3 research outputs found
A Characterization Result for Non-Distributive Logics
Recent published work has addressed the Shalqvist correspondence problem for
non-distributive logics. The natural question that arises is to identify the
fragment of first-order logic that corresponds to logics without distribution,
lifting van Benthem's characterization result for modal logic to this new
setting. Carrying out this project is the contribution of the present article.
The article is intended as a demonstration and application of a project of
reduction of non-distributive logics to (sorted) residuated modal logics. The
reduction is an application of recent representation results by this author for
normal lattice expansions and a generalization of a canonical and fully
abstract translation of the language of substructural logics into the language
of their companion sorted, residuated modal logics. The reduction of
non-distributive logics to sorted modal logics makes the proof of a van Benthem
characterization of non-distributive logics nearly effortless, by adapting and
reusing existing results, demonstrating the usefulness and suitability of this
approach in studying logics that may lack distribution