We prove strong completeness of a range of substructural logics with respect to their relational semantics by completeness-viacanonicity. 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.
CITATION STYLE
Dahlqvist, F., & Pym, D. (2015). Completeness via canonicity for distributive substructural logics: A coalgebraic perspective. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 9348, pp. 119–135). Springer Verlag. https://doi.org/10.1007/978-3-319-24704-5_8
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