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

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  1. Proving in Finite Many-Valued Propositional (forthcoming). An Algorithm for Axiomatizing and Theorem Proving in Finite Many-Valued Propositional Logics* Walter A. Carnielli. Logique Et Analyse.score: 160.0
     
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  2. Theodore Hailperin & Ontologically Neutral Logic (2001). Kenneth Harris and Branden Fitelson/Comments on Some Completeness Theorems of Urquhart and Méndez & Salto 51–55 Dominic Gregory/Completeness and Decidability Results for Some Propositional Modal Logics Containing “Actu. [REVIEW] Journal of Philosophical Logic 30:617-618.score: 140.0
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  3. Claes Strannegård, Simon Ulfsbäcker, David Hedqvist & Tommy Gärling (2010). Reasoning Processes in Propositional Logic. Journal of Logic, Language and Information 19 (3):283-314.score: 93.0
    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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  4. Konrad Zdanowski (2009). On Second Order Intuitionistic Propositional Logic Without a Universal Quantifier. Journal of Symbolic Logic 74 (1):157-167.score: 93.0
    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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  5. Xingxing He, Jun Liu, Yang Xu, Luis Martínez & Da Ruan (2012). On Α-Satisfiability and its Α-Lock Resolution in a Finite Lattice-Valued Propositional Logic. Logic Journal of the Igpl 20 (3):579-588.score: 93.0
    Automated reasoning issues are addressed for a finite lattice-valued propositional logic LnP(X) with truth-values in a finite lattice-valued logical algebraic structure—lattice implication algebra. We investigate extended strategies and rules from classical logic to LnP(X) to simplify the procedure in the semantic level for testing the satisfiability of formulas in LnP(X) at a certain truth-value level α (α-satisfiability) while keeping the role of truth constant formula played in LnP(X). We propose a lock resolution method at a certain truth-value (...)
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  6. Kevin C. Klement, Propositional Logic. Internet Encyclopedia of Philosophy.score: 90.0
    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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  7. Michael Kaminski & Nissim Francez (2014). Relational Semantics of the Lambek Calculus Extended with Classical Propositional Logic. Studia Logica 102 (3):479-497.score: 90.0
    We show that the relational semantics of the Lambek calculus, both nonassociative and associative, is also sound and complete for its extension with classical propositional logic. Then, using filtrations, we obtain the finite model property for the nonassociative Lambek calculus extended with classical propositional logic.
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  8. R. Alonderis (2013). A Proof-Search Procedure for Intuitionistic Propositional Logic. Archive for Mathematical Logic 52 (7-8):759-778.score: 87.0
    A sequent root-first proof-search procedure for intuitionistic propositional logic is presented. The procedure is obtained from modified intuitionistic multi-succedent and classical sequent calculi, making use of Glivenko’s Theorem. We prove that a sequent is derivable in a standard intuitionistic multi-succedent calculus if and only if the corresponding prefixed-sequent is derivable in the procedure.
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  9. Dimitar P. Guelev (1999). A Propositional Dynamic Logic with Qualitative Probabilities. Journal of Philosophical Logic 28 (6):575-604.score: 84.0
    This paper presents an w-completeness theorem for a new propositional probabilistic logic, namely, the dynamic propositional logic of qualitative probabilities (DQP), which has been introduced by the author as a dynamic extension of the logic of qualitative probabilities (Q P) introduced by Segerberg.
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  10. Stefano Cavagnetto (2009). Some Applications of Propositional Logic to Cellular Automata. Mathematical Logic Quarterly 55 (6):605-616.score: 78.0
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  11. K. Ishii (2003). New Sequent Calculi for Visser's Formal Propositional Logic. Mathematical Logic Quarterly 49 (5):525.score: 78.0
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  12. M. Alizadeh & M. Ardeshir (2004). On the Linear Lindenbaum Algebra of Basic Propositional Logic. Mathematical Logic Quarterly 50 (1):65.score: 78.0
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  13. Kosta Dosen & Zoran Petric (2012). Isomorphic Formulae in Classical Propositional Logic. Mathematical Logic Quarterly 58 (1):5-17.score: 78.0
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  14. Karl Dürr (1951/1980). The Propositional Logic of Boethius. Greenwood Press.score: 77.0
    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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  15. Michael J. Carroll (1976). On Interpreting the S5 Propositional Calculus: An Essay in Philosophical Logic. Dissertation, University of Iowascore: 75.0
    Discusses alternative interpretations of the modal operators, for the modal propositional logic S5.
