Results for 'propositional logic'

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  1.  25
    Propositional Logics of Dependence.Fan Yang & Jouko Väänänen - 2016 - Annals of Pure and Applied Logic 167 (7):557-589.
  2. The Propositional Logic of Ordinary Discourse.William S. Cooper - 1968 - Inquiry: An Interdisciplinary Journal of Philosophy 11 (1-4):295 – 320.
    The logical properties of the 'if-then' connective of ordinary English differ markedly from the logical properties of the material conditional of classical, two-valued logic. This becomes apparent upon examination of arguments in conversational English which involve (noncounterfactual) usages of if-then'. A nonclassical system of propositional logic is presented, whose conditional connective has logical properties approximating those of 'if-then'. This proposed system reduces, in a sense, to the classical logic. Moreover, because it is equivalent to a certain (...)
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  3.  96
    A Propositional Logic with Explicit Fixed Points.Albert Visser - 1981 - Studia Logica 40 (2):155 - 175.
    This paper studies a propositional logic which is obtained by interpreting implication as formal provability. It is also the logic of finite irreflexive Kripke Models.A Kripke Model completeness theorem is given and several completeness theorems for interpretations into Provability Logic and Peano Arithmetic.
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  4.  73
    Propositional Logics Related to Heyting's and Johansson's.Krister Segerberg - 1968 - Theoria 34 (1):26-61.
  5. A Propositional Logic with Subjunctive Conditionals.R. B. Angell - 1962 - Journal of Symbolic Logic 27 (3):327-343.
  6.  53
    Propositional Logic of Supposition and Assertion.John T. Kearns - 1997 - Notre Dame Journal of Formal Logic 38 (3):325-349.
    This presentation of a system of propositional logic is a foundational paper for systems of illocutionary logic. The language contains the illocutionary force operators '' for assertion and ' ' for supposition. Sentences occurring in proofs of the deductive system must be prefixed with one of these operators, and rules of take account of the forces of the sentences. Two kinds of semantic conditions are investigated; familiar truth conditions and commitment conditions. Accepting a statement A or rejecting (...)
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  7.  1
    Intuitionistic Propositional Logic with Galois Negations.Minghui Ma & Guiying Li - forthcoming - Studia Logica:1-36.
    Intuitionistic propositional logic with Galois negations ) is introduced. Heyting algebras with Galois negations are obtained from Heyting algebras by adding the Galois pair \\) and dual Galois pair \\) of negations. Discrete duality between GN-frames and algebras as well as the relational semantics for \ are developed. A Hilbert-style axiomatic system \ is given for \, and Galois negation logics are defined as extensions of \. We give the bi-tense logic \ which is obtained from the (...)
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  8.  49
    On Second Order Intuitionistic Propositional Logic Without a Universal Quantifier.Konrad Zdanowski - 2009 - Journal of Symbolic Logic 74 (1):157-167.
    We examine second order intuitionistic propositional logic, IPC². Let $F_\exists $ be the set of formulas with no universal quantification. We prove Glivenko's theorem for formulas in $F_\exists $ that is, for φ € $F_\exists $ φ is a classical tautology if and only if ¬¬φ is a tautology of IPC². We show that for each sentence φ € $F_\exists $ (without free variables), φ is a classical tautology if and only if φ is an intuitionistic tautology. As (...)
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  9. Propositional Logic.Kevin C. Klement - 2004 - Internet Encyclopedia of Philosophy.
    Propositional logic, also known as sentential logic and statement logic, is the branch of logic that studies ways of joining and/or modifying entire propositions, statements or sentences to form more complicated propositions, statements or sentences, as well as the logical relationships and properties that are derived from these methods of combining or altering statements. In propositional logic, the simplest statements are considered as indivisible units, and hence, propositional logic does not study (...)
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  10. Propositional Logic of Essence.Fabrice Correia - 2000 - Journal of Philosophical Logic 29 (3):295-313.
    This paper presents a propositional version of Kit Fine's (quantified) logic for essentialist statements, provides it with a semantics, and proves the former adequate (i.e. sound and complete) with respect to the latter.
