The finite model property for knotted extensions of propositional linear logic

Abstract

Abstract The logics considered here are the propositional Linear Logic and propositional Intuitionistic Linear Logic extended by a knotted structural rule : . It is proved that the class of algebraic models for such a logic has the finite embeddability property , meaning that every finite partial subalgebra of an algebra in the class can be embedded into a finite full algebra in the class. It follows that each such logic has the finite model property with respect to its algebraic semantics and hence that the logic is decidable.