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Relevant bibliographies by topics / Classical propositional logic

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Journal articles

Academic literature on the topic 'Classical propositional logic'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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Journal articles on the topic "Classical propositional logic"

1

Devesas Campos, Marco, and Marcelo Fiore. "Classical logic with Mendler induction." Journal of Logic and Computation 30, no. 1 (2020): 77–106. http://dx.doi.org/10.1093/logcom/exaa004.

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Abstract We investigate (co-) induction in classical logic under the propositions-as-types paradigm, considering propositional, second-order and (co-) inductive types. Specifically, we introduce an extension of the Dual Calculus with a Mendler-style (co-) iterator and show that it is strongly normalizing. We prove this using a reducibility argument.

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Citkin, Alex. "Deductive systems with unified multiple-conclusion rules." Logical Investigations 26, no. 2 (2020): 87–105. http://dx.doi.org/10.21146/2074-1472-2020-26-2-87-105.

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Our goal is to develop a syntactical apparatus for propositional logics in which the accepted and rejected propositions have the same status and are being treated in the same way. The suggested approach is based on the ideas of Ƚukasiewicz used for the classical logic and in addition, it includes the use of multiple conclusion rules. A special attention is paid to the logics in which each proposition is either accepted or rejected.

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3

Oldofredi, Andrea. "Classical Logic in the Quantum Context." Quantum Reports 2, no. 4 (2020): 600–616. http://dx.doi.org/10.3390/quantum2040042.

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It is generally accepted that quantum mechanics entails a revision of the classical propositional calculus as a consequence of its physical content. However, the universal claim according to which a new quantum logic is indispensable in order to model the propositions of every quantum theory is challenged. In the present essay, we critically discuss this claim by showing that classical logic can be rehabilitated in a quantum context by taking into account Bohmian mechanics. It will be argued, indeed, that such a theoretical framework provides the necessary conceptual tools to reintroduce a classical logic of experimental propositions by virtue of its clear metaphysical picture and its theory of measurement. More precisely, it will be shown that the rehabilitation of a classical propositional calculus is a consequence of the primitive ontology of the theory, a fact that is not yet sufficiently recognized in the literature concerning Bohmian mechanics. This work aims to fill this gap.

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4

WHITEN, BILL. "A SIMPLE ALGORITHM FOR DEDUCTION." ANZIAM Journal 51, no. 1 (2009): 102–22. http://dx.doi.org/10.1017/s1446181109000352.

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AbstractIt is shown that a simple deduction engine can be developed for a propositional logic that follows the normal rules of classical logic in symbolic form, but the description of what is known about a proposition uses two numeric state variables that conveniently describe unknown and inconsistent, as well as true and false. Partly true and partly false can be included in deductions. The multi-valued logic is easily understood as the state variables relate directly to true and false. The deduction engine provides a convenient standard method for handling multiple or complicated logical relations. It is particularly convenient when the deduction can start with different propositions being given initial values of true or false. It extends Horn clause based deduction for propositional logic to arbitrary clauses. The logic system used has potential applications in many areas. A comparison with propositional logic makes the paper self-contained.

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5

Томова, Н. Е. "Natural three-valued logics and classical logic." Logical Investigations 19 (April 9, 2013): 344–52. http://dx.doi.org/10.21146/2074-1472-2013-19-0-344-352.

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In this paper implicative fragments of natural three- valued logic are investigated. It is proved that some fragments are equivalent by set of tautologies to implicative fragment of classical logic. It is also shown that some natural three-valued logics verify all tautologies of classical propositional logic.

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6

MA, MINGHUI, and AHTI-VEIKKO PIETARINEN. "PEIRCE’S CALCULI FOR CLASSICAL PROPOSITIONAL LOGIC." Review of Symbolic Logic 13, no. 3 (2018): 509–40. http://dx.doi.org/10.1017/s1755020318000187.

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AbstractThis article investigates Charles Peirce’s development of logical calculi for classical propositional logic in 1880–1896. Peirce’s 1880 work on the algebra of logic resulted in a successful calculus for Boolean algebra. This calculus, denoted byPC, is here presented as a sequent calculus and not as a natural deduction system. It is shown that Peirce’s aim was to presentPCas a sequent calculus. The law of distributivity, which Peirce states in 1880, is proved using Peirce’s Rule, which is a residuation, inPC. The transitional systems of the algebra of the copula that Peirce develops since 1880 paved the way to the 1896 graphical system of the alpha graphs. It is shown how the rules of the alpha system reinterpret Boolean algebras, answering Peirce’s statement that logical graphs supply a new system of fundamental assumptions to logical algebra. A proof-theoretic analysis is given for the connection betweenPCand the alpha system.

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7

Došen, Kosta, and Zoran Petrić. "Isomorphic formulae in classical propositional logic." Mathematical Logic Quarterly 58, no. 1-2 (2011): 5–17. http://dx.doi.org/10.1002/malq.201020020.

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8

KREMER, PHILIP. "COMPLETENESS OF SECOND-ORDER PROPOSITIONAL S4 AND H IN TOPOLOGICAL SEMANTICS." Review of Symbolic Logic 11, no. 3 (2018): 507–18. http://dx.doi.org/10.1017/s1755020318000229.

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AbstractWe add propositional quantifiers to the propositional modal logic S4 and to the propositional intuitionistic logic H, introducing axiom schemes that are the natural analogs to axiom schemes typically used for first-order quantifiers in classical and intuitionistic logic. We show that the resulting logics are sound and complete for a topological semantics extending, in a natural way, the topological semantics for S4 and for H.

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9

Mason, Ian. "The metatheory of the classical propositional calculus is not axiomatizable." Journal of Symbolic Logic 50, no. 2 (1985): 451–57. http://dx.doi.org/10.2307/2274233.

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In this paper we investigate the first order metatheory of the classical propositional logic. In the first section we prove that the first order metatheory of the classical propositional logic is undecidable. Thus as a mathematical object even the simplest of logics is, from a logical standpoint, quite complex. In fact it is of the same complexity as true first order number theory.This result answers negatively a question of J. F. A. K. van Benthem (see [van Benthem and Doets 1983]) as to whether the interpolation theorem in some sense completes the metatheory of the calculus. Let us begin by motivating the question that we answer. In [van Benthem and Doets 1983] it is claimed that a folklore prejudice has it that interpolation was the final elementary property of first order logic to be discovered. Even though other properties of the propositional calculus have been discovered since Craig's orginal paper [Craig 1957] (see for example [Reznikoff 1965]) there is a lot of evidence for the fundamental nature of the property. In abstract model theory for example one finds that very few logics have the interpolation property. There are two well-known open problems in this area. These are1. Is there a logic satisfying the full compactness theorem as well as the interpolation theorem that is not equivalent to first order logic even for finite models?2. Is there a logic stronger than L(Q), the logic with the quantifierthere exist uncountably many, that is countably compact and has the interpolation property?

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10

Malhas, Othman Qasim. "Quantum Logic and the Classical Propositional Calculus." Journal of Symbolic Logic 52, no. 3 (1987): 834. http://dx.doi.org/10.2307/2274369.

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