Terminological cycles in a description logic with existential restrictions
Franz Baader · 2002
Cyclic definitions in description logics have until now been investigated only for description logics allowing for value restrictions. Even for the most basic language FL₀, which allows for conjunction and value restrictions only, deciding subsumption in the presence of terminological cycles is a PSPACE-complete problem. This report investigates subsumption in the presence of terminological cycles for the language EL, which allows for conjunction and existential restrictions. In contrast to the results for FL₀, subsumption in EL remains polynomial, independent of wether we use least fixpoint semantics, greatest fixpoint semantics, or descriptive semantics. These results are shown via a characterization of subsumption through the existence of certain simulation relations between nodes of the description graph associated with a given cyclic terminology.