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A remark on a paper of van Alten. (English) Zbl 1244.03078
Chajda, I. (ed.) et al., Proceedings of the 79th workshop on general algebra “79. Arbeitstagung Allgemeine Algebra”, 25th conference of young algebraists, Palacký University Olomouc, Olomouc, Czech Republic, February 12–14, 2010. Klagenfurt: Verlag Johannes Heyn (ISBN 978-3-7084-0407-3/pbk). Contributions to General Algebra 19, 173-177 (2010).
Summary: In his paper [“The finite model property for knotted extensions of propositional linear logic”, J. Symb. Log. 70, No. 1, 84–98 (2005; Zbl 1089.03015)], C. J. van Alten shows that both the classical and intuitionistic propositional versions of Girard’s linear logic, when extended by a knotted structural rule $$\frac{\Gamma,x^n\Rightarrow y}{\Gamma,x^m \Rightarrow y}$$, have the finite model property. The purpose of this remark is to show that quantized versions of these logics extended by a knotted structural rule have also the finite model property.
For the entire collection see [Zbl 1201.08001].
##### MSC:
 03B47 Substructural logics (including relevance, entailment, linear logic, Lambek calculus, BCK and BCI logics) 06F05 Ordered semigroups and monoids 08A50 Word problems (aspects of algebraic structures)