Robert Goldblatt
Published 2016-10-28Version 1
Ono's modal FL-algebras are models of an extension of Full Lambek logic that has the modalities ! and ? of linear logic. Here we define a notion of modal FL-cover system that combines aspects of Beth-Kripke-Joyal semantics with Girard's interpretation of the ! modality, and has structured subsets that interpret propositions. We show that any modal FL-algebra can be represented as an algebra of propositions of some modal FL-cover system.
On Fragments without Implications of both the Full Lambek Logic and some of its Substructural Extensions
An algebraic investigation of Linear Logic
Linear logic for constructive mathematics
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