an:01902541
Zbl 1028.06007
Di Nola, Antonio; Georgescu, George; Iorgulescu, Afrodita
Pseudo-BL algebras. I
EN
Mult.-Valued Log. 8, No. 5-6, 673-714 (2002).
00091273
2002
j
06D35
basic logic; continuous t-norms; pseudo-MV algebras; pseudo-BL algebras
\textit{P. H??jek}'s basic logic [see his book: Metamathematics of fuzzy logic, Dordrecht: Kluwer (1998; Zbl 0937.03030)] is the logic of all continuous t-norms and their residua. The Lindenbaum algebras of basic logic are known as BL algebras. Pseudo-BL algebras are a noncommutative generalization of BL algebras. They include pseudo-MV algebras, the latter being categorically equivalent to lattice-ordered groups with a distinguished strong unit: this is Dvure??enskij's generalization of the present reviewer's categorical equivalence between MV algebras and abelian lattice-ordered groups with strong unit. The aim of this paper is to survey the theory of pseudo-BL algebras, give examples, and establish a number of basic (mainly equational or quasi-equational) properties. The authors also deal with homomorphisms and filters. A sequel to this paper, covering more advanced topics, is reviewed below [ibid. 8, 717-750 (2002; Zbl 1028.06008)].
D.Mundici (Milano)
Zbl 0937.03030; Zbl 1028.06008