Conservative Extensions In The Description Logic εL With Cyclic Terminologies

In computer science, ontologies are dynamic entities:to adapt them to new and evolving appli-cations, it is necessary to constantly perform modifications such as the extension with new axioms and merging with other ontologies. Based on the different requires and application domains, users choose the appropriate ontology to import another ontology and implement the extension of the existing ontology in many application domains of developing ontologies. We argue that it is very significant to know that the resulting ontology remains a conservative extension of the original one after performing such modifications. If this is not the case, there may be unexpected consequences when using the modified ontology in the place of the the existing one in applications.Silvio Ghilardi etc first introduced conservative extensions of the description logic ALC reasoning algorithm, and had proved that ALC conservative extension established2ExpTime-completeness. Subsequently, Carsten Lutz etc studied the conservative extensions problem of de-scription logic εL and proved that εL conservative extensions remained ExpTime-completeness. On the base of Carsten Lutz resulting, we will study conservative extensions problem of the de-scription logics with cyclic terminologies and give the corresponding reasoning algorithm in this paper.The main work and research results are summarized as follows:(1) This paper studies simulation, bisimulation between interpretation and interpretation, and the properties of simulation and bisimulation in the description logic εL.(2) Terminological cycles have been a extremely difficult problem in description logics for a long time, and their essential problems, i.e. semantics and reasoning problems, have not gotten a reasonable solution. At present, the study of cyclic TBox semantics mainly has the greatest fixpoint semantics、 the least fixpoint semantics and descriptive semantics. On the extensions of the canonical model, in this paper, the greatest fixpoint model is the model of εL terminological cycles. We study conservative extensions of EL terminological cycles with respect to the greatest fixpoint semantics, and the reasoning algorithm is exponential time complexity.(3) In this paper, the sufficient condition of conservative extensions w.r.t. greatest fixpoint se-mantics in the description logic εL with cyclic TBox has the same primitive concepts, and can be decided in polynomial time. But this reasoning algorithm is not complete.