Connections between Relation Algebras and Cylindric Algebras

Abstract. We give an informal description of a recursive representability-preserving reduction of relation algebras to cylindric algebras.

Theories with the independence property

A first-order theory T has the Independence Property provided T ⊢ (Q)(Φ⇒

Residuated Kleene algebras

We show that there is no finitely axiomatizable class of algebras that would serve as an analogue to Kozen’s class of Kleene algebras if we include the residuals of composition in the similarity type of relation algebras

The impact of transitive closure on the boolean expressiveness of navigational query languages on graphs

Several established and novel applications motivate us to study the expressive power of navigational query languages on graphs, which represent binary relations. Our basic language has only the operators union and composition, together with the identity relation. Richer languages can be obtained by adding other features such as other set operators, projection and coprojection, converse, and the diversity relation. In this paper, we show that, when evaluated at the level of boolean queries with an unlabeled input graph (i.e. a single relation), adding transitive closure to the languages with coprojection adds expressive power, while this is not the case for the basic language to which none, one, or both of projection and the diversity relation are added. In combination with earlier work [10], these results yield a complete understanding of the impact of transitive closure on the languages under consideration. © 2012 Springer-Verlag .SCOPUS: cp.kinfo:eu-repo/semantics/publishe

Normal Forms and Reduction for Theories of Binary Relations

We consider equational theories of binary relations, in a language expressing composition, converse, and lattice operations. We treat the equations valid in the standard model of sets and also defne a hierachy of equational axiomatizations stratifying the standard theory. By working directly with a presentation of relation-expressions as graphs we are able to de ne a notion of reduction which is conuent and strongly normalizing, in sharp contrast to traditional treatments based on rst-order terms. As consequences we obtain unique normal forms, decidability of the decision problem for equality for each theory, indeed an non-deterministic polynomial-time upper bound for the complexity of the decision problems

Two proof systems for Peirce algebras

Abstract. This paper develops and compares two tableaux-style proof systems for Peirce algebras. One is a tableau refutation proof system, the other is a proof system in the style of Rasiowa-Sikorski.