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Mixed pseudo-associativities of Bandler-Kohout compositions of relations

Jolanta Sobera (2007)

Kybernetika

This paper considers compositions of relations based on the notion of the afterset and the foreset, i. e., the subproduct, the superproduct and the square product introduced by Bandler and Kohout with modification proposed by De Baets and Kerre. There are proven all possible mixed pseudo-associativity properties of Bandler – Kohout compositions of relations.

Multiple left distributive systems

Patrick Dehornoy (1997)

Commentationes Mathematicae Universitatis Carolinae

We describe the free objects in the variety of algebras involving several mutually distributive binary operations. Also, we show how an associative operation can be constructed on such systems in good cases, thus obtaining a two way correspondence between LD-monoids (sets with a left self-distributive and a compatible associative operation) and multi-LD-systems (sets with a family of mutually distributive operations).

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