indicators is adopted to define signed consequences which can be viewed as the bilateral counterpart of Tarskian consequence relations. Its relation to some other bilateral approaches is discussed. It is shown how David Nelson’s logic N4 can be characterized bilaterally and the corresponding completeness result is proved. Further, bilateral variants of three familiar notions are considered and investigated: that of (...)
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  7.  68
    Some Supervaluation-Based Consequence Relations.Philip Kremer & Michael Kremer - 2003 - Journal of Philosophical Logic 32 (3):225-244.
    In this paper, we define some consequence relations based on supervaluation semantics for partial models, and we investigate their properties. For our main consequence relation, we show that natural versions of the following fail: upwards and downwards Lowenheim-Skolem, axiomatizability, and compactness. We also consider an alternate version for supervaluation semantics, and show both axiomatizability and compactness for the resulting consequence relation.
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  8.  46
    A Primer on Rational Consequence Relations, Popper Functions, and Their Ranked Structures.James Hawthorne - 2014 - Studia Logica 102 (4):731-749.
    Rational consequence relations and Popper functions provide logics for reasoning under uncertainty, the former purely qualitative, the latter probabilistic. But few researchers seem to be aware of the close connection between these two logics. I’ll show that Popper functions are probabilistic versions of rational consequence relations. I’ll not assume that the reader is familiar with either logic. I present them, and explicate the relationship between them, from the ground up. I’ll also present alternative axiomatizations for each (...)
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  9.  17
    Graded Consequence Relations and Fuzzy Closure Operator.Giangiacomo Gerla - 1996 - Journal of Applied Non-Classical Logics 6 (4):369-379.
    ABSTRACT In this work the connections between the fuzzy closure operators and the graded consequence relations are examined Namely, as it is well known, in the crisp case there is a complete equivalence between the notion of closure operator and the one of consequence relation. We extend this result by proving that the graded consequence relations are related to a particular class of fuzzy closure operators, namely the class of fuzzy closure operators that can be (...)
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  10. Abductive Consequence Relations.Jorge Lobo & Carlos Uzcátegui - 1997 - Artificial Intelligence 89 (1-2):149-171.
  11. Contractions of Noncontractive Consequence Relations.Rohan French & David Ripley - 2015 - Review of Symbolic Logic 8 (3):506-528.
    Some theorists have developed formal approaches to truth that depend on counterexamples to the structural rules of contraction. Here, we study such approaches, with an eye to helping them respond to a certain kind of objection. We define a contractive relative of each noncontractive relation, for use in responding to the objection in question, and we explore one example: the contractive relative of multiplicative-additive affine logic with transparent truth, or MAALT. -/- .
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  12.  41
    The Consequence Relation Preserving Logical Information.Andrzej Pietruszczak - 2004 - Logic and Logical Philosophy 13:89-120.
    Information is contained in statements and «flows» from their structure and meaning of expressions they contain. The information that flows only from the meaning of logical constants and logical structure of statements we will call logical information. In this paper we present a formal explication of this notion which is proper for sentences being Boolean combination of atomic sentences. 1 Therefore we limit ourselves to analyzing logical information flowing only from the meaning of truth-value connectives and logical structure of sentences (...)
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  13.  52
    Fixed Points for Consequence Relations.Toby Meadows - unknown
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  14. The Consequence Relation of Tautological Entailment is Maximally Relevant: Answering a Question of Graham Priest.Lloyd Humberstone - manuscript
    Graham Priest has asked whether the consequence relation associated with the Anderson–Belnap system of Tautological Entailment,1 in the language with connectives ¬, ∧, ∨, and countably many propositional variables as tomic formulas, maximal amongst the substitution-invariant relevant consequence relations on this language. Here a consequence relation is said to be relevant just in case whenever for a set of formulas Γ and formula B, we have Γ B only if some propositional variable occurring in B occurs (...)
     
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  15.  37
    Functional Dependencies, Supervenience, and Consequence Relations.I. L. Humberstone - 1993 - Journal of Logic, Language and Information 2 (4):309-336.