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  16. Balder ten Cate (2006). Expressivity of Second Order Propositional Modal Logic. Journal of Philosophical Logic 35 (2):209-223.score: 75.0
    We consider second-order propositional modal logic (SOPML), an extension of the basic modal language with propositional quantifiers introduced by Kit Fine in 1970. We determine the precise expressive power of SOPML by giving analogues of the Van Benthem–Rosen theorem and the Goldblatt Thomason theorem. Furthermore, we show that the basic modal language is the bisimulation invariant fragment of SOPML, and we characterize the bounded fragment of first-order logic as being the intersection of first-order logic and (...)
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  17. Jan Krajíček (1995). Bounded Arithmetic, Propositional Logic, and Complexity Theory. Cambridge University Press.score: 74.0
    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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  18. Brian Hill & Francesca Poggiolesi (2010). A Contraction-Free and Cut-Free Sequent Calculus for Propositional Dynamic Logic. Studia Logica 94 (1):47 - 72.score: 72.0
    In this paper we present a sequent calculus for propositional dynamic logic built using an enriched version of the tree-hypersequent method and including an infinitary rule for the iteration operator. We prove that this sequent calculus is theoremwise equivalent to the corresponding Hilbert-style system, and that it is contraction-free and cut-free. All results are proved in a purely syntactic way.
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  19. Mauro Ferrari, Camillo Fiorentini & Guido Fiorino (2004). A Secondary Semantics for Second Order Intuitionistic Propositional Logic. Mathematical Logic Quarterly 50 (2):202-210.score: 72.0
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  20. James W. Garson (2010). Expressive Power and Incompleteness of Propositional Logics. Journal of Philosophical Logic 39 (2):159-171.score: 69.0
    Natural deduction systems were motivated by the desire to define the meaning of each connective by specifying how it is introduced and eliminated from inference. In one sense, this attempt fails, for it is well known that propositional logic rules (however formulated) underdetermine the classical truth tables. Natural deduction rules are too weak to enforce the intended readings of the connectives; they allow non-standard models. Two reactions to this phenomenon appear in the literature. One is to try to (...)
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  21. Morten H. Sørensen & Paweł Urzyczyn (2010). A Syntactic Embedding of Predicate Logic Into Second-Order Propositional Logic. Notre Dame Journal of Formal Logic 51 (4):457-473.score: 69.0
    We give a syntactic translation from first-order intuitionistic predicate logic into second-order intuitionistic propositional logic IPC2. The translation covers the full set of logical connectives ∧, ∨, →, ⊥, ∀, and ∃, extending our previous work, which studied the significantly simpler case of the universal-implicational fragment of predicate logic. As corollaries of our approach, we obtain simple proofs of nondefinability of ∃ from the propositional connectives and nondefinability of ∀ from ∃ in the second-order intuitionistic (...)
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  22. Peter Roeper & Hugues Leblanc (1999). Absolute Probability Functions for Intuitionistic Propositional Logic. Journal of Philosophical Logic 28 (3):223-234.score: 69.0
    Provided here is a characterisation of absolute probability functions for intuitionistic (propositional) logic L, i.e. a set of constraints on the unary functions P from the statements of L to the reals, which insures that (i) if a statement A of L is provable in L, then P(A) = 1 for every P, L's axiomatisation being thus sound in the probabilistic sense, and (ii) if P(A) = 1 for every P, then A is provable in L, L's axiomatisation (...)
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  23. A. D. Yashin (1999). Irreflexive Modality in the Intuitionistic Propositional Logic and Novikov Completeness. Journal of Philosophical Logic 28 (2):175-197.score: 69.0
    A. Kuznetsov considered a logic which extended intuitionistic propositional logic by adding a notion of 'irreflexive modality'. We describe an extension of Kuznetsov's logic having the following properties: (a) it is the unique maximal conservative (over intuitionistic propositional logic) extension of Kuznetsov's logic; (b) it determines a new unary logical connective w.r.t. Novikov's approach, i.e., there is no explicit expression within the system for the additional connective; (c) it is axiomatizable by means of (...)
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  24. Diderik Batens (forthcoming). Propositional Logic Extended with a Pedagogically Useful Relevant Implication. Logic and Logical Philosophy.score: 69.0
    First and foremost, this paper concerns the combination of classical propositional logic with a relevant implication. The proposed combination is simple and transparent from a proof theoretic point of view and at the same time extremely useful for relating formal logic to natural language sentences. A specific system will be presented and studied, also from a semantic point of view. The last sections of the paper contain more general considerations on combining classical propositional logic with (...)
