Following the feasibility assessments on marrying Rough Sets with Description Logic languages last year [1,2], which I blogged about before, I looked into ‘squeezing’ into OWL 2 DL the very basic aspects of rough sets. The resulting language is called, rOWL, which is described in a paper  accepted at SAICSIT’11—the South African CS and IT conference (which thus also gives me the opportunity to meet the SA research community in CS and IT).
DLs are not just about investigating decidable languages, but, perhaps more importantly, also about reasoning over the logical theories. The obvious addition to the basic crisp automated reasoning services is to add the roughness component, somehow. There are various ways to do that. Crisp subsumption (and definite and possible satisfiability) of rough concepts have been defined by Jiang and co-authors , and there was a presentation at DL 2011 about paraconsistent rough DL . I have added the notion of rough subsumption.
There are two principal cases to consider (the “” before the OWL class name denotes it is a rough class):
- If is asserted in the ontology, what can be said about the subsumption relations among their respective approximations?
- Given a subsumption between any of the lower and upper approximations of C and D, then can one deduce ?
Addressing this raises questions: because being rough or not depends entirely on the chosen properties for C together with the available data, should these two cases be solved only at the TBox level or necessarily include the ABox for it to make sense? And should that be under the assumption of standard instantiation and instance checking, or in the presence of a novel DL notion of rough instantiation and rough instance checking?
These questions are answered in the second part of the paper Rough Subsumption Reasoning with rOWL . In an attempt to make the proofs more readable and because the presence of instances is intuitively tied to the matter, the proofs are done by counterexample, which is relatively ‘easy’ to grasp. But maybe I should have obfuscated it with another proof technique to make the results look more profound.
Last, but not least: just in case you thought there is little motivation to bother with rough ontologies: the hypothesis testing and experimentation described in  still holds, and a small example is added to .
The succinct paper abstract is as follows:
There are various recent efforts to broaden applications of ontologies with vague knowledge, motivated in particular by applications of bio(medical)-ontologies, as well as to enhance rough set information systems with a knowledge representation layer by giving more attention to the intension of a rough set. This requires not only representation of vague knowledge but, moreover, reasoning over it to make it interesting for both ontology engineering and rough set information systems. We propose a minor extension to OWL 2 DL, called rOWL, and define the novel notions of rough subsumption reasoning and classification for rough concepts and their approximations.
I’ll continue looking into the topic, and more is in the pipeline w.r.t. the logic aspects of rough ontologies (in collaboration with Arina Britz).
 C. M. Keet. On the feasibility of description logic knowledge bases with rough concepts and vague instances. Proceedings of the 23rd International Workshop on Description Logics (DL’10), CEUR-WS, pages 314-324, 2010. 4-7 May 2010, Waterloo, Canada.
 C. M. Keet. Ontology engineering with rough concepts and instances. P. Cimiano and H. Pinto, editors, 17th International Conference on Knowledge Engineering and Knowledge Management (EKAW’10), volume 6317 of LNCS, pages 507-517. Springer, 2010. 11-15 October 2010, Lisbon, Portugal.
 C.M. Keet. Rough Subsumption Reasoning with rOWL. SAICSIT Annual Research Conference 2011 (SAICSIT’11), Cape Town, South Africa, October 3-5, 2011. ACM Conference Proceedings. (accepted).
 Y. Jiang, J. Wang, S. Tang, and B. Xiao. Reasoning with rough description logics: An approximate concepts approach. Information Sciences, 179:600-612, 2009.
 H. Viana, J. Alcantara, and A.T. Martins. Paraconsistent rough description logic. Proceedings of the 24th International Workshop on Description Logics (DL’11), 2011. Barcelona, Spain, July 13-16, 2011.