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Coalgebraic completeness-via-canonicity for distributive substructural logics

Dahlqvist, F; Pym, D; (2017) Coalgebraic completeness-via-canonicity for distributive substructural logics. Journal of Logical and Algebraic Methods in Programming , 93 pp. 1-22. 10.1016/j.jlamp.2017.07.002. Green open access

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Abstract

We prove strong completeness of a range of substructural logics with respect to a natural poset-based relational semantics using a coalgebraic version of completeness-via-canonicity. By formalizing the problem in the language of coalgebraic logics, we develop a modular theory which covers a wide variety of different logics under a single framework, and lends itself to further extensions. Moreover, we believe that the coalgebraic framework provides a systematic and principled way to study the relationship between resource models on the semantics side, and substructural logics on the syntactic side.

Type: Article
Title: Coalgebraic completeness-via-canonicity for distributive substructural logics
Open access status: An open access version is available from UCL Discovery
DOI: 10.1016/j.jlamp.2017.07.002
Publisher version: https://doi.org/10.1016/j.jlamp.2017.07.002
Language: English
Additional information: This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions.
Keywords: Completeness, Canonicity, Coalgebraic logic, Substructural logic, Resource modelling, Separation logic
UCL classification: UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Computer Science
URI: https://discovery.ucl.ac.uk/id/eprint/10045065
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