$\textsf{M}\textsf{T}\textsf{L}$-algebras as rotations of basic hoops. (5th March 2019)

• Record Type: Journal Article
• Authors: Aglianò, Paolo; Ugolini, Sara
• Is Part Of: Journal of logic and computation. Volume 29:Number 5(2019)
• Page Start: 763
• Page End: 784
• Publication Date: 2019-03-05
• Subjects: MTL-algebras -- BL-algebras -- basic hoops -- disconnected rotations -- splitting algebras; Logic programming -- Periodicals; Logic, Symbolic and mathematical -- Periodicals; Computational complexity -- Periodicals; 005.115
• DOI: 10.1093/logcom/exz005
• Languages: English
• ISSNs: 0955-792X

Abstract

Abstract: In this paper, we use the generalize d rotation construction to lift results from the lattice of subvarieties of basic hoops to some parts of the lattice of subvarieties of monoidal t-norm based logic-algebras. In particular, we study splitting algebras for (the lattice of subvarieties of) varieties generated by generalized rotations of basic hoops and relevant subvarieties such as Wajsberg hoops, cancellative hoops and Gödel hoops. Finally, we show that the generalized rotation construction preserves the amalgamation property.