Similarity convergence in residuated structures. (English) Zbl 1082.03058

Georgescu, George; Popescu, Andrei

Log. J. IGPL 13, No. 4, 389-413 (2005).

Summary: We introduce and study a notion of logical convergence in residuated lattices (with operators). We consider a convergence in similarity degree, rather than a bare order convergence – the lack of symmetry of residuated lattices brings our approach closer to the logical structure than to the set of truth values.

MSC:

03G25	Other algebras related to logic
06F05	Ordered semigroups and monoids
06F30	Ordered topological structures

Keywords:

logical convergence; residuated lattices; similarity convergence; Cauchy completion; Łukasiewicz-Moisil algebra; relation algebra