On The Expressive Power of First Order Logic Extended with Allen’s Relations in the Strict Case

We consider the languages of first order-logic (with equality) extended with Allen's relations for temporal intervals. We give a complete classification of such languages in terms of relative expressive power, thus determining how many, and which, are the intrinsically different extensions of first-order logic with one or more of Allen's relations. Classifications are obtained for three different classes of interval structures, namely those based on arbitrary, discrete, and dense linear orders. The strict semantics (where point-intervals are excluded) is assumed throughout.