Results for 'sentential logic'

973 found
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  1.  53
    1. Intuitionistic sentential calculus with iden-tity.Intuitionistic Sentential Calculus - 1990 - Bulletin of the Section of Logic 19 (3):92-99.
  2. Complementary Sentential Logics.Achille C. Varzi - 1990 - Bulletin of the Section of Logic 19 (4):112-116.
    It is shown that a complete axiomatization of classical non-tautologies can be obtained by taking F (falsehood) as the sole axiom along with the two inference rules: (i) if A is a substitution instance of B, then A |– B; and (ii) if A is obtained from B by replacement of equivalent sentences, then A |– B (counting as equivalent the pairs {T, ~F}, {F, F&F}, {F, F&T}, {F, T&F}, {T, T&T}). Since the set of tautologies is also specifiable by (...)
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  3.  42
    Sentential logics and Maehara interpolation property.Janusz Czelakowski - 1985 - Studia Logica 44 (3):265 - 283.
    With each sentential logic C, identified with a structural consequence operation in a sentential language, the class Matr * (C) of factorial matrices which validate C is associated. The paper, which is a continuation of [2], concerns the connection between the purely syntactic property imposed on C, referred to as Maehara Interpolation Property (MIP), and three diagrammatic properties of the class Matr* (C): the Amalgamation Property (AP), the (deductive) Filter Extension Property (FEP) and Injections Transferable (IT). The (...)
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  4.  50
    Sub-sentential logical form. On Robert J. Stainton's "words and thoughts".Axel Arturo Barceló Aspeitia - 2011 - Critica 43 (129):53-63.
    Stainton argues that since sub-sentential speech acts lack the proper syntactic structure to have logical form, it is not from them that subsententially propositions conveyed derive their logical form, in this brief comment, I develop an argument for the claim that sub-sentential speech acts not only do have the proper syntactic structure, but that according to Stainton's own general pragmatic account of sub-sentential speech, they also satisfy all the criteria put forward by him to be the primary (...)
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  5.  44
    Sentential Logic for Psychologists.Richard Grandy & Daniel Osherson - unknown
    Students often study logic on the assumption that it provides a normative guide to reasoning in English. In particular, they are taught to associate connectives like “and” with counterparts in Sentential Logic. English conditionals go over to formulas with → as principal connective. The well-known difficulties that arise from such translation are not emphasized. The result is the conviction that ordinary reasoning is faulty when discordant with the usual representation in standard logic. Psychologists are particularly susceptible (...)
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  6. Every sentential logic has a two-valued worlds semantics.Richard Routley & Robert K. Meyer - 1976 - Logique Et Analyse 19 (74-76):345-365.
     
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  7.  32
    Number of non-Fregean sentential logics that have adequate models.Joanna Golińska-Pilarek - 2006 - Mathematical Logic Quarterly 52 (5):439–443.
    We show that there are continuum many different non-Fregean sentential logics that have adequate models. The proof is based on the construction of a special class of models of the power of the continuum.
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  8. A Simplified System Of Sentential Logic.Michael Goodman - 2011 - Annales Philosophici 2:35-40.
    In thinking about reducing the symbolization of sentential logic to a minimum , where the conditional no longer appears in system, and hence in no proof in the system, one might wonder what would become of the Rule of Conditional Proof. Where this rule is said to be essential for the completeness of the system, some rule or other needs to be developed to do the work of Conditional Proof. The author attempts to accomplish this while specifying a (...)
     
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  9. Two-Sided Trees for Sentential Logic, Predicate Logic, and Sentential Modal Logic.Jesse Fitts & David Beisecker - 2019 - Teaching Philosophy 42 (1):41-56.
    This paper will present two contributions to teaching introductory logic. The first contribution is an alternative tree proof method that differs from the traditional one-sided tree method. The second contribution combines this tree system with an index system to produce a user-friendly tree method for sentential modal logic.
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  10.  30
    Well‐Defined Fuzzy Sentential Logic.Esko Turunen - 1995 - Mathematical Logic Quarterly 41 (2):236-248.
    A many-valued sentential logic with truth values in an injective MV-algebra is introduced and the axiomatizability of this logic is proved. The paper develops some ideas of Goguen and generalizes the results of Pavelka on the unit interval. The proof for completeness is purely algebraic. A corollary of the Completeness Theorem is that fuzzy logic on the unit interval is semantically complete if and only if the algebra of the truth values is a complete MV-algebra. In (...)
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  11.  59
    Base-extension semantics for intuitionistic sentential logic.Tor Sandqvist - 2015 - Logic Journal of the IGPL 23 (5):719-731.
