PP-2015-16: Canonical formulas for k-potent commutative, integral residuated lattices

PP-2015-16: Bezhanishvili, Nick and Galatos, Nick and Spada, Luca (2015) Canonical formulas for k-potent commutative, integral residuated lattices. [Report]

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Canonical formulas are a powerful tool for studying intuitionistic and modal logics. Actually, they provide a uniform and semantic way to axiomatise all extensions of intuitionistic logic and all modal logics above K4. Although the method originally hinged on the relational semantics of those logics, recently it has been completely recast in algebraic terms. In this new perspective canonical formulas are built from a finite subdirectly irreducible algebra by describing completely the behaviour of some operations and only partially the behaviour of some others. In this paper we export the machinery of canonical formulas to substructural logics by introducing canonical formulas for k-potent, commutative, integral, residuated lattices (k-CIRL). We show that any subvariety of k-CIRL is axiomatised by canonical formulas. The paper ends with some applications and examples.

Item Type: Report
Report Nr: PP-2015-16
Series Name: Prepublication (PP) Series
Year: 2015
Uncontrolled Keywords: Residuated lattices, substructural logics, axiomatisation, canonical formulas
Subjects: Logic
Depositing User: Nick Bezhanishvili
Date Deposited: 12 Oct 2016 14:37
Last Modified: 12 Oct 2016 14:37
URI: https://eprints.illc.uva.nl/id/eprint/527

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