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Your search keyword '"Intuitionism"' showing total 5 results
Start Over Descriptor "Intuitionism" Journal bulletin of the section of logic
5 results on '"Intuitionism"'

1. Empirical Negation, Co-Negation and the Contraposition Rule II: Proof-Theoretical Investigations

Author

Satoru Niki

Subjects
empirical negation, co-negation, labelled sequent calculus, intuitionism, Logic, BC1-199
Abstract

We continue the investigation of the first paper where we studied logics with various negations including empirical negation and co-negation. We established how such logics can be treated uniformly with R. Sylvan's CCω as the basis. In this paper we use this result to obtain cut-free labelled sequent calculi for the logics.

Published
2020
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2. Empirical Negation, Co-negation and Contraposition Rule I: Semantical Investigations

Author

Satoru Niki

Subjects
empirical negation, co-negation, beth semantics, kripke semantics, intuitionism, Logic, BC1-199
Abstract

We investigate the relationship between M. De's empirical negation in Kripke and Beth Semantics. It turns out empirical negation, as well as co-negation, corresponds to different logics under different semantics. We then establish the relationship between logics related to these negations under unified syntax and semantics based on R. Sylvan's CCω.

Published
2020
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3. EMPIRICAL NEGATION, CO-NEGATION AND THE CONTRAPOSITION RULE I: SEMANTICAL INVESTIGATIONS.

Author

Satoru Niki

Subjects
KRIPKE semantics, NEGATION (Logic), SEMANTICS, LOGIC
Abstract

We investigate the relationship between M. De's empirical negation in Kripke and Beth Semantics. It turns out empirical negation, as well as co-negation, corresponds to different logics under different semantics. We then establish the relationship between logics related to these negations under unified syntax and semantics based on R. Sylvan's CCw. [ABSTRACT FROM AUTHOR]

Published
2020
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4. From Intuitionism to Brouwer's Modal Logic

Author

Zofia Kostrzycka

Subjects
Logic, Modal logic, Intuitionistic logic, intuitionistic logic, Propositional calculus, lcsh:Logic, Algebra, Philosophy, Lattice (module), Modal, kripke frames, Intuitionism, brouwer's modal logic, Algebra over a field, lcsh:BC1-199, Axiom, Mathematics
Abstract

We try to translate the intuitionistic propositional logic INT into Brouwer's modal logic KTB. Our translation is motivated by intuitions behind Brouwer's axiom p →☐◊p The main idea is to interpret intuitionistic implication as modal strict implication, whereas variables and other positive sentences remain as they are. The proposed translation preserves fragments of the Rieger-Nishimura lattice which is the Lindenbaum algebra of monadic formulas in INT. Unfortunately, INT is not embedded by this mapping into KTB.

Published
2020

5. THREE DOCTRINES OF THE NATURE OF MATHEMATICS (SOME COMMENTS OF A KNOWLEDGE THEORIST).

Author

Wójcicki, Ryszard

Subjects
*THEORY of knowledge, *INTUITIONISTIC mathematics, *ETHICAL intuitionism, *MATHEMATICIANS, *MATHEMATICAL logic, *MATHEMATICAL analysis
Abstract

In this note I am re ecting on interrelations between three concepts of truth: (1) that employed by Hilbert arguing his formalist view on the nature of math- ematics, (2) Freges idea of truth supported by mathematical intuition, and (3) known as Aristotelian correspondence idea of truth concerning any propositions not merely mathematical. [ABSTRACT FROM AUTHOR]

Published
2017
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