    An analogy between functional dependencies and implicational formulas of sentential logic has been discussed in the literature. We feel that a somewhat different connexion between dependency theory and sentential logic is suggested by the similarity between Armstrong's axioms for functional dependencies and Tarski's defining conditions for consequence relations, and we pursue aspects of this other analogy here for their theoretical interest. The analogy suggests, for example, a different semantic interpretation of consequence relations: instead of thinking ofB (...)
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  16. Consequence Relations with Real Truth Values.Daniele Mundici - 2021 - In Ofer Arieli & Anna Zamansky (eds.), Arnon Avron on Semantics and Proof Theory of Non-Classical Logics. Springer Verlag. pp. 249-264.
    Syntax and semantics in Łukasiewicz infinite-valued sentential logic Ł are harmonized by revising the Bolzano-Tarski paradigm of “semantic consequence,” according to which, θ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\theta $$\end{document} follows from Θ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Theta $$\end{document} iff every valuation v that satisfies all formulas in Θ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Theta $$\end{document} also satisfies θ.\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\theta.$$\end{document} For θ\documentclass[12pt]{minimal} (...)
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  17. Normative Consequence Relation and Dyadic Deontic Consequence Operations.Kazimierz Swirydowicz - 1992 - Theoria 60 (1):27-48.
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  18.  19
    Tarskian Structured Consequence Relations and Functional Completeness.Heinrich Wansing - 1995 - Mathematical Logic Quarterly 41 (1):73-92.
    In this paper functional completeness results are obtained for certain positive and constructive propositional logics associated with a Tarski-type structured consequence relation as defined by Gabbay.
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  19. A Certain Consequence Relation for Solving Paradoxes of Vagueness.Krystyna Misiuna - 2010 - Logique Et Analyse 53 (209):25.
    A consequence relation in the framework of preferential semantics based on the four-valued Belnap-Dunn logic is constructed which proves that the sorites paradoxes are unsound or invalid inferences .
     
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  20.  34
    Normative Consequence Relation and Consequence Operations on the Language of Dyadic Deontic Logic.Kazimierz Swirydowicz - 1994 - Theoria 60 (1):27-47.
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  21.  49
    Judgment and Consequence Relations.Marcus Kracht - 2010 - Journal of Applied Non-Classical Logics 20 (4):423-435.
    In this paper I argue that a variety of consequence relations can be subsumed under a common core. The reduction proceeds by taking the unconditional consequence, or judgment, as basic and deriving the conditional consequence via a uniform abstraction scheme. A specific outcome is that it is better not to base such a scheme on the semantic notion of a matrix and valuation but rather on theories and substitutions. I will also briefly look at consequence (...)
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  22.  10
    Structure, Consequence Relation and Logic.Gabriella Crocco & L. Farinas del Cerro - 1994 - In Dov M. Gabbay (ed.), What is a Logical System? Oxford University Press.
  23.  24
    An Abstract Approach to Consequence Relations.Petr Cintula, José Gil-férez, Tommaso Moraschini & Francesco Paoli - 2019 - Review of Symbolic Logic 12 (2):331-371.
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  24. What is a Nonmonotonic Consequence Relation?Robert Stalnaker - 1991 - Fundamenta Informaticae 21:7-21.
  25.  11
    On Nonmonotonic Consequence Relations.Alexei Muravitsky - 2021 - Logica Universalis 15 (2):227-249.
    We discuss nonmonotonic reasoning in terms of consequence relations and corresponding operators. Based on the matrix consequence that gives the monotonic case, we define a restricted matrix consequence that illustrates the nonmonotonic case. The latter is a generalization of the relation of logical friendliness introduced by D. Makinson. We prove that any restricted single matrix consequence, although it may be nonmonotonic, is always weakly monotonic and, in the case of a finite matrix, the restricted matrix (...)
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  26.  42
    The Proof by Cases Property and its Variants in Structural Consequence Relations.Petr Cintula & Carles Noguera - 2013 - Studia Logica 101 (4):713-747.
    This paper is a contribution to the study of the rôle of disjunction inAlgebraic Logic. Several kinds of (generalized) disjunctions, usually defined using a suitable variant of the proof by cases property, were introduced and extensively studied in the literature mainly in the context of finitary logics. The goals of this paper are to extend these results to all logics, to systematize the multitude of notions of disjunction (both those already considered in the literature and those introduced in this paper), (...)
