Towards a Complete Classification of Tractability in Allen's Algebra

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 that is not known in the literature can contain more than the three basic relations (≡), (b) and (b-), where b ∈ {d,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. Furthermore, we show that there are exactly two maximal tractable algebras which contain the relation ( ). Both of these algebras can express the notion of sequentially; thus we have a complete characterisation of tractable inference using that notion.

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