Islands of tractability for relational constraints: towards dichotomy results for the description logic EL
Agi Kurucz, Frank Wolter, Michael Zakharyaschev · BIROn (Birkbeck, University of London) · 2010
EL is a tractable description logic serving as the logical underpinning of large-scale ontologies. We launch a systematic investigation of the boundary between tractable and intractable reasoning in EL under relational constraints. E.g., we show that there are (modulo equivalence) exactly 3 universal constraints on a transitive and reexive relation under which reasoning is tractable: being a singleton set, an equivalence relation, or the empty constraint. We prove a number of results of this type and discuss a spectrum of open problems including generalisations to the algebraic semantics for EL (semi-lattices with monotone operators).