Mathematical Logic Quarterly 58 (6):468-481 (2012)

Abstract
The Craig interpolation property is investigated for substructural logics whose algebraic semantics are varieties of semilinear pointed commutative residuated lattices. It is shown that Craig interpolation fails for certain classes of these logics with weakening if the corresponding algebras are not idempotent. A complete characterization is then given of axiomatic extensions of the “R-mingle with unit” logic that have the Craig interpolation property. This latter characterization is obtained using a model-theoretic quantifier elimination strategy to determine the varieties of Sugihara monoids admitting the amalgamation property
Keywords substructural logics  MSC (2010) 03B47  amalgamation  semilinearity  03C40  Sugihara monoids  R‐mingle  Interpolation  06D30
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DOI 10.1002/malq.201200004
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References found in this work BETA

On an Implication Connective of RM.Arnon Avron - 1986 - Notre Dame Journal of Formal Logic 27 (2):201-209.
Interpolation in Fuzzy Logic.Matthias Baaz & Helmut Veith - 1999 - Archive for Mathematical Logic 38 (7):461-489.

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Uniform Interpolation and Compact Congruences.Samuel J. van Gool, George Metcalfe & Constantine Tsinakis - 2017 - Annals of Pure and Applied Logic 168 (10):1927-1948.

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