Logics for Finite UL and IUL-Algebras Are Substructural Fuzzy Logics

Substructural fuzzy logics

Kleene Algebras, Regular Languages and Substructural Logics

We introduce the two substructural propositional logics KL, KL, which use disjunction, fusion and a unary, (quasi-)exponential connective. For both we prove strong completeness with respect to the interpretation in Kleene algebras and a variant thereof. We also prove strong completeness for language models, where each logic comes with a different interpretation. We show that for both logics the...

Relevant and substructural logics

This is a history of relevant and substructural logics, written for the Handbook of the History and Philosophy of Logic, edited by Dov Gabbay and John Woods.

Modalities in Substructural Logics

This paper generalises Girard's results which embed intuitionistic logic into linear logic by showing how arbitrary substructural logics can be embedded into weaker substructural logics, using a single modality whichèncodes' the new structural rules. Logics 1 1. Logics Logic is about valid deduction. One central result in logic is the deduction theorem. A; ` B if and only if`A ! B This result t...

Herbrand Theorems for Substructural Logics

Herbrand and Skolemization theorems are obtained for a broad family of first-order substructural logics. These logics typically lack equivalent prenex forms, a deduction theorem, and reductions of semantic consequence to satisfiability. The Herbrand and Skolemization theorems therefore take various forms, applying either to the left or right of the consequence relation, and to restricted classe...