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Download PDFOpen PDF in browserMiscellaneous Extensions of Four-Valued Expansions of Belnap's LogicEasyChair Preprint 407823 pages•Date: August 25, 2020AbstractAs a generic tool, we prove that the poset of (axiomatic) disjunctive [non-pseudo-axiomatic] extensions of the logic of a finite set M of [(truth-non-empty)] finite disjunctive matrices is dual to the distributive lattice of relative universal (positive) Horn model subclasses of the set S of [truth-non-empty] consistent submatrices of members of M [(the duality preserving axiomatic relative axiomatizations)]. If M consists of a single matrix with equality determinant, relative universal Horn model subclasses of S are proved constructively to be exactly lower cones of S that covers any four-valued expansion L4 of Belnap's four-valued logic B4. Moreover, we find algebraic criteria of the [inferential] paracompleteness of the extension of L4 relatively axiomatized by the Resolution} rule. We also find lattices of extensions of L4 satisfying certain rules (in particular, non-paracomplete extensions) under certain conditions covering many interesting four-valued expansions of B4 including both itself and its bounded version (as well as their purely implicative expansions). Keyphrases: extension, logic, matrix, model Download PDFOpen PDF in browser |
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