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The decision problem of membership in the Representation Class of RelationAlgebras (RRA) for finite structures is undecidable. However, this does nothold for many Relation Algebra reduct languages. Two well known properties thatare sufficient for decidability are the Finite Axiomatisability (FA) of therepresentation class and the Finite Representation Property (FRP). Furthermore,neither of the properties is stronger that the other, and thus, neither is alsoa necessary condition. Although many results are known in the area of FA, theFRP remains unknown for the majority of the reduct languages. Here weconjecture that the FRP fails for a Relation Algebra reduct if and only if itcontains both composition and negation, or both composition and meet. We thenshow the right-to-left implication of the conjecture holds and presentpreliminary results that suggest the left-to-right implication.

Finite Representation Property for Relation Algebra Reducts