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  27.  11
    Proof Systems for BAT Consequence Relations.Pawel Pawlowski - 2018 - Logic Journal of the IGPL 26 (1):96-108.
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  28.  15
    The Logical Consequence Relation of Propositional Tense Logic.S. K. Thomason - 1975 - Mathematical Logic Quarterly 21 (1):29-40.
  29.  9
    Axiomatizing Non-Deterministic Many-Valued Generalized Consequence Relations.Sérgio Marcelino & Carlos Caleiro - 2019 - Synthese 198 (S22):5373-5390.
    We discuss the axiomatization of generalized consequence relations determined by non-deterministic matrices. We show that, under reasonable expressiveness requirements, simple axiomatizations can always be obtained, using inference rules which can have more than one conclusion. Further, when the non-deterministic matrices are finite we obtain finite axiomatizations with a suitable generalized subformula property.
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  30.  2
    Disjunctive Multiple-Conclusion Consequence Relations.Marek Nowak - 2019 - Bulletin of the Section of Logic 48 (4).
    The concept of multiple-conclusion consequence relation from [8] and [7] is considered. The closure operation C assigning to any binary relation r the least multiple-conclusion consequence relation containing r, is dened on the grounds of a natural Galois connection. It is shown that the very closure C is an isomorphism from the power set algebra of a simple binary relation to the Boolean algebra of all multiple-conclusion consequence relations.
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  31.  21
    On Intermediate Consequence Relations.W. Darsow & Phyllis M. Kittel - 1980 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 26 (1-6):33-34.
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  32.  26
    Direct Dynamic Proofs for the Rescher–Manor Consequence Relations: The Flat Case.Diderik Batens & Timothy Vermeir - 2002 - Journal of Applied Non-Classical Logics 12 (1):63-84.
    In [BAT 00b], the flat Rescher–Manor consequence relations — the Free, Strong, Argued, C-Based, andWeak consequence relation—were shown to be characterized by inconsistency-adaptive logics defined from the paraconsistent logic CLuN. This provided these consequence relations with a dynamic proof theory. In the present paper we show that the detour via an inconsistency-adaptive logic is not necessary. We present a direct dynamic proof theory, formulated in the language of Classical Logic, and prove its adequacy. The present (...)
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  33.  10
    On Intermediate Consequence Relations.W. Darsow & Phyllis M. Kittel - 1980 - Mathematical Logic Quarterly 26 (1‐6):33-34.
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  34.  10
    Undecidability of Consequence Relation in Full Non-Associative Lambek Calculus.Karel Chvalovský - 2015 - Journal of Symbolic Logic 80 (2):567-586.
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  35.  57
    The Axiomatization of Horst Wessel's Strict Logical Consequence Relation.Andrzej Pietruszczak - 2004 - Logic and Logical Philosophy 13:121-138.
    In his book from 1984 Horst Wessel presents the system of strict logical consequence Fs (see also (Wessel, 1979)). The author maintained that this system axiomatized the relation |=s of strict logical consequence between formulas of Classical Propositional Calculi (CPC). Let |= be the classical consequence relation in CPC. The relation |=s is defined as follows: phi |=s psi iff phi |= psi, every variable from psi occurs in phi and neither phi is a contradiction nor psi (...)
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  36.  61
    A General Theory of Structured Consequence Relations.Dov M. Gabbay - 1995 - Theoria 10 (2):49-78.
    There are several areas in logic where the monotonicity of the consequence relation fails to hold. Roughly these are the traditional non-monotonic systems arising in Artificial Intelligence (such as defeasible logics, circumscription, defaults, ete), numerical non-monotonic systems (probabilistic systems, fuzzy logics, belief functions), resource logics (also called substructural logics such as relevance logic, linear logic, Lambek calculus), and the logic of theory change (also called belief revision, see Alchourron, Gärdenfors, Makinson [2224]). We are seeking a common axiomatic and semantical (...)
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  37.  35
    Concerning the Method of Logical Schemes, the Notion of Logical Calculus and the Role of Consequence Relations.Roman Suszko - 1961 - Studia Logica 11 (1):185 - 216.
  38.  6
    A General Theory of Structured Consequence Relations.Dov M. Gabbay - 1995 - Theoria: Revista de Teoría, Historia y Fundamentos de la Ciencia 10 (2):49-78.
