The Complexity of Probabilistic EL

We analyze the complexity of subsumption in probabilistic variants of the description logic EL. In the case where probabilities apply only to concepts, we map out the borderline between tractability and EXPTIME-completeness. One outcome is that any probability value except zero and one leads to intractability in the presence of general TBoxes, while this is not the case for classical TBoxes. In the case where probabilities can also be applied to roles, we show PSPACEcompleteness. This result is (positively) surprising as the best previously known upper bound was 2-EXPTIME and there were reasons to believe in completeness for this class.

• Type: Journal
• Year: 2011
• Where: DLOG
• Authors: Jean Christoph Jung, Víctor Gutiérrez-Basulto, Carsten Lutz, Lutz Schröder
• Keywords: Automated Reasoning, DLOG 2011, Probability Value, Subsumption, Upper Bound