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Título: | Craig interpolation for semilinear substructural logics |
Autor: | Marchioni, Enrico; Metcalfe, George | Palabras clave: | Substructural logics Semilinearity R-mingle Interpolation Amalgamation Sugihara monoids |
Fecha de publicación: | 2012 | Editor: | John Wiley & Sons | Citación: | Mathematical Logic Quarterly 58 (6): 468- 481 (2012) | Resumen: | The Craig interpolation property is investigated for substructural logics whose algebraic semantics are varieties of semilinear (subdirect products of linearly ordered) 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 (corresponding to varieties of Sugihara monoids) 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. © 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim. | URI: | http://hdl.handle.net/10261/134404 | DOI: | 10.1002/malq.201200004 | Identificadores: | doi: 10.1002/malq.201200004 issn: 0942-5616 |
Aparece en las colecciones: | (IIIA) Artículos |
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