# Reblogging 2010: Rough ontologies from an ontology engineering perspective

From the “10 years of keetblog – reblogging: 2010”: two solid papers on the feasibility of rough ontologies, presented at DL’10 (logic stuff) and EKAW’10 (ontology engineering aspects). Short answer: not really feasible from a computational viewpoint. Notwithstanding, I did give it a try afterwards with ‘rOWL’ (SAICSIT’11 paper) before giving up on it, and other people do try, too (see citations of the DL and EKAW papers).

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Somewhere buried in the blogpost about the DL’10 workshop, I mentioned the topic of my paper [1] at the 23rd International Description Logics Workshop (DL’10), which concerned the feasibility of rough DL knowledge bases. That paper was focussed on the theoretical assessment (result: there are serious theoretical hurdles for rough DL KBs) and had a rather short section where experimental results were crammed into the odd page (result: one can squeeze at least something out of the extant languages and tools, but more should be possible in the near future). More recently, my paper [2] submitted to the 17th International Conference on Knowledge Engineering and Knowledge Management (EKAW’10) got accepted, which focuses on the ontology engineering side of rough ontologies and therefore has a lot more information on how one can squeeze something out of the extant languages and tools; if that is not enough, there is also supplementary material that people can play with.

Ideally, they ought to go together in on paper to get a good overview at once, but there are page limits for conference papers and anyhow the last word has not been said about rough ontologies. For what it is worth, I have put the two together in the slides for the weekly KRDB Lunch Seminar that I will present tomorrow at, well, lunch hour in the seminar room on the first floor of the POS building.

References

[1] Keet, C. M. On the feasibility of Description Logic knowledge bases with rough concepts and vague instances. Proc. of DL’10, 4-7 May 2010, Waterloo, Canada. pp314-324.

[2] Keet, C. M. Ontology engineering with rough concepts and instances17th International Conference on Knowledge Engineering and Knowledge Management (EKAW’10). 11-15 October 2010, Lisbon, Portugal.  Springer LNCS.

# The rough ontology language rOWL and basic rough subsumption reasoning

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 [3] 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 [4], and there was a presentation at DL 2011 about paraconsistent rough DL [5]. I have added the notion of rough subsumption.

There are two principal cases to consider (the “$\wr$” before the OWL class name denotes it is a rough class):

• If $\wr C \sqsubseteq \wr D$ 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 $\wr C \sqsubseteq \wr D$?

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 [3]. 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 [2] still holds, and a small example is added to [3].

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).

References

[1] 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.

[2] 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.

[3] 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).

[4] Y. Jiang, J. Wang, S. Tang, and B. Xiao. Reasoning with rough description logics: An approximate concepts approach. Information Sciences, 179:600-612, 2009.

[5] 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.

# New book on Novel Developments in Granular Computing

Late 2008 I mentioned the forthcoming invited book chapter [1] I wrote for “Novel Developments in Granular Computing: Applications for Advanced Human Reasoning and Soft Computation”, edited by JingTao Yao. Finally, it has been published.

The topics of the book focus on modelling with/representation of granularity, rough sets and logic, data mining, classification, and fuzzy aspects; see the preface and abstracts of the 19 chapters. The free sample chapter is an interesting analysis by Yiyu Yao on Human-Inspired Granular Computing (see menu bar on the left of the page). My contribution is in the modelling section: basically, the book chapter is a self-contained version of chapter 2 of my PhD thesis, with some minor additions from chapters 4 and 5; in short:

Multiple different understandings and uses exist of what granularity is and how to implement it, where the former influences success of the latter with regards to storing granular data and using granularity for automated reasoning over the data or information, such as granular querying for information retrieval. We propose a taxonomy of types of granularity and discuss for each leaf type how the entities or instances relate within its granular level and between levels. Such distinctions give guidelines to a modeler to better distinguish between the types of granularity in the design phase and the software developer to improve on implementations of granularity. Moreover, these foundational semantics of granularity provide a basis from which to develop a comprehensive theory of granularity.

Anyone who has published with IGI before knows about the unusual editing policies and their preferred layout; hence, I will upload the latex-ed preprint soon… here is the preprint.

References

[1] Keet, C.M. A top-level categorization of types of granularity. In: Novel Developments in Granular Computing: Applications for Advanced Human Reasoning and Soft Computation. JingTao Yao (Ed.). IGI Global. 2010. pp81-117.

# Rough ontologies from an ontology engineering perspective

Somewhere buried in the blogpost about the DL’10 workshop, I mentioned the topic of my paper [1] at the 23rd International Description Logics Workshop (DL’10), which concerned the feasibility of rough DL knowledge bases. That paper was focussed on the theoretical assessment (result: there are serious theoretical hurdles for rough DL KBs) and had a rather short section where experimental results were crammed into the odd page (result: one can squeeze at least something out of the extant languages and tools, but more should be possible in the near future). More recently, my paper [2] submitted to the 17th International Conference on Knowledge Engineering and Knowledge Management (EKAW’10) got accepted, which focuses on the ontology engineering side of rough ontologies and therefore has a lot more information on how one can squeeze something out of the extant languages and tools; if that is not enough, there is also supplementary material that people can play with.

Ideally, they ought to go together in on paper to get a good overview at once, but there are page limits for conference papers and anyhow the last word has not been said about rough ontologies. For what it is worth, I have put the two together in the slides for the weekly KRDB Lunch Seminar that I will present tomorrow at, well, lunch hour in the seminar room on the first floor of the POS building.

References

[1] Keet, C. M. On the feasibility of Description Logic knowledge bases with rough concepts and vague instances. Proc. of DL’10, 4-7 May 2010, Waterloo, Canada. pp314-324.

[2] Keet, C. M. Ontology engineering with rough concepts and instances17th International Conference on Knowledge Engineering and Knowledge Management (EKAW’10). 11-15 October 2010, Lisbon, Portugal.  Springer LNCS.