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  11.  33
    The Propositional Logic of Boethius.Karl Dürr - 1951 - Amsterdam, Netherlands: Greenwood Press.
    The text of the treatise “The Propositional Logic of Boethius” was finished in 1939. Prof. Jan Lukasiewicz wished at that time to issue it in the second volume of “Collectanea Logica”; as a result of political events, he was not able to carry out his plan. In 1938, I published an article in “Erkenntnis” entitled “AUS- sagenlogik im Mittelalter”; this article included the contents of a paper which I read to the International Congress for the Unity of Science (...)
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  12.  28
    Bounded Arithmetic, Propositional Logic and Complexity Theory.Jan Krajíček - 1995 - Cambridge University Press.
    This book presents an up-to-date, unified treatment of research in bounded arithmetic and complexity of propositional logic, with emphasis on independence proofs and lower bound proofs. The author discusses the deep connections between logic and complexity theory and lists a number of intriguing open problems. An introduction to the basics of logic and complexity theory is followed by discussion of important results in propositional proof systems and systems of bounded arithmetic. More advanced topics are then (...)
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  13.  30
    Propositional Logic (Chapter 1) - The Conceptual Knapsack.Saja Parvizian - manuscript
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  14. Propositional Logic And Erotetic Inferences.Andrzej Wisniewski - 1985 - Bulletin of the Section of Logic 14 (1):72-76.
    There are inferences from a sentence or a set of sentences to a question. The relation between the premises and conclusions of such inferences is sometimes called arising.
     
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  15.  24
    Propositional Logic of Imperfect Information: Foundations and Applications.Ahti-Veikko Pietarinen - 2001 - Notre Dame Journal of Formal Logic 42 (4):193-210.
    I will show that the semantic structure of a new imperfect-information propositional logic can be described in terms of extensive forms of semantic games. I will discuss some ensuing properties of these games such as imperfect recall, informational consistency, and team playing. Finally, I will suggest a couple of applications that arise in physics, and most notably in quantum theory and quantum logics.
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  16.  7
    A Propositional Logic with Subjunctive Conditionals.R. B. Angell - 1970 - Journal of Symbolic Logic 35 (3):464-465.
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  17.  29
    Propositional Logics of Closed and Open Substitutions Over Heyting's Arithmetic.Albert Visser - 2006 - Notre Dame Journal of Formal Logic 47 (3):299-309.
    In this note we compare propositional logics for closed substitutions and propositional logics for open substitutions in constructive arithmetical theories. We provide a strong example where these logics diverge in an essential way. We prove that for Markov's Arithmetic, that is, Heyting's Arithmetic plus Markov's principle plus Extended Church's Thesis, the logic of closed and the logic of open substitutions are the same.
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  18. Propositional Logic.Howard Pospesel - 1974 - Englewood Cliffs, N.J., Prentice-Hall.
  19.  10
    Intuitionistic Propositional Logic with Galois Connections.Wojciech Dzik, Jouni Järvinen & Michiro Kondo - 2010 - Logic Journal of the IGPL 18 (6):837-858.
    In this work, an intuitionistic propositional logic with a Galois connection is introduced. In addition to the intuitionistic logic axioms and inference rule of modus ponens, the logic contains only two rules of inference mimicking the performance of Galois connections. Both Kripke-style and algebraic semantics are presented for IntGC, and IntGC is proved to be complete with respect to both of these semantics. We show that IntGC has the finite model property and is decidable, but Glivenko's (...)
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  20.  30
    Propositional Logic of Continuous Transformations in Cantor Space.Grigori Mints & Ting Zhang - 2005 - Archive for Mathematical Logic 44 (6):783-799.
  21.  16
    Bayesian Propositional Logic.Tomasz Jarmużek, Mateusz Klonowski & Jacek Malinowski - 2017 - Bulletin of the Section of Logic 46 (3/4).
    We define and investigate from a logical point of view a family of consequence relations defined in probabilistic terms. We call them relations of supporting, and write: |≈w where w is a probability function on a Boolean language. A |≈w B iff the fact that A is the case does not decrease a probability of being B the case. Finally, we examine the intersection of |≈w, for all w, and give some formal properties of it.
