The University of Southampton
University of Southampton Institutional Repository

Craig interpolation for semilinear substructural logics

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
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), 468-481. (doi:10.1002/malq.201200004).

Record type: Article

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.

Full text not available from this repository.

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: 13 Mar 2019 19:04

Export record

Altmetrics

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

Atom RSS 1.0 RSS 2.0

Contact ePrints Soton: eprints@soton.ac.uk

ePrints Soton supports OAI 2.0 with a base URL of http://eprints.soton.ac.uk/cgi/oai2

This repository has been built using EPrints software, developed at the University of Southampton, but available to everyone to use.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.

×