Commutative integral bounded residuated lattices with an added involution

Annals of Pure and Applied Logic 161 (2):150-160 (2010)
  Copy   BIBTEX

Abstract

A symmetric residuated lattice is an algebra such that is a commutative integral bounded residuated lattice and the equations x=x and =xy are satisfied. The aim of the paper is to investigate the properties of the unary operation ε defined by the prescription εx=x→0. We give necessary and sufficient conditions for ε being an interior operator. Since these conditions are rather restrictive →0)=1 is satisfied) we consider when an iteration of ε is an interior operator. In particular we consider the chain of varieties of symmetric residuated lattices such that the n iteration of ε is a boolean interior operator. For instance, we show that these varieties are semisimple. When n=1, we obtain the variety of symmetric stonean residuated lattices. We also characterize the subvarieties admitting representations as subdirect products of chains. These results generalize and in many cases also simplify, results existing in the literature

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 93,296

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Analytics

Added to PP
2013-12-22

Downloads
12 (#1,115,280)

6 months
24 (#121,857)

Historical graph of downloads
How can I increase my downloads?

References found in this work

Essais sur les logiques non chrysippiennes.Grigore C. Moisil - 1972 - Bucarest,: Éditions de l'Académie de la République Socialiste de Roumanie.
Heyting Algebras with a Dual Lattice Endomorphism.Hanamantagouda P. Sankappanavar - 1987 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 33 (6):565-573.
Heyting Algebras with a Dual Lattice Endomorphism.Hanamantagouda P. Sankappanavar - 1987 - Mathematical Logic Quarterly 33 (6):565-573.

View all 7 references / Add more references