Craig interpolation for semilinear substructural logics
Craig interpolation for semilinear substructural logics
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.
Amalgamation, Interpolation, R-mingle, Semilinearity, Substructural logics, Sugihara monoids
468-481
Marchioni, Enrico
729c9984-5949-438e-8de7-0e079bdb9f96
Metcalfe, George
e657aa5e-b104-445f-ba16-adcf6e6a8e99
November 2012
Marchioni, Enrico
729c9984-5949-438e-8de7-0e079bdb9f96
Metcalfe, George
e657aa5e-b104-445f-ba16-adcf6e6a8e99
Marchioni, Enrico and Metcalfe, George
(2012)
Craig interpolation for semilinear substructural logics.
Mathematical Logic Quarterly, 58 (6), .
(doi:10.1002/malq.201200004).
Abstract
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.
This record has no associated files available for download.
More information
e-pub ahead of print date: 19 October 2012
Published date: November 2012
Keywords:
Amalgamation, Interpolation, R-mingle, Semilinearity, Substructural logics, Sugihara monoids
Identifiers
Local EPrints ID: 416589
URI: http://eprints.soton.ac.uk/id/eprint/416589
PURE UUID: db5c426a-7d2c-4f02-af3a-ca43ce13a157
Catalogue record
Date deposited: 03 Jan 2018 17:30
Last modified: 15 Mar 2024 17:37
Export record
Altmetrics
Contributors
Author:
Enrico Marchioni
Author:
George Metcalfe
Download statistics
Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.
View more statistics