Abstract
The aim of this paper is to study the variety \({\mathbb{IMT}n}\) and some of its subvarieties. After proving some general properties of IMTn-chains, we characterize IMT4-chains and we provide a complete description of some subvarieties of \({\mathbb{IMT}4}\). We establish a relationship between totally symmetric partitions of the m-cube and IMT4-chains, and as a consequence of this relationship, we give a procedure to construct all finite IMT4-chains.
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Esteva F., Gispert J., Godo L., Montagna F.: On the standard and rational completeness of some axiomatic extensions of monoidal t-norm based logic. Studia Logica 71, 199–226 (2002)
Esteva, F., Godo, L.: Monoidal t-norm based logic: towards a logic for left-continuous t-norms. Fuzzy logic (Palma, 1999/Liptovský Ján, 2000). Fuzzy Sets and Systems 124, 271–288 (2001)
Esteva F., Godo L., Montagna F.: Equational characterization of the subvarieties of BL generated by t-norm algebras. Studia Logica 76, 161–200 (2004)
Galatos, N., Jipsen, P., Kowalski, T., Ono, H.: Residuated Lattices. An Algebraic Glimpse at Substructural Logics, Studies in Logic and the Foundations of Mathematics, vol. 151. Elsevier, Amsterdam (2007)
Gispert J., Torrens A.: Axiomatic Extensions of IMT3 Logic. Studia Logica 81, 311–324 (2005)
Horčík, R., Noguera, C., Petrík, M.: On n-contractive fuzzy logics. MLQ Math. Log. Q. 53, 268–288 (2007)
Komori Y.: Super Łukasiewicz propositional logics. Nagoya Math. J. 84, 119–133 (1981)
Kowalski T.: Semisimplicity, EDPC and discriminator varieties of residuated lattices. Studia Logica 77, 255–265 (2004)
Kowalski, T., Ono, H.: Residuated lattices: an algebraic glimpse at logics without contraction. Japan Advanced Institut of Science and Technology (2001)
Noguera, C.: Algebraic study of axiomatic extensions of triangular norm based fuzzy logics. PhD thesis, Monografies de l’Institut d’Investigació en Intel·ligència Artificial vol. 27, Barcelona (2007)
Noguera C., Esteva F., Gispert J.: Perfect and bipartite IMTL-algebras and disconnected rotations of prelinear semihoops. Arch. Math. Logic 44, 869–886 (2005)
Noguera C., Esteva F., Gispert J.: On some varieties of MTL-algebras. Log. J. IGPL 13, 443–466 (2005)
Stembridge J.: The enumeration of totally symmetric plane partitions. Adv. Math. 111, 227–243 (1995)
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Presented by C. Tsinakis.
The support of CONICET is gratefully acknowledged by the first author.
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Cornejo, J.M., Rueda, L.A. On some subvarieties of IMTn-algebras and the partitions of the m-cube. Algebra Univers. 73, 23–42 (2015). https://doi.org/10.1007/s00012-014-0312-1
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DOI: https://doi.org/10.1007/s00012-014-0312-1