The Time Ontology of Allen\u27s Interval Algebra

Allen\u27s interval algebra is a set of thirteen jointly exhaustive and pairwise disjoint binary relations representing temporal relationships between pairs of timeintervals. Despite widespread use, there is still the question of which time ontology actually underlies Allen\u27s algebra. Early work specified a first-order ontology that can interpret Allen\u27s interval algebra; in this paper, we identify the first-order ontology that is logically synonymous with Allen\u27s interval algebra, so that there is a one-to-one correspondence between models of the ontology and solutions to temporal constraints that are specified using the temporal relations. We further prove a representation theorem for the ontology, thus characterizing its models up to isomorphism