zbMATH — the first resource for mathematics

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, Palack√Ĺ 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].
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)