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

Coalgebraic completeness-via-canonicity for distributive substructural logics