    Intuitionistic sentential logic is shown to be sound and complete with respect to a semantics centered around extensions of atomic bases (i.e. sets of inference rules for atomic sentences). The result is made possible through a non-standard interpretation of disjunction, whereby, roughly speaking, a disjunction is taken to hold just in case every atomic sentence that follows from each of the disjuncts separately holds; it is argued that this interpretation makes good sense provided that rules in atomic bases (...)
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  12.  52
    On decision procedures for sentential logics.Tomasz Skura - 1991 - Studia Logica 50 (2):173 - 179.
    In Section 2 I give a criterion of decidability that can be applied to logics (i.e. Tarski consequence operators) without the finite model property. In Section 3 I study ukasiewicz-style refutation procedures as a method of obtaining decidability results.This method also proves to be more general than Harrop's criterion.
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  13.  19
    Axiomatization of the sentential logic dual to Sobocinski's n-valued logic.Anetta Górnicka - 2011 - Bulletin of the Section of Logic 40 (1/2):47-54.
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  14.  16
    Axiomatzation of the Sentential Logic Dual with Respect to Lukasiewicz's Three-valued Logic.Anetta Górnicka - 2006 - Bulletin of the Section of Logic 35 (2/3):85-94.
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  15. Notes on Sentential Logic with Identity.G. Malinowski - 1985 - Logique Et Analyse 28 (112):341-352.
  16.  35
    Full Models for Sentential Logics.Josep Maria Font & Ramon Jansana - 1995 - Bulletin of the Section of Logic 24 (3):123-131.
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  17. No Rational Sentential Logic has a Finite Characteristic Matrix.Richard Routley & R. Wolf - 1974 - Logique Et Analyse 17 (67):317-321.
  18.  58
    Rasiowa-Sikorski proof system for the non-Fregean sentential logic SCI.Joanna Golinska-Pilarek - 2007 - Journal of Applied Non-Classical Logics 17 (4):509–517.
    The non-Fregean logic SCI is obtained from the classical sentential calculus by adding a new identity connective = and axioms which say ?a = ß' means ?a is identical to ß'. We present complete and sound proof system for SCI in the style of Rasiowa-Sikorski. It provides a natural deduction-style method of reasoning for the non-Fregean sentential logic SCI.
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  19. Knot and Tonk: Nasty Connectives on Many-Valued Truth-Tables for Classical Sentential Logic.Tim Button - 2016 - Analysis 76 (1):7-19.
    Prior’s Tonk is a famously horrible connective. It is defined by its inference rules. My aim in this article is to compare Tonk with some hitherto unnoticed nasty connectives, which are defined in semantic terms. I first use many-valued truth-tables for classical sentential logic to define a nasty connective, Knot. I then argue that we should refuse to add Knot to our language. And I show that this reverses the standard dialectic surrounding Tonk, and yields a novel solution (...)
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  20.  27
    The Strong Version of a Sentential Logic.Ramon Jansana, Josep Maria Font & Hugo Albuquerque - 2017 - Studia Logica 105 (4):703-760.
    This paper explores a notion of “the strong version” of a sentential logic S, initially defined in terms of the notion of a Leibniz filter, and shown to coincide with the logic determined by the matrices of S whose filter is the least S-filter in the algebra of the matrix. The paper makes a general study of this notion, which appears to unify under an abstract framework the relationships between many pairs of logics in the literature. The (...)
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  21.  39
    The Strong Version of a Sentential Logic.Hugo Albuquerque, Josep Maria Font & Ramon Jansana - 2017 - Studia Logica 105 (4):703-760.
    This paper explores a notion of “the strong version” of a sentential logic S, initially defined in terms of the notion of a Leibniz filter, and shown to coincide with the logic determined by the matrices of S whose filter is the least S-filter in the algebra of the matrix. The paper makes a general study of this notion, which appears to unify under an abstract framework the relationships between many pairs of logics in the literature. The (...)
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  22.  88
    A theorem about infinite-valued sentential logic.Robert McNaughton - 1951 - Journal of Symbolic Logic 16 (1):1-13.
  23. Some remarks on the consequence operation in sentential logics.Ryszard Wójcicki - 1970 - Fundamenta Mathematicae 68 (1):269--279.
  24.  41
    On the degree of complexity of sentential logics. A couple of examples.Jacek Hawranek & Jan Zygmunt - 1981 - Studia Logica 40 (2):141 - 153.
    The first part of the paper is a reminder of fundamental results connected with the adequacy problem for sentential logics with respect to matrix semantics. One of the main notions associated with the problem, namely that of the degree of complexity of a sentential logic, is elucidated by a couple of examples in the second part of the paper. E.g., it is shown that the minimal logic of Johansson and some of its extensions have degree of (...)
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  25.  6
    A lower bound for the complexity of Craig's interpolants in sentential logic.Daniele Mundici - 1983 - Archive for Mathematical Logic 23 (1):27-36.