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  22.  4
    Propositional Logic From The Principles of Mathematics to Principia Mathematica.Bernard Linsky - 2016 - In Sorin Costreie (ed.), Early Analytic Philosophy – New Perspectives on the Tradition. Springer Verlag.
    Bertrand Russell presented three systems of propositional logic, one first in Principles of Mathematics, University Press, Cambridge, 1903 then in “The Theory of Implication”, Routledge, New York, London, pp. 14–61, 1906) and culminating with Principia Mathematica, Cambridge University Press, Cambridge, 1910. They are each based on different primitive connectives and axioms. This paper follows “Peirce’s Law” through those systems with the aim of understanding some of the notorious peculiarities of the 1910 system and so revealing some of the (...)
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  23.  41
    A Propositional Logic with 4 Values: True, False, Divergent and Meaningless.Jan A. Bergstra, Inge Bethke & Piet Rodenburg - 1995 - Journal of Applied Non-Classical Logics 5 (2):199-217.
  24.  28
    Incompleteness of Intuitionistic Propositional Logic with Respect to Proof-Theoretic Semantics.Thomas Piecha & Peter Schroeder-Heister - 2019 - Studia Logica 107 (1):233-246.
    Prawitz proposed certain notions of proof-theoretic validity and conjectured that intuitionistic logic is complete for them [11, 12]. Considering propositional logic, we present a general framework of five abstract conditions which any proof-theoretic semantics should obey. Then we formulate several more specific conditions under which the intuitionistic propositional calculus turns out to be semantically incomplete. Here a crucial role is played by the generalized disjunction principle. Turning to concrete semantics, we show that prominent proposals, including Prawitz’s, (...)
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  25.  87
    A Propositional Logic with Relative Identity Connective and a Partial Solution to the Paradox of Analysis.Xuefeng Wen - 2007 - Studia Logica 85 (2):251-260.
    We construct a a system PLRI which is the classical propositional logic supplied with a ternary construction , interpreted as the intensional identity of statements and in the context . PLRI is a refinement of Roman Suszko’s sentential calculus with identity (SCI) whose identity connective is a binary one. We provide a Hilbert-style axiomatization of this logic and prove its soundness and completeness with respect to some algebraic models. We also show that PLRI can be used to (...)
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  26.  88
    Propositional Logic in Ammonius.Susanne Bobzien - 2002 - In Helmut Linneweber-Lammerskitten & Georg Mohr (eds.), Interpretation und Argument. Koenigshausen & Neumann.
    ABSTRACT: This paper collects the evidence in Ammonius' surviving works for elements of a propositional logic, coming to the conclusion that Ammonius had a theory of hypothetical syllogisms in the tradition of Aristotle and the Peripatetics, with Platonic elements mixed in, and using some Stoic elements, but not a propositional logic in the narrower sense as we find it in Stoic logic.
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  27.  20
    The Propositional Logic of Principia Mathematica and Some of Its Forerunners.Daniel O'leary - 1988 - Russell: The Journal of Bertrand Russell Studies 8 (1).
  28. Propositional Logic Based on the Dynamics of Belief.Peter Gärdenfors - 1985 - Journal of Symbolic Logic 50 (2):390-394.
  29.  14
    Partiality and Games: Propositional Logic.G. Sandu & A. Pietarinen - 2001 - Logic Journal of the IGPL 9 (1):101-121.
    We study partiality in propositional logics containing formulas with either undefined or over-defined truth-values. Undefined values are created by adding a four-place connective W termed transjunction to complete models which, together with the usual Boolean connectives is shown to be functionally complete for all partial functions. Transjunction is seen to be motivated from a game-theoretic perspective, emerging from a two-stage extensive form semantic game of imperfect information between two players. This game-theoretic approach yields an interpretation where partiality is generated (...)
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  30.  44
    Informational Interpretation of Substructural Propositional Logics.Heinrich Wansing - 1993 - Journal of Logic, Language and Information 2 (4):285-308.
    This paper deals with various substructural propositional logics, in particular with substructural subsystems of Nelson's constructive propositional logics N– and N. Doen's groupoid semantics is extended to these constructive systems and is provided with an informational interpretation in terms of information pieces and operations on information pieces.
