Open AccessSyntax and semantics of simple paracomplete logics
Author(s) -
В. М. Попов,
Vasilyi Shangin
Publication year - 2013
Publication title -
logičeskie issledovaniâ
Language(s) - English
Resource type - Journals
eISSN - 2413-2713
pISSN - 2074-1472
DOI - 10.21146/2074-1472-2013-19-0-325-333
Subject(s) - sequent , sequent calculus , natural deduction , calculus (dental) , programming language , simple (philosophy) , semantics (computer science) , mathematics , syntax , computer science , discrete mathematics , algebra over a field , pure mathematics , mathematical proof , artificial intelligence , philosophy , epistemology , medicine , geometry , dentistry
For an arbitrary fixed element $\beta$ in $\{1; 2; 3; ...; \omega\}$ both a sequent calculus and a natural deduction calculus which axiomatise simple paracomplete logic $I_{2;\beta}$ are built. Additionally, a valuation semantic which is adequate to logic $I_{2;\beta}$ is constructed. For an arbitrary fixed element $\gamma$ in $\{1; 2; 3;...\}$ a cortege semantic which is adequate to logic $I_{2;\gamma}$ is described. A number of results obtainable with the axiomatisations and semantics in question are formulated.