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  26.  37
    Grounding from a Syntactic Point of View: A Sentential-Logical Approach.Alexander Zimmermann, Reinhard Kleinknecht & Georg J. W. Dorn - 2020 - Erkenntnis 87 (2):717-746.
    We define the term \a set T of sentential-logical formulae grounds a sentential-logical formula A from a syntactic point of view\ in such a way that A is a syntactic sentential-logical consequence of T, and specific additional syntactic requirements regarding T and A are fulfilled. These additional requirements are developed strictly within the syntactics of sentential-logical languages, the three most important being new, namely: to be atomically minimal, to be minimal in degree, and not to be (...)
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  27.  40
    A theorem of the degree of complexity of some sentential logics.Jacek Hawranek & Jan Zygmunt - 1980 - Bulletin of the Section of Logic 9 (2):67-69.
    x1. This paper is a contribution to matrix semantics for sentential logics as presented in Los and Suszko [1] and Wojcicki [3], [4]. A generalization of Lindenbaum completeness lemma says that for each sentential logic there is a class K of matrices of the form such that the class is adequate for the logic, i.e., C = CnK.
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  28.  9
    Grounding from a Syntactic Point of View: A Sentential-Logical Approach.Georg J. W. Dorn, Reinhard Kleinknecht & Alexander Zimmermann - 2020 - Erkenntnis 87 (2):717-746.
    We define the term ⌜\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\ulcorner $$\end{document}a set T of sentential-logical formulae grounds a sentential-logical formula A from a syntactic point of view⌝\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\urcorner $$\end{document} in such a way that A is a syntactic sentential-logical consequence of T, and specific additional syntactic requirements regarding T and A are fulfilled. These additional requirements are developed strictly within the syntactics of sentential-logical languages, (...)
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  29.  20
    Notes on decidability and finite approximability of sentential logics.Jana Zygmunt - 1981 - Bulletin of the Section of Logic 10 (1):38-40.
    This is an abstract of the paper accepted for publication in \Acta Uni- versitatis Wratislaviensis", series \Prace Filozoczne { Logika". The paper was presented at the 25th Conference for the History of Logic, Krakow, October 5-7, 1979.
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  30.  12
    A Theorem About Infinite-Valued Sentential Logic.Robert Mcnaughton - 1951 - Journal of Symbolic Logic 16 (3):227-228.
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  31.  51
    Introduction to Sentential Logic[REVIEW]Neil R. Luebke - 1977 - Teaching Philosophy 2 (1):73-74.
  32.  34
    On the degree of complexity of sentential logics.II. An example of the logic with semi-negation.Jacek Hawranek & Jan Zygmunt - 1984 - Studia Logica 43 (4):405 - 413.
    In this paper being a sequel to our [1] the logic with semi-negation is chosen as an example to elucidate some basic notions of the semantics for sentential calculi. E.g., there are shown some links between the Post number and the degree of complexity of a sentential logic, and it is proved that the degree of complexity of the sentential logic with semi-negation is 20. This is the first known example of a logic (...)
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  33.  21
    On pure refutation formulations of sentential logics.Tomasz Skura - 1990 - Bulletin of the Section of Logic 19 (3):102-107.
  34.  37
    Distributivity in Lℵ0 and Other Sentential Logics.Kenneth Harris & Branden Fitelson - unknown
    Certain distributivity results for Lukasiewicz’s infinite-valued logic Lℵ0 are proved axiomatically (for the first time) with the help of the automated reasoning program Otter [16]. In addition, non -distributivity results are established for a wide variety of positive substructural logics by the use of logical matrices discovered with the automated model findingprograms Mace [15] and MaGIC [25].
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  35.  24
    Distributivity in lℵ0 and other sentential logics.Branden Fitelson - manuscript
    Certain distributivity results for Lukasiewicz’s infinite-valued logic Lℵ0..
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  36. " A general algebraic semantics for sentential logics", de JMJ Font y R. Jansana.Carlos Pelta Resano - 2000 - Teorema: International Journal of Philosophy 19 (1):130-132.
     
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  37. Weak and strong completeness in sentential logics.John Corcoran - 1972 - Logique Et Analyse 15:429.
     
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  38.  34
    Functors of Lindenbaum-Tarski, Schematic Interpretations, and Adjoint Cylinders between Sentential Logics.J. Climent Vidal & J. Soliveres Tur - 2008 - Notre Dame Journal of Formal Logic 49 (2):185-202.
    We prove, by using the concept of schematic interpretation, that the natural embedding from the category ISL, of intuitionistic sentential pretheories and i-congruence classes of morphisms, to the category CSL, of classical sentential pretheories and c-congruence classes of morphisms, has a left adjoint, which is related to the double negation interpretation of Gödel-Gentzen, and a right adjoint, which is related to the Law of Excluded Middle. Moreover, we prove that from the left to the right adjoint there is (...)
