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Start Over Descriptor "03G27" Topic 03b22
11 results on '"03G27"'

6. Selfextensional logics with a distributive nearlattice term.

Author

González, Luciano J.

Subjects
*MATHEMATICAL logic, *ALGEBRA, *MATHEMATICAL analysis, *NUMERICAL analysis, *MATHEMATICS theorems
Abstract

We define when a ternary term m of an algebraic language L is called a distributive nearlattice term (DN-term) of a sentential logic S. Distributive nearlattices are ternary algebras generalising Tarski algebras and distributive lattices. We characterise the selfextensional logics with a DN-term through the interpretation of the DN-term in the algebras of the algebraic counterpart of the logics. We prove that the canonical class of algebras (under the point of view of Abstract Algebraic Logic) associated with a selfextensional logic with a DN-term is a variety, and we obtain that the logic is in fact fully selfextensional. [ABSTRACT FROM AUTHOR]

Published
2019
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9. Admissible Rules and the Leibniz Hierarchy

Author

James G. Raftery

Subjects
[order] algebraizable logic, Pure mathematics, Hierarchy, Logic, 010102 general mathematics, Foundation (engineering), BCIW, 0102 computer and information sciences, structural completeness, 03G27, admissible rule, 01 natural sciences, reduced matrix, Leibniz hierarchy, Admissible rule, Work (electrical), 03B47, 010201 computation theory & mathematics, Computer Science::Logic in Computer Science, 0101 mathematics, deductive system, 03B22, 08C10, Mathematical economics, Mathematics
Abstract

This paper provides a semantic analysis of admissible rules and associated completeness conditions for arbitrary deductive systems, using the framework of abstract algebraic logic. Algebraizability is not assumed, so the meaning and significance of the principal notions vary with the level of the Leibniz hierarchy at which they are presented. As a case study of the resulting theory, the nonalgebraizable fragments of relevance logic are considered.

Published
2016

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