The third advanced ontology engineering topic concerns how to cope with uncertainty and vagueness in ontology languages and their reasoners—and what we can gain from all the extra effort.
For instance, consider information retrieval: to which degree is a web site, a page, a text passage, an image, or a video segment relevant to the information need and an acceptable answer to what the user was searching for? In the context of ontology alignment, one would want to know (automatically) to which degree the focal concepts of two or more ontologies represent the same thing, or are sufficiently overlapping. In an electronic health record system, one may want to classify patients based on their symptoms, such as throwing up often, having a high blood pressure, and yellowish eye colour. How can software agents do the negotiation for your holiday travel plans that are specified imprecisely, alike “I am looking for a package holiday of preferably less than 1000 euro, but really no more that 1150 euro, for about 12 days in a warm country”?
The main problem to solve, then, is what and how to incorporate such vague or uncertain knowledge in OWL and its reasoners. To clarify these two terms upfront:
- Uncertainty: statements are true or false, but due to lack of knowledge we can only estimate to which probability / possibility / necessity degree they are true or false;
- Vagueness: statements involve concepts for which there is no exact definition (such as tall, small, close, far, cheap, expensive), which are then true to some degree, taken from a truth space.
The two principal approaches regarding uncertainty and the semantic web are probabilistic and possibilistic languages, ontologies, and reasoning services, where the former way of dealing with uncertainty receives a lot more attention than the latter. The two principal approaches regarding vagueness and the semantic web are fuzzy and rough extensions, where fuzzy receives more attention compared to the rough approach. The lecture will cover all four approaches to a greater (probabilistic, fuzzy) and lesser (possibilistic, rough) extent.
None of the extant languages and automated reasoners that can cope with vague or uncertain knowledge have made it into ‘mainstream’ Semantic Web tools yet. There was a W3C incubator group on uncertainty, but it remained at that. This has not stopped research in this area; on the contrary. There are two principle strands in these endeavours: one with respect to extending DL languages and its reasoners, such as Pronto that combines the pellet reasoner with a probabilistic extension and FuzzyDL that is a reasoner for fuzzy SHIF(D), and another strand to uses different techniques underneath OWL, such as Bayesian networks and constraint programming-based reasoning for probabilistic ontologies (e.g., PR-OWL), and Mixed Integer Logic Programming for fuzzy ontologies. Within the former approach, one can make a further distinction between extensions of tableaux algorithms and rewritings to a non-uncertain/non-vague standard OWL language so that one of the generic DL reasoners can be used. For each of these branches, there are differences as to which aspects of probabilistic/possibilistic/fuzzy/rough are actually included—just like we saw in the previous lecture about temporal logics.
We shall not cover all such permutations in the lecture, but instead focus on general aspects of the languages and tools. A good introductory overview can be found in  (which also has a very long list of references to start delving into the topics [you may skip the DLP section]). Depending on your background education and the degree programme you are studying now, you may find the more technical overview  of interest as well. To get an idea of one of the more recent results on rough DL-based ontologies, you might want to glance over . Last, I assume you have a basic knowledge of probability theory and fuzzy sets; if there are many people who do not, I will adjust the lecture somewhat, but you are warmly advised to look it up before the lecture if you do not know about it (even if it is only the respective Wikipedia entry here and here).
 Umberto Straccia. Managing Uncertainty and Vagueness in Description Logics, Logic Programs and Description Logic Programs. In Reasoning Web, 4th International Summer School, 2008.
 Thomas Lukasiewicz and Umberto Straccia. 2008. Managing Uncertainty and Vagueness in Description Logics for the Semantic Web. Journal of Web Semantics, 6:291-308.
 Jiang, Y., Wang, J., Tang, S., and Xiao, B. 2009. Reasoning with rough description logics: An approximate concepts approach. Information Sciences, 179:600-612.
Note: references 1 or 2 is mandatory reading, 3 optional.
Lecture notes: lecture 7 – Uncertainty and vagueness