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 addit ion contain certain basic relations. The conclusion is that no tractable subalgebra that is not known in the l i terature can contain more than the three basic relations This means that concerning algebras for specifying complete knowledge about temporal informa­ t ion, there is no hope of finding yet unknown classes w i th 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 com­ plete characterisation of tractable inference us­ ing that notion.