Axiomatizability of positive algebras of binary relations

Residuated Algebras of Binary Relations and Positive Fragments of Relevance Logic

The aim of this paper is to apply some results obtained jointly with Hajnal Andréka and István Németi about finite axiomatizability of Tarski’s representable relation algebras in the context of completeness of fragments of relevance logic.

Complexity of Equations Valid in Algebras of Relations: Part I: Strong Non-Finitizability

We study algebras whose elements are relations, and the operations are natural \manipulations" of relations. This area goes back to 140 years ago to works of De Morgan, Peirce, Schrr oder (who expanded the Boolean tradition with extra operators to handle algebras of binary relations). Well known examples of algebras of relations are the varieties RCA n of cylindric algebras of n-ary relations, ...

Complexity of Equations Valid in Algebras of Relations: Part II: Finite Axiomatizations

We study algebras whose elements are relations, and the operations are natural \manipulations" of relations. This area goes back to 140 years ago to works of De Morgan, Peirce, Schrr oder (who expanded the Boolean tradition with extra operators to handle algebras of binary relations). Well known examples of algebras of relations are the varieties RCA n of cylindric algebras of n-ary relations, ...

Axiomatizability of algebras of binary relations

Let Λ be a signature and A = (A, Λ) be an algebra. We say that A is an algebra of binary relations if A ⊆ P(U × U) for some set U and each operation in Λ is interpreted as a natural operation on relations. 0 is the empty set. Other possible operations include reexive-transitive closure * , the residuals \ and / of composition, domain d and range r, etc. Algebras of binary relations Let Λ be a s...

Axiomatizability of Reducts of Algebras of Relations