Title :
Quotient Structures of Non-Commutative Residuated Lattices
Author_Institution :
Sch. of Inf. Environ., Tokyo Denki Univ., Inzai, Japan
Abstract :
In this paper we consider some properties of noncommutative residuated lattices which are considered as an algebraic semantics of substructural logic. We show that there are always prime filters in a non-commutative residuated lattice X and that the intersection of the class Spec(X) of all prime filters of X is identical with {1}, that is, ∩ Spec(X) = {1}.
Keywords :
algebra; formal logic; algebraic semantics; class Spec(X); noncommutative residuated lattices; prime filters; quotient structures; substructural logic; Boolean algebra; Electronic mail; Fuzzy logic; Kernel; Lattices; Semantics; (prime) filters; non-commutative residuated lattices; representation theorem;
Conference_Titel :
Multiple-Valued Logic (ISMVL), 2015 IEEE International Symposium on
Conference_Location :
Waterloo, ON
DOI :
10.1109/ISMVL.2015.30
