Trois couleurs: A new non-equational theory

Non-computability of the Equational Theory of Polyadic Algebras

In [3] Daigneault and Monk proved that the class of (ω dimensional) representable polyadic algebras (RPAω for short) is axiomatizable by finitely many equationschemas. However, this result does not imply that the equational theory of RPAω would be recursively enumerable; one simple reason is that the language of RPAω contains a continuum of operation symbols. Here we prove the following. Roughl...

A Generalization of Equational Proof Theory?

Recently rule based languages focussed on the use of rewriting as a modeling tool which results in making specifications executable. To extend the modeling capabilities of rule based languages, we explored in a previous work the possibility of making the rule applications subject to probabilistic choices, and started to study the generalization of the results in the rewriting community about ab...

The Equational Theory of Pomsets

Pomsets have been introduced as a mode2 of concurrency. Since a pomset is a string in which the total order has been relaxed to be a partial order, in this paper we view them as a generalization cf Strings, and investigate their algebraic properties. In particular, we investigate the axiomatic properties of pornsets, sets of pomsets and ideals of pornsets, under such operations as concatenation...

An Equational Theory for Transactions

Transactions are commonly described as being Atomic, Consistent, Isolated and Durable: the ACID properties. However, although these words convey a powerful intuition, the properties of atomicity, consistency, isolation and durability have never been given a precise semantics, in a way that disentangles each property from the others but allows their composition. Among the benefits of such a sema...

Equational Theory of Kleene Algebra