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Copies of Classical Logic in Intuitionistic Logic [PDF]

Philosophia Scientiæ, 2014
La logique classique (la logique des mathématiques non-constructives) est plus forte que la logique intuitionniste (la logique des mathématiques constructives).
Jaime Gaspar
doaj   +4 more sources

Classical Combinatory Logic [PDF]

Discrete Mathematics & Theoretical Computer Science, 2005
Combinatory logic shows that bound variables can be eliminated without loss of expressiveness. It has applications both in the foundations of mathematics and in the implementation of functional programming languages.
Karim Nour
doaj   +4 more sources

Classical propositional logic and decidability of variables in intuitionistic propositional logic [PDF]

Logical Methods in Computer Science, 2014
We improve the answer to the question: what set of excluded middles for propositional variables in a formula suffices to prove the formula in intuitionistic propositional logic whenever it is provable in classical propositional logic.
Hajime Ishihara
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New Directions in Categorical Logic, for Classical, Probabilistic and Quantum Logic [PDF]

Logical Methods in Computer Science, 2015
Intuitionistic logic, in which the double negation law not-not-P = P fails, is dominant in categorical logic, notably in topos theory. This paper follows a different direction in which double negation does hold.
Bart Jacobs
doaj   +6 more sources

Game semantics for first-order logic [PDF]

Logical Methods in Computer Science, 2010
We refine HO/N game semantics with an additional notion of pointer (mu-pointers) and extend it to first-order classical logic with completeness results.
Olivier Laurent
doaj   +7 more sources

Stone-Type Dualities for Separation Logics [PDF]

Logical Methods in Computer Science, 2019
Stone-type duality theorems, which relate algebraic and relational/topological models, are important tools in logic because -- in addition to elegant abstraction -- they strengthen soundness and completeness to a categorical equivalence, yielding a ...
Simon Docherty, David Pym
doaj   +5 more sources

The Logic of Khārijī Propositions [PDF]

حکمت سینوی, 2023
There are two general methods for interpreting and analyzing khārijī and ḥaqīqī propositions: first, by analyzing them within a unified logic; second, by assigning separate logics to khārijī and ḥaqīqī propositions.
Asadollah Fallahi
doaj   +1 more source

Classical Logic and Neutrosophic Logic. Answers to K. Georgiev [PDF]

Neutrosophic Sets and Systems, 2016
In this paper, we make distinctions between Classical Logic (where the propositions are 100% true, or 100 false) and the Neutrosophic Logic (where one deals with partially true, partially indeterminate and partially false propositions) in order to ...
Florentin Smarandache
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Structural Rules in Natural Deduction with Alternatives

Bulletin of the Section of Logic, 2023
Natural deduction with alternatives extends Gentzen–Prawitz-style natural deduction with a single structural addition: negatively signed assumptions, called alternatives.
Greg Restall
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Traditional Logic and Computational Thinking

Philosophies, 2021
In this contribution, we try to show that traditional Aristotelian logic can be useful (in a non-trivial way) for computational thinking. To achieve this objective, we argue in favor of two statements: (i) that traditional logic is not classical and (ii)
J.-Martín Castro-Manzano
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