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# The Finite Model Property for Knotted Extensions of Propositional Linear Logic

C. J. Van Alten
The Journal of Symbolic Logic
Vol. 70, No. 1 (Mar., 2005), pp. 84-98
Stable URL: http://www.jstor.org/stable/27588349
Page Count: 15
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## 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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