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  25. Ioana Leuştean (2006). Non-Commutative Łukasiewicz Propositional Logic. Archive for Mathematical Logic 45 (2):191-213.score: 69.0
    The non-commutative counterpart of the well-known Łukasiewicz propositional logic is developed, in strong connection with the algebraic theory of psMV-algebras. An extension by a new unary logical connective is also considered and a stronger completeness result is proved for this system.
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  26. Yehoshua Sagiv (1979). An Algorithm for Inferring Multivalued Dependencies That Works Also for a Subclass of Propositional Logic. Dept. Of Computer Science, University of Illinois at Urbana-Champaign.score: 69.0
     
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  27. Vítězslav Švejdar (2003). On the Polynomial-Space Completeness of Intuitionistic Propositional Logic. Archive for Mathematical Logic 42 (7):711-716.score: 69.0
    We present an alternative, purely semantical and relatively simple, proof of the Statman's result that both intuitionistic propositional logic and its implicational fragment are PSPACE-complete.
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  28. Albert Visser (2006). Propositional Logics of Closed and Open Substitutions Over Heyting's Arithmetic. Notre Dame Journal of Formal Logic 47 (3):299-309.score: 67.0
    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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  29. Fabrice Correia (2000). Propositional Logic of Essence. Journal of Philosophical Logic 29 (3):295-313.score: 66.0
    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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  30. Marcello D'Agostino & Luciano Floridi (2009). The Enduring Scandal of Deduction: Is Propositional Logic Really Uninformative? Synthese 167 (2):271 - 315.score: 66.0
    Deductive inference is usually regarded as being "tautological" or "analytical": the information conveyed by the conclusion is contained in the information conveyed by the premises. This idea, however, clashes with the undecidability of first-order logic and with the (likely) intractability of Boolean logic. In this article, we address the problem both from the semantic and the proof-theoretical point of view. We propose a hierarchy of propositional logics that are all tractable (i.e. decidable in polynomial time), although by (...)
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  31. Giorgi Japaridze (2000). The Propositional Logic of Elementary Tasks. Notre Dame Journal of Formal Logic 41 (2):171-183.score: 66.0
    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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  32. Richard Zach (1999). Completeness Before Post: Bernays, Hilbert, and the Development of Propositional Logic. Bulletin of Symbolic Logic 5 (3):331-366.score: 63.0
    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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  33. John T. Kearns (1997). Propositional Logic of Supposition and Assertion. Notre Dame Journal of Formal Logic 38 (3):325-349.score: 63.0
    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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  34. Theodore Hailperin (1984). Boole's Abandoned Propositional Logic. History and Philosophy of Logic 5 (1):39-48.score: 63.0
    The approach used by Boole in Mathematical analysis of logic to develop propositional logic was based on the idea of ?cases? or ?conjunctures of circumstances?. But this was dropped in Laws of thought in favor of one which Boole considered to be more satisfactory, that of using the notion of ?time for which a proposition is true?. We show that, when suitable clarifications and corrections are made, the earlier approach? which accords with modern logic in eschewing (...)
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  35. Rosalie Iemhoff (2001). On the Admissible Rules of Intuitionistic Propositional Logic. Journal of Symbolic Logic 66 (1):281-294.score: 63.0
    We present a basis for the admissible rules of intuitionistic propositional logic. Thereby a conjecture by de Jongh and Visser is proved. We also present a proof system for the admissible rules, and give semantic criteria for admissibility.
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  36. Robert A. Bull (1992). Cut Elimination for Propositional Dynamic Logic Without. Mathematical Logic Quarterly 38 (1):85-100.score: 63.0
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  37. René David & Marek Zaionc (2009). Counting Proofs in Propositional Logic. Archive for Mathematical Logic 48 (2):185-199.score: 63.0
    We give a procedure for counting the number of different proofs of a formula in various sorts of propositional logic. This number is either an integer (that may be 0 if the formula is not provable) or infinite.
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  38. Eric M. Brown, Logic II: The Theory of Propositions.score: 61.0
    This is part two of a complete exposition of Logic, in which there is a radically new synthesis of Aristotelian-Scholastic Logic with modern Logic. Part II is the presentation of the theory of propositions. Simple, composite, atomic, compound, modal, and tensed propositions are all examined. Valid consequences and propositional logical identities are rigorously proven. Modal logic is rigorously defined and proven. This is the first work of Logic known to unite Aristotelian logic and (...)
