Abstract
We study a class of finite models for the Lambek Calculus with additive conjunction and with and without empty antecedents. The class of models enables us to prove the finite model property for each of the above systems, and for some axiomatic extensions of them. This work strengthens the results of [3] where only product-free fragments of these systems are considered. A characteristic feature of this approach is that we do not rely on cut elimination in opposition to e.g. [5], [9].
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References
BUSZKOWSKI, W., ‘Some decision problems in the theory of syntactic categories’, Zeitschrift für mathematische Logic and Grundlagen der Mathematik 28 (1982), 539–548.
BUSZKOWSKI, W., ‘The finite model property for BCI and related systems’, Studia Logica 57(1996), 303–323.
BUSZKOWSKI, W., ‘Finite Models of Some Substructural Logics’, Mathematical Logic Quarterly 48,1 (2002), 63–72.
DOŠEN,K., ‘A Completeness theorem for the Lambek calculus of syntactic categories’, Zeitschriftfür mathematische Logic and Grundlagen der Mathematik 31 (1985), 235–241.
LAFONT,Y., ‘The finite model property for various fragments of linear logic’, Journal of Symbolic Logic 62 (1997), 1202–1208.
LAMBEK,J., ‘The mathematics of sentence structure’, American Mathematical Monthly 65(1958), 154–170.
LAMBEK,J., ‘On the calculus of syntactic types’, in R. Jacobson, (ed.), Structure of Languageand Its Mathematical Aspects, American Mathematical Society, 1961, pp. 166–178.
MEYER,R.K., and H. ONO, ‘The finite model property for BCK and BCIW’, Studia Logica 53(1994), 107–118.
OKADA,M., and K. TERUI, ‘The finite model property for various fragments of intuitionistic linear logic’, Journal of Symbolic Logic 64, 2 (1999), 780–802.
ONO, H., ‘Substructural logics and residuated lattices — an introduction’, in V.F. Hendricks and J. Malinowski, (eds.), Trends in Logic: 50 Years of Studia Logica, Kluwer, 2002, pp. 177–212.
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Farulewski, M. On Finite Models of the Lambek Calculus. Stud Logica 80, 63–74 (2005). https://doi.org/10.1007/s11225-005-6776-4
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DOI: https://doi.org/10.1007/s11225-005-6776-4