Fariborz Maseeh Department of Mathematics and Statistics, Portland State University
The Maseeh Mathematics and Statistics Colloquium Series*
Jean B. Nganou, Ph.D., Department of Mathematics, University of Oregon
On MV-algebras and BL-algebras
Friday, January 11th, 2013 at 3:15pm
Neuberger Hall room 454
(Refreshments served at 2:45 in NH 344)
Many-valued logic (MV-logic) was introduced in 1920 by J. Lukasiewicz as a generalization
of the two-value logic (Boolean logic). Just as Boolean algebras constitute the
algebraic counterpart of Boolean logic, MV-algebras were introduced by C. Chang
(1958) as the algebraic counterpart of the MV-logic in order to o↵er an algebraic
proof of the completeness theorem of the MV-logic. Much later and recently (1998),
BL-algebras (basic logic algebras) were introduced by P. H´ajek in order to study the
basic logic framework of fuzzy set theory. Then it was noted that MV-algebras were
simply BL-algebras whose negations are involutions. The talk will give an overview
of the algebraic studies of both MV-algebras and BL-algebras. Most notably, I
will highlight the connection between this field and that of lattice ordered groups.
The study of MV-algebras has been completely centered around their ideals and
their natural algebraic additions. Both items were still not formulated within the
BL-algebras framework until very recently. I will discuss our recently introduced
notions of ideal and algebraic addition in BL-algebras and related consequences.
The most notable applications of MV/BL-logic are found in theoretical Computer
Science and Electrical Engineering with complex circuits switching designs.
* Sponsored by the Maseeh Mathematics and Statistics Colloquium Series Fund and the Fariborz Maseeh Department of Mathematics & Statistics, PSU. This event is free and open to the public.