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Completeness via Canonicity for Distributive Substructural Logics: A Coalgebraic Perspective

Dahlqvist, F; Pym, D; (2015) Completeness via Canonicity for Distributive Substructural Logics: A Coalgebraic Perspective. In: Kahl, W and Winter, M and Oliveira, JN, (eds.) International Conference on Relational and Algebraic Methods in Computer Science, 15th International Conference, RAMiCS 2015, Braga, Portugal, September 28 - October 1, 2015,. (pp. pp. 119-135). Springer: Cham, Switzerland. Green open access

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Abstract

We prove strong completeness of a range of substructural logics with respect to their relational semantics by completeness-via-canonicity. Specifically, we use the topological theory of canonical (in) equations in distributive lattice expansions to show that distributive substructural logics are strongly complete with respect to their relational semantics. 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.

Type: Proceedings paper
Title: Completeness via Canonicity for Distributive Substructural Logics: A Coalgebraic Perspective
Event: 15th International Conference on Relational and Algebraic Methods in Computer Science (RAMiCS)
Location: Braga, PORTUGAL
Dates: 28 September 2015 - 01 October 2015
ISBN-13: 978-3-319-24703-8
Open access status: An open access version is available from UCL Discovery
DOI: 10.1007/978-3-319-24704-5_8
Publisher version: http://doi.org/10.1007/978-3-319-24704-5_8
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: Harman
UCL classification: UCL
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/1495347
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