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Four-valued expansions of Dunn-Belnap's logic (I): Basic characterizations

Alexej P. Pynko

Bulletin of the Section of Logic > 2020 > 49 > 4 > 401-437

Basic results of the paper are that any four-valued expansion L4 of Dunn-Belnap's logic DB4 is de_ned by a unique (up to isomorphism) conjunctive matrix ℳ4 with exactly two distinguished values over an expansion 𝔄4 of a De Morgan non-Boolean four-valued diamond, but by no matrix with either less than four values or a single [non-]distinguished value, and has no proper extension satisfying Variable...

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Subquasivarieties of implicative locally‐finite quasivarieties

Alexej P. Pynko

Mathematical Logic Quarterly > 56 > 6 > 643 - 658

A quasivariety is said to be implicative if it is generated by a class of algebras with equationally‐definable implication of equalities. Implicative finitely‐generated quasivarieties appear naturally within logic, for instance, as equivalent quasivarieties of Gentzen‐style calculi for finitely‐valued propositional logics with equality determinant (cf. [17], [18, Subsection 7.5] and Section A). Furthermore,...

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Keywords

EQUALITY DETERMINANT (2)
DUNN-BELNAP'S LOGIC (1)
EXPANSION (1)
FINITELY‐VALUED LOGIC (1)
IMPLICATIVE QUASIVARIETY (1)
LOCALLY‐FINITE QUASIVARIETY (1)
LOGICAL MATRIX (1)
PROPOSITIONAL LOGIC (1)
QUASIVARIETY (1)
RELATIVELY‐SIMPLE ALGEBRA (1)
SEQUENT CALCULUS (1)
[BOUNDED] DISTRIBUTIVE/DE MORGAN LATTICE (1)
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Four-valued expansions of Dunn-Belnap's logic (I): Basic characterizations

Subquasivarieties of implicative locally‐finite quasivarieties

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