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open-access-imgOpen AccessON THE PROBLEM OF EXPANSION OF MATRIX SEMANTICS ADEQUATE TO CLASSICAL IMPLICATIVE LOGIC TO MATRIX SEMANTICS ADEQUATE TO CLASSICAL IMPLICATIVE-NEGATIVE LOGIC (PART 4)
Author(s)
В.М. Попов
Publication year2021
Publication title
логико-философские штудии
Resource typeJournals
PublisherPhilosophical Society
Эта статья находится в русле исследований проблемы расширения семантики, адекватной собственному фрагменту логики, до семантики, адекватной этой логике. Основное содержание статьи представлено в двух разделах (первый раздел и второй раздел). В первом разделе установлено следующее: ⟨M (1/2, 0, 1, 1), ¬(1/2, 1, 1)⟩ и ⟨M (1/2, 0, 1, 1), ¬(0, 1, 1)⟩ — все L⊃¬ -матрицы вида ⟨M (1/2, 0, 1, 1), f⟩, адекватные классической импликативно-негативной логике Cl⊃¬ , а ⟨M (0, 1/2, 1, 1), ¬(1/2, 1, 1)⟩ и ⟨M (0, 1/2, 1, 1), ¬(0, 1, 1)⟩ — все L⊃¬-матрицы вида ⟨M (0, 1/2, 1, 1), f⟩, адекватные классической импликативно-негативной логике Cl⊃¬. Во втором разделе перечислены все L⊃¬ -матрицы вида ⟨{1, 1/2, 0}, {1}, g, f⟩, адекватные классической импликативно-негативной логике Cl⊃¬ . This article is in the mainstream of research into the problem of expansion of a semantics adequate to a proper fragment of a logic to semantics adequate to this logic. The main content of the article is presented in two sections, the first section and the second section. The first section establishes the following: ⟨M (1/2, 0, 1, 1), ¬(1/2, 1, 1)⟩ and ⟨M (1/2, 0, 1, 1), ¬(0, 1, 1)⟩ are all L⊃¬-matrices of the form ⟨M (1/2, 0, 1, 1), f⟩ adequate to the classical implicativenegative logic Cl⊃¬ , and ⟨M (0, 1/2, 1, 1), ¬(1/2, 1, 1)⟩ and ⟨M (0, 1/2, 1, 1), ¬(0, 1, 1)⟩ are all L⊃¬-matrices of the form ⟨M (0, 1/2, 1, 1), f⟩ adequate to the classical implicative-negative logic Cl⊃¬ . In the second section we give a list of all L⊃¬ -matrices of the form ⟨{1, 1/2, 0}, {1}, g, f⟩ each of which is adequate to the classical implicative-negative logic Cl⊃¬.
Subject(s)algebra over a field , algorithm , chemistry , chromatography , computer science , discrete mathematics , fragment (logic) , mathematics , matrix (chemical analysis) , operating system , programming language , pure mathematics , section (typography) , semantics (computer science)
Language(s)English
ISSN2071-9183
DOI10.52119/lphs.2021.19.10.001

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