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  31.  36
    Propositional Logic.Richard A. Wright - 1975 - Teaching Philosophy 1 (1):71-72.
  32.  54
    Propositional Logic in the Sixteenth and Early Seventeenth Centuries.E. J. Ashworth - 1968 - Notre Dame Journal of Formal Logic 9 (2):179-192.
  33.  24
    Modal Propositional Logic on an Orthomodular Basis. I.L. Herman & R. Piziak - 1974 - Journal of Symbolic Logic 39 (3):478-488.
  34.  38
    Propositional Logic Extended with a Pedagogically Useful Relevant Implication.Diderik Batens - 2014 - Logic and Logical Philosophy 23 (3).
    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 (...)
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  35. « The propositional Logic of Avicenna. ».Nabil Shehaby - 1975 - Revue de Métaphysique et de Morale 80 (1):140-141.
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  36.  23
    Structural Completeness in Propositional Logics of Dependence.Rosalie Iemhoff & Fan Yang - 2016 - Archive for Mathematical Logic 55 (7-8):955-975.
    In this paper we prove that three of the main propositional logics of dependence, none of which is structural, are structurally complete with respect to a class of substitutions under which the logics are closed. We obtain an analogous result with respect to stable substitutions, for the negative variants of some well-known intermediate logics, which are intermediate theories that are closely related to inquisitive logic.
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  37. Peirce’s Propositional Logic.Randall R. Dipert - 1981 - Review of Metaphysics 34 (3):569 - 595.
    BEFORE Frege’s Begriffsschrift, propositional logic was submerged in the often murky theory of the "hypothetical syllogism." With the exception of the Stoa, a handful of astute mediaeval logicians, Leibniz, and Bolzano, one might well obtain the impression from studying the history of logic that Frege created his theory ex nihilo—which is substantially true, since Frege was apparently little influenced by previous work. One might also obtain the impression, especially by reading Frege himself, that very little was being (...)
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  38.  57
    Propositional Logic Card Games.Anthony Shiver - 2013 - Teaching Philosophy 36 (1):51-58.
    In this paper I discuss card games designed to supplement or replace exercise sets on derivability and entailment in propositional logic. I present rules for two propositional logic card games that introduce chance and competition into discussions of propositional logic. The latter sections provide brief practical and theoretical notes on this kind of game, including ways courses that use these games can be more effective than courses that do not.
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  39.  21
    The Propositional Logic of Elementary Tasks.Giorgi Japaridze - 2000 - Notre Dame Journal of Formal Logic 41 (2):171-183.
    The paper introduces a semantics for the language of propositional additive-multiplicative linear logic. It understands formulas as tasks that are to be accomplished by an agent (machine, robot) working as a slave for its master (user, environment). This semantics can claim to be a formalization of the resource philosophy associated with linear logic when resources are understood as agents accomplishing tasks. I axiomatically define a decidable logic TSKp and prove its soundness and completeness with respect to (...)
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  40. Completeness Before Post: Bernays, Hilbert, and the Development of Propositional Logic.Richard Zach - 1999 - Bulletin of Symbolic Logic 5 (3):331-366.
    Some of the most important developments of symbolic logic took place in the 1920s. Foremost among them are the distinction between syntax and semantics and the formulation of questions of completeness and decidability of logical systems. David Hilbert and his students played a very important part in these developments. Their contributions can be traced to unpublished lecture notes and other manuscripts by Hilbert and Bernays dating to the period 1917-1923. The aim of this paper is to describe these results, (...)
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  41. Paraconsistent extensional propositional logics.Diderik Batens - 1980 - Logique and Analyse 90 (90):195-234.
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  42.  33
    Fuzzy Propositional Logic. Algebraic Approach.Slava Meskhi - 1977 - Studia Logica 36 (3):189 - 194.
    The present paper contains some technical results on a many-valued logic with truth values from the interval of real numbers [0; 1]. This logic, discussed originally in [1], latter in [2] and [3], was called the logic of fuzzy concepts. Our aim is to give an algebraic axiomatics for fuzzy propositional logic. For this purpose the variety of L-algebras with signature en- riched with a unary operation { involution is stud- ied. A one-to-one correspondence between (...)