    There are several areas in logic where the monotonicity of the consequence relation fails to hold. Roughly these are the traditional non-monotonic systems arising in Artificial Intelligence, numerical non-monotonic systems, resource logics, and the logic of theory change. We are seeking a common axiomatic and semantical approach to the notion of consequence whieh can be specialised to any of the above areas. This paper introduces the notions of structured consequence relation, shift operators and structural connectives, and shows (...)
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  39.  5
    Logics of Variable Inclusion and the Lattice of Consequence Relations.Michele Pra Baldi - 2020 - Journal of Applied Non-Classical Logics 30 (4):367-381.
    In this paper, first, we determine the number of sublogics of variable inclusion of an arbitrary finitary logic ⊢ with a composition term. Then, we investigate their position into the lattice of co...
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  40.  7
    Tree-Like Proof Systems for Finitely-Many Valued Non-Deterministic Consequence Relations.Pawel Pawlowski - 2020 - Logica Universalis 14 (4):407-420.
    The main goal of this paper is to provide an abstract framework for constructing proof systems for various many-valued logics. Using the framework it is possible to generate strongly complete proof systems with respect to any finitely valued deterministic and non-deterministic logic. I provide a couple of examples of proof systems for well-known many-valued logics and prove the completeness of proof systems generated by the framework.
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  41.  62
    On Representation Theorems for Nonmonotonic Consequence Relations.Ramón Pino Pérez & Carlos Uzcátegui - 2000 - Journal of Symbolic Logic 65 (3):1321-1337.
    One of the main tools in the study of nonmonotonic consequence relations is the representation of such relations in terms of preferential models. In this paper we give an unified and simpler framework to obtain such representation theorems.
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  42.  29
    Sequent Calculi for Global Modal Consequence Relations.Minghui Ma & Jinsheng Chen - 2019 - Studia Logica 107 (4):613-637.
    The global consequence relation of a normal modal logic \ is formulated as a global sequent calculus which extends the local sequent theory of \ with global sequent rules. All global sequent calculi of normal modal logics admits global cut elimination. This property is utilized to show that decidability is preserved from the local to global sequent theories of any normal modal logic over \. The preservation of Craig interpolation property from local to global sequent theories of any normal (...)
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  43.  24
    Proof Theories for Some Prioritized Consequence Relations.Liza Verhoeven - 2003 - Logique Et Analyse 183 (184):325-344.
  44. A Strengthening of the Rescher--Manor Consequence Relations.Diderik Batens - 2003 - Logique Et Analyse 183:289-313.
  45.  19
    Disjunctive and Conjunctive Multiple-Conclusion Consequence Relations.Marek Nowak - 2020 - Studia Logica 108 (6):1125-1143.
    Two different kinds of multiple-conclusion consequence relations taken from Shoesmith and Smiley and Galatos and Tsinakis or Nowak, called here disjunctive and conjunctive, respectively, defined on a formal language, are considered. They are transferred into a bounded lattice and a complete lattice, respectively. The properties of such abstract consequence relations are presented.
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  46.  45
    Thomason’s Paradox for Belief, and Two Consequence Relations.Bas C. van Fraassen - 2011 - Journal of Philosophical Logic 40 (1):15 - 32.
    Thomason (1979/2010)'s argument against competence psychologism in semantics envisages a representation of a subject's competence as follows: he understands his own language in the sense that he can identify the semantic content of each of its sentences, which requires that the relation between expression and content be recursive. Then if the scientist constructs a theory that is meant to represent the body of the subject's beliefs, construed as assent to the content of the pertinent sentences, and that theory satisfies certain (...)
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  47.  11
    Thomason’s Paradox for Belief, and Two Consequence Relations.Bas Fraassen - 2011 - Journal of Philosophical Logic 40 (1):15-32.
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  48. Dana Scott's Work with Generalized Consequence Relations.Ian Humberstone - unknown
     
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  49.  25
    A Proof of the Characterization Theorem for Consequence Relations.Zvonimir Šikić - 1991 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 37 (2-4):41-43.
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  50.  14
    A Proof of the Characterization Theorem for Consequence Relations.Zvonimir Šikić - 1991 - Mathematical Logic Quarterly 37 (2‐4):41-43.
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