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  39. A Note On Adequate Models For Non-fregean Sentential Logics.Roman Suszko - 1972 - Bulletin of the Section of Logic 1 (4):42-45.
  40.  16
    Some examples concerning uniformity and complexity of sentential logics.Jacek Hawranek - 1980 - Bulletin of the Section of Logic 9 (2):71-72.
    This abstract is a contribution to the paper by R. Wojcicki [2]. We use the terminology introduced there, . In this note we show that 1 0 For each n 2 there exists a logic whose degree of uniformity and degree of complexity are both equal to n. 2 0 There is a logic with the degree of uniformity equal to 2 @0 but with the degree of complexity equal to @0.
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  41.  14
    Complete rings of sets and sentential logic.Melven R. Krom - 1977 - Studia Logica 36 (3):173 - 175.
  42.  27
    On the degree of complexity of sentential logics, III. An example of Johansson's minimal logic.Jacek Hawranek - 1987 - Studia Logica 46 (4):283 - 289.
    The present paper is to be considered as a sequel to [1], [2]. It is known that Johansson's minimal logic is not uniform, i.e. there is no single matrix which determines this logic. Moreover, the logic C J is 2-uniform. It means that there are two uniform logics C 1, C 2 (each of them is determined by a single matrix) such that the infimum of C 1 and C 2 is C J. The aim of this (...)
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  43.  22
    A simple strong completeness proof for sentential logic.Charles Silver - 1980 - Notre Dame Journal of Formal Logic 21 (1):179-181.
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  44.  17
    McNaughton Robert. A theorem about infinite-valued sentential logic.H. E. Vaughan - 1951 - Journal of Symbolic Logic 16 (3):227-228.
  45.  18
    Review: J. Los, R. Suszko, Remarks on Sentential Logics. [REVIEW]Alonzo Church - 1975 - Journal of Symbolic Logic 40 (4):603-604.
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  46.  13
    E. W. Beth. Remarks on natural deduction. Koninklijke Nederlandse Akademie van Wetenschappen, Proceedings, series A, Vol. 58 , pp. 322–325; also Indagationes mathematicae, vol. 17 pp. 322–325. - E. W. Beth. Semantic entailment and formal derivability. Mededelingen der Koninklijke Nederlandse Akademie van Wetenschappen, Afd. letterkunde, n.s. vol. 18 no. 13 , pp. 309–342. - K. Jaakko J. Hintikka. A new approach to sentential logic. Societas Scientiarum Fennica, Commentationes physico-mathematicae, vol. 17 no. 2 , 14 pp. - K. Jaakko J. Hintikka. Form and content in quantification theory. Two papers on symbolic logic, Acta philosophica Fennica no. 8, Helsinki1955, pp. 7–55. - K. Jaakko J. Hintikka. Notes on quantification theory. Societas Scientiarum Fennica, Commentationes physico-mathematicae, vol. 17 no. 12 , 13 pp. [REVIEW]William Craig - 1957 - Journal of Symbolic Logic 22 (4):360-363.
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  47.  16
    J. Łos and R. Suszko. Remarks on sentential logics. Koninklijke Nederlandse Akademie van Wetenschappen, Proceedings, ser. A vol. 61 , pp. 177–183; also Indagationes mathematicae, vol. 20 , pp. 177-183. [REVIEW]Alonzo Church - 1975 - Journal of Symbolic Logic 40 (4):603-604.
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  48.  21
    Intra‐sentential context effects on the interpretation of logical metonymy⋆.Mirella Lapata, Frank Keller & Christoph Scheepers - 2003 - Cognitive Science 27 (4):649-668.
    Verbs such as enjoy in the student enjoyed the book exhibit logical metonymy: enjoy is interpreted as enjoy reading. Theoreticalwork [Computational Linguistics 17 (4) (1991) 409; The Generative Lexicon, MIT Press, Cambridge, MA, 1995] predicts that this interpretation can be influenced by intra‐sentential context, e.g., by the subject of enjoy. In this article, we test this prediction using a completion experiment and find that the interpretation of a metonymic verb is influenced by the semantic role of its subject. We (...)
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  49.  11
    Review: Robert McNaughton, A Theorem About Infinite-Valued Sentential Logic[REVIEW]H. E. Vaughan - 1951 - Journal of Symbolic Logic 16 (3):227-228.
  50.  49
    The logics stronger than Łukasiewicz's three valued sentential calculus-the notion of degree of maximality versus the notion of degree of completeness.Ryszard Wójcicki - 1974 - Studia Logica 33 (2):201-214.
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