A complete classification of tractability in Allen's algebra relative to subsets of basic relations

摘要

We characterise the set of subalgebras of Allen's algebra which have a tractable satisfiability problem, and in addition contain certain basic relations. The conclusion is that no tractable subalgebra dial is not known in the literature can contain more than the three basic relations (≡), (b) and (b⪰), where bϵd, o, s, f. This means that concerning algebras for specifying complete knowledge about temporal information, there is no hope of finding yet unknown classes with much expressivity. We also classify completely some cases where we cannot even express complete information (but close to complete), showing that there are exactly two maximal tractable algebras containing the relation (≺ ≻), exactly two containing the relation (≺ ≻ m m≤), and exactly three containing the relation (≺ m). The algebras containing (≺ ≻) can express the notion of sequentiality; thus we have a complete characterization of tractable inference using that notion.