Algebraic Semantics: Semilinear FL-Algebras. Chapter 4

Autoři: Rostislav Horčík
Rok vydání: 2011
Typ publikace: Kapitola v monografii
Periodikum: Handbook of Mathematical Fuzzy Logic
Projekty: Logické modely usuzovaní s vagními informacemi
Matematická fuzzy logika v informatice
Bibliografická citace: HORČÍK, Rostislav. Algebraic Semantics: Semilinear FL-Algebras. Chapter 4. In: CINTULA, P., HÁJEK, P., NOGUERA, C., eds. Handbook of Mathematical Fuzzy Logic. 1. London: College Publications, 2011, S. 283-353. Studies in Logic - Mathematical Logic and Foundations, 37. ISBN 978-1-84890-039-4.
ID: 372983

Abstrakt

The chapter summarizes the most important results in the theory of semilinear FL-algebras which form an equivalent algebraic semantics for most of fuzzy logics studied in the literature. The first part focuses on basic algebraic properties and constructions, e.g. structure theory, axiomatization of the variety of semilinear FL-algebras, or Dedekind-McNeille completion. The second part deals with various completeness properties for varieties of semilinear FL-algebras. The last part presents several results on the structure of the subvariety lattice of the variety of semilinear FL-algebras.