BL-algebras are the algebraic semantics of Basic logic BL, the logic of all continuous t-norms and their residua. In a previous work, we provided the classification of the amalgamation property (AP) for the varieties of BL-algebras generated by one BL-chain with finitely many components. As an open problem, we left the analysis of the AP for varieties of BL-algebras generated by one finite set of BL-chains with finitely many components. In this paper we provide a partial solution to this problem. We provide a classification of the AP for the varieties of BL-algebras generated by one finite set of BL-chains with finitely many components, which are either cancellative hoops or finite Wajsberg hoops. We also discuss the difficulties to generalize this approach to the more general case.
Amalgamation Property for Some Varieties of BL-Algebras Generated by One Finite Set of BL-Chains with Finitely Many Components / S. Aguzzoli, M. Bianchi (LECTURE NOTES IN COMPUTER SCIENCE). - In: Relational and Algebraic Methods in Computer Science / [a cura di] R. Glück, L. Santocanale, M. Winter. - [s.l] : Springer, 2023. - ISBN 978-3-031-28082-5. - pp. 1-16 (( Intervento presentato al 20. convegno RAMiCS tenutosi a Augbsburg nel 2023 [10.1007/978-3-031-28083-2_1].
Amalgamation Property for Some Varieties of BL-Algebras Generated by One Finite Set of BL-Chains with Finitely Many Components
S. Aguzzoli;M. Bianchi
2023
Abstract
BL-algebras are the algebraic semantics of Basic logic BL, the logic of all continuous t-norms and their residua. In a previous work, we provided the classification of the amalgamation property (AP) for the varieties of BL-algebras generated by one BL-chain with finitely many components. As an open problem, we left the analysis of the AP for varieties of BL-algebras generated by one finite set of BL-chains with finitely many components. In this paper we provide a partial solution to this problem. We provide a classification of the AP for the varieties of BL-algebras generated by one finite set of BL-chains with finitely many components, which are either cancellative hoops or finite Wajsberg hoops. We also discuss the difficulties to generalize this approach to the more general case.File | Dimensione | Formato | |
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