On the expressive power of first order-logic extended with Allen's relations in the strict case

Authors:
Willem Conradie;Guido Sciavicco
Affiliations:
Department of Mathematics, University of Johannesburg, Johannesburg, South Africa;Department of Information, Engineering and Communications, University of Murcia, Murcia, Spain
Venue:
CAEPIA'11 Proceedings of the 14th international conference on Advances in artificial intelligence: spanish association for artificial intelligence
Year:
2011

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Abstract

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.