Equational characterization of Nelson algebra.

Equational Theory of Kleene Algebra

Equational Axioms of Test Algebra

We present a complete axiomatization of test algebra the two sorted algebraic variant of Propositional Dynamic Logic PDL The axiomatization consists of adding a nite number of equations to any axiomatization of Kleene algebra and algebraic translations of the Segerberg axioms for PDL Kleene algebras are not nitely axiomatizable so our result does not give us a nite axiomatization of test algebr...

Relational Algebra and Equational Proofs

We show that two concepts involving equational provability can be elegantly formalized in terms of a relational algebra, equipped with two special-purpose mappings. We derive some calculus in order to prove that these concepts are equivalent, and that they are sound and complete. We illustrate the use of the relational framework by a few examples. We show how decidability of provability of an e...

1995 Frank Nelson Cole Prize in Algebra

The Frank Nelson Cole Prize in Algebra is awarded every five years for a notable research memoir in algebra which has appeared in the previous five years. This prize and the Frank Nelson Cole Prize in Number Theory were established in honor of Professor Frank Nelson Cole, who served as secretary of the AMS from 1896 to 1920 and also served as editor-in-chief of the Bulletin for twenty-one years...

The algebra of metric betweenness II: Geometry and equational characterization of weakly median graphs

We elaborate on the convexity properties of (not necessarily finite) weakly median graphs and their prime constituents in order to establish a number of equations in terms of the weakly median operation. Then the weakly median graphs can be identified with the discrete members of an equational class of ternary algebras satisfying five independent axioms on two to four points. This demonstrates ...