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  39. C. Anthony Anderson (ed.) (1990). Propositional Attitudes: The Role of Content in Logic, Language, and Mind. Stanford: CSLI.score: 60.0
  40. Hector-Neri Castañeda (1990). Leibniz's Complete Propositional Logic. Topoi 9 (1):15-28.score: 60.0
    I have shown (to my satisfaction) that Leibniz's final attempt at a generalized syllogistico-propositional calculus in the Generales Inquisitiones was pretty successful. The calculus includes the truth-table semantics for the propositional calculus. It contains an unorthodox view of conjunction. It offers a plethora of very important logical principles. These deserve to be called a set of fundamentals of logical form. Aside from some imprecisions and redundancies the system is a good systematization of propositional logic, its semantics, (...)
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  41. Albert Visser (1981). A Propositional Logic with Explicit Fixed Points. Studia Logica 40 (2):155 - 175.score: 60.0
    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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  42. Xuefeng Wen (2007). A Propositional Logic with Relative Identity Connective and a Partial Solution to the Paradox of Analysis. Studia Logica 85 (2):251 - 260.score: 60.0
    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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  43. Susanne Bobzien (2002). Propositional Logic in Ammonius. In Helmut Linneweber-Lammerskitten & Georg Mohr (eds.), Interpretation und Argument. Koenigshausen & Neumann.score: 60.0
    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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  44. Mojtaba Aghaei & Mohammad Ardeshir (2001). Gentzen-Style Axiomatizations for Some Conservative Extensions of Basic Propositional Logic. Studia Logica 68 (2):263-285.score: 60.0
    We introduce two Gentzen-style sequent calculus axiomatizations for conservative extensions of basic propositional logic. Our first axiomatization is an ipmrovement of, in the sense that it has a kind of the subformula property and is a slight modification of. In this system the cut rule is eliminated. The second axiomatization is a classical conservative extension of basic propositional logic. Using these axiomatizations, we prove interpolation theorems for basic propositional logic.
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  45. William S. Cooper (1968). The Propositional Logic of Ordinary Discourse. Inquiry 11 (1-4):295 – 320.score: 60.0
    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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  46. Carlo Dalla Pozza & Claudio Garola (1995). A Pragmatic Interpretation of Intuitionistic Propositional Logic. Erkenntnis 43 (1):81 - 109.score: 60.0
    We construct an extension P of the standard language of classical propositional logic by adjoining to the alphabet of a new category of logical-pragmatic signs. The well formed formulas of are calledradical formulas (rfs) of P;rfs preceded by theassertion sign constituteelementary assertive formulas of P, which can be connected together by means of thepragmatic connectives N, K, A, C, E, so as to obtain the set of all theassertive formulas (afs). Everyrf of P is endowed with atruth value (...)
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  47. Gerald J. Massey (1965). Four Simple Systems of Modal Propositional Logic. Philosophy of Science 32 (3/4):342-355.score: 60.0
    Four progressively ambitious systems of modal propositional logic are set forth, together with decision procedures. The simultaneous employment of parenthesis notation and parenthesis-free notation, the dual use of symbols as primitive and defined, and the introduction of a new modal operator (the truth operator) are the principal devices used to effect the development of these logics. The first two logics turn out to be "the same" as two of von Wright's systems.
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  48. Marvin J. Croy (2010). Teaching the Practical Relevance of Propositional Logic. Teaching Philosophy 33 (3):253-270.score: 60.0
    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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  49. Merlijn Sevenster (2006). On the Computational Consequences of Independence in Propositional Logic. Synthese 149 (2):257 - 283.score: 60.0
    Sandu and Pietarinen [Partiality and Games: Propositional Logic. Logic J. IGPL 9 (2001) 101] study independence friendly propositional logics. That is, traditional propositional logic extended by means of syntax that allow connectives to be independent of each other, although the one may be subordinate to the other. Sandu and Pietarinen observe that the IF propositional logics have exotic properties, like functional completeness for three-valued functions. In this paper we focus on one of their (...)
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  50. Ernst Zimmermann (2002). A Predicate Logical Extension of a Subintuitionistic Propositional Logic. Studia Logica 72 (3):401-410.score: 60.0
    We develop a predicate logical extension of a subintuitionistic propositional logic. Therefore a Hilbert type calculus and a Kripke type model are given. The propositional logic is formulated to axiomatize the idea of strategic weakening of Kripke''s semantic for intuitionistic logic: dropping the semantical condition of heredity or persistence leads to a nonmonotonic model. On the syntactic side this leads to a certain restriction imposed on the deduction theorem. By means of a Henkin argument strong (...)
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