Abstract
We prove the Finite Model Property (FMP) for Distributive Full Lambek Calculus (DFL) whose algebraic semantics is the class of distributive residuated lattices (DRL). The problem was left open in [8, 5]. We use the method of nuclei and quasi–embedding in the style of [10, 1].
Similar content being viewed by others
References
Belardinelli F., Jipsen P., Ono H.: Algebraic Aspects of Cut Elimination. Studia Logica 77(2), 209–240 (2004)
Brady R.: Gentzenization and Decidability of some Contraction–less Relevant Logics. Journal of Philosophical Logic 20(1), 97–117 (1991)
Buszkowski W., and Farulewski M., ‘Nonassociative Lambek Calculus with Additives and Context–Free Languages’, Lecture Notes in Computer Science. To appear.
Dunn M., A Gentzen System for Positive Relevant Implication, Journal of Symbolic Logic, 38 (1973), 356–357. Abstract.
Galatos N., Jipsen P., Kowalski T., and Ono H., Residuated Lattices: An Algebraic Glimpse at Substructural Logics, vol. 151 of Studies in Logic and the Foundations of Mathematics, Elsevier, 2007.
Galatos N., Raftery J.: Adding Involution to Residuated Structures. Studia Logica 77(2), 181–207 (2004)
Giambrone S., TW+ and RW+ are Decidable, Journal of Philosophical Logic, 14 (1985), 3, 235–254.
Jipsen P., and Tsinakis C., ‘A Survey of Residuated Lattices’, in J. Martinez, (ed.), Ordered Algebraic Structures, Kluwer Academic Publishers, 2002, 19–56.
Mints G., ‘Cut Elimination Theorem for Relevant Logics’, Journal of Mathematical Sciences, 6 (1976), 4, 422–428. Translated from Issledovanija po konstructivnoj mathematike i matematiceskoj logike V, Izdatelstvo Nauka, 1972.
Okada M., and Terui K., The Finite Model Property for Various Fragments of Intuitionistic Linear Logic, Journal of Symbolic Logic, 64 (1999), 2, 790–802.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Kozak, M. Distributive Full Lambek Calculus Has the Finite Model Property. Stud Logica 91, 201–216 (2009). https://doi.org/10.1007/s11225-009-9172-7
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11225-009-9172-7