Foundations of Information and Knowledge Systems

The standard model of relations as sets of k-tuples, though well-suited to mathematical discourse, has been criticized as being neither flexible nor natural for commonsense reasoning. The interpretation of predicates in first-order logic is classically limited to the standard model of relations, which makes first-order representation and reasoning conceptually simple, but sometimes far from natural and much less parsimonious when compared to, say, natural language predication. We address these issues by considering a model of relations as sets of variablelength tuples, and by introducing a first-order language where predication is interpreted using said model. Allowing relations to be of variable adicity, introduces new properties that do not make sense in the standard model. By investigating the interaction among these properties, we are lead to efficient, sound, and (sometimes) complete analytical inference mechanisms for the proposed language.