Intuitionistic logic with strong negation

Studia Logica 36 (1-2):49 - 59 (1977)
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Abstract

This paper is a reaction to the following remark by grzegorczyk: "the compound sentences are not a product of experiment. they arise from reasoning. this concerns also negations; we see that the lemon is yellow, we do not see that it is not blue." generally, in science the truth is ascertained as indirectly as falsehood. an example: a litmus-paper is used to verify the sentence "the solution is acid." this approach gives rise to a (very intuitionistic indeed) conservative extension of the heyting logic satisfying natural duality laws

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Citations of this work

HYPE: A System of Hyperintensional Logic.Hannes Leitgeb - 2019 - Journal of Philosophical Logic 48 (2):305-405.
Connexive logic.Heinrich Wansing - 2008 - Stanford Encyclopedia of Philosophy.
Constructive negation, implication, and co-implication.Heinrich Wansing - 2008 - Journal of Applied Non-Classical Logics 18 (2-3):341-364.
There is More to Negation than Modality.Michael De & Hitoshi Omori - 2018 - Journal of Philosophical Logic 47 (2):281-299.
Modal logics with Belnapian truth values.Serge P. Odintsov & Heinrich Wansing - 2010 - Journal of Applied Non-Classical Logics 20 (3):279-304.

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References found in this work

Introduction to metamathematics.Stephen Cole Kleene - 1952 - Groningen: P. Noordhoff N.V..
Constructible falsity.David Nelson - 1949 - Journal of Symbolic Logic 14 (1):16-26.
Intuitionistic logic, model theory and forcing.Melvin Fitting - 1969 - Amsterdam,: North-Holland Pub. Co..
A semantical study of constructible falsity.Richmond H. Thomason - 1969 - Mathematical Logic Quarterly 15 (16-18):247-257.
A semantical study of constructible falsity.Richmond H. Thomason - 1969 - Mathematical Logic Quarterly 15 (16‐18):247-257.

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