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  43.  19
    The Propositional Logic of Frege’s Grundgesetze: Semantics and Expressiveness.Eric D. Berg & Roy T. Cook - 2017 - Journal for the History of Analytical Philosophy 5 (6).
    In this paper we compare the propositional logic of Frege’s Grundgesetze der Arithmetik to modern propositional systems, and show that Frege does not have a separable propositional logic, definable in terms of primitives of Grundgesetze, that corresponds to modern formulations of the logic of “not”, “and”, “or”, and “if…then…”. Along the way we prove a number of novel results about the system of propositional logic found in Grundgesetze, and the broader system obtained (...)
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  44.  32
    Modal Companions of Intermediate Propositional Logics.Alexander Chagrov & Michael Zakharyashchev - 1992 - Studia Logica 51 (1):49 - 82.
    This paper is a survey of results concerning embeddings of intuitionistic propositional logic and its extensions into various classical modal systems.
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  45.  11
    Sequent Calculi for the Propositional Logic of HYPE.Martin Fischer - 2021 - Studia Logica 110 (3):1-35.
    In this paper we discuss sequent calculi for the propositional fragment of the logic of HYPE. The logic of HYPE was recently suggested by Leitgeb as a logic for hyperintensional contexts. On the one hand we introduce a simple \-system employing rules of contraposition. On the other hand we present a \-system with an admissible rule of contraposition. Both systems are equivalent as well as sound and complete proof-system of HYPE. In order to provide a cut-elimination (...)
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  46.  32
    Intuitionistic Propositional Logic Without 'Contraction' but with 'Reductio'.J. M. Méndez & F. Salto - 2000 - Studia Logica 66 (3):409-418.
    Routley- Meyer type relational complete semantics are constructed for intuitionistic contractionless logic with reductio. Different negation completions of positive intuitionistic logic without contraction are treated in a systematical, unified and semantically complete setting.
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  47.  24
    On Argumentation Logic and Propositional Logic.Antonis C. Kakas, Paolo Mancarella & Francesca Toni - 2018 - Studia Logica 106 (2):237-279.
    This paper studies the relationship between Argumentation Logic, a recently defined logic based on the study of argumentation in AI, and classical Propositional Logic. In particular, it shows that AL and PL are logically equivalent in that they have the same entailment relation from any given classically consistent theory. This equivalence follows from a correspondence between the non-acceptability of sentences in AL and Natural Deduction proofs of the complement of these sentences. The proof of this equivalence (...)
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  48.  70
    Quantified Propositional Logic and the Number of Lines of Tree-Like Proofs.Alessandra Carbone - 2000 - Studia Logica 64 (3):315-321.
    There is an exponential speed-up in the number of lines of the quantified propositional sequent calculus over Substitution Frege Systems, if one considers proofs as trees. Whether this is true also for the number of symbols, is still an open problem.
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  49.  98
    Reasoning Processes in Propositional Logic.Claes Strannegård, Simon Ulfsbäcker, David Hedqvist & Tommy Gärling - 2010 - Journal of Logic, Language and Information 19 (3):283-314.
    We conducted a computer-based psychological experiment in which a random mix of 40 tautologies and 40 non-tautologies were presented to the participants, who were asked to determine which ones of the formulas were tautologies. The participants were eight university students in computer science who had received tuition in propositional logic. The formulas appeared one by one, a time-limit of 45 s applied to each formula and no aids were allowed. For each formula we recorded the proportion of the (...)
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  50.  12
    Meaning and Proscription in Formal Logic: Variations on the Propositional Logic of William T. Parry.Thomas Macaulay Ferguson - 2017 - Cham, Switzerland: Springer Verlag.
    This book aids in the rehabilitation of the wrongfully deprecated work of William Parry, and is the only full-length investigation into Parry-type propositional logics. A central tenet of the monograph is that the sheer diversity of the contexts in which the mereological analogy emerges – its effervescence with respect to fields ranging from metaphysics to computer programming – provides compelling evidence that the study of logics of analytic implication can be instrumental in identifying connections between topics that would otherwise (...)
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