The Finite Model Property for Knotted Extensions of Propositional Linear Logic

Journal of Symbolic Logic 70 (1):84 - 98 (2005)
Abstract
The logics considered here are the propositional Linear Logic and propositional Intuitionistic Linear Logic extended by a knotted structural rule: $\frac{\Gamma,\,x^{n}\,\Rightarrow \,y}{\Gamma,\,x^{m}\,\Rightarrow \,y}$ . 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.
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