Vagueness, Logic, and Ontology: Fuzzy Ontologies

In traditional ontology theory, concepts and roles are crisp sets. However, there is a great deal of fuzziness in the real world.

For example, one may be interested in finding “a very strong flavored red wine” or in reasoning with concepts such as “a cold place”, “an expensive item”, “a fast motorcycle”, etc.

A possible solution to handling uncertain data is to incorporate fuzzy logic into ontologies. Unfortunately, these fuzzy ontologies have shortcomings – reasoners for fuzzy ontologies are not yet so polished as those for crisp (aka traditional) ontologies.

Possible use of a fuzzy ontology

When performing a query on a document, it is a usual practice to extend the set of concepts already present in the query with other ones which can be derived from an ontology. Typically, given a concept, its parents and children can also be added to the query and then searched in the document.

Extending queries

A possible use of fuzzy ontology is to extend queries with, besides children and parents, instances of concepts which satisfy to a certain degree the query. Here’s an example. You are given a clothes ontology and a query looking for “a very long and black coat.” In the ontology there are two instances of coat: X which has property “long” with value 0.7 and Y which has property “long” with value 0.3. Thus, it is natural to extend the original query adding, not only parents and children of the concept “coat”, but also the instance X, because \long = 0.7 can be interpreted as “very long”. On the other hand, the instance Y is not added to the extended query since \long = 0.3 does not mean “very long”.

Mathematical representation of a fuzzy concept

The fuzzy concept “Young_Person” is defined as follow:



The linguistic term Young may be defined by a trapezoidal function as shown graphically in the next figure, its mathematical representation.



{click on the image above for larger view}


Representation of a fuzzy ontology in Protégé




Fuzzy Protégé for Fuzzy Ontology Models

A good deal of work has been conducted to build tools for the creation of fuzzy ontologies.

Fuzzy Protégé is a semi-automatic collaborative tool for the construction of fuzzy ontology models, built as a Protégé 3.3.1 tab plug-in. For more information on this plug-in, click the following link.

http://protege.stanford.edu/conference/2009/abstracts/S10P2Ghorbel.pdf





Fuzzy OWL 2

The prior post to this blog introduced Web Ontology Language 2 (OWL 2), a new version of a standard for representing knowledge on the Web that had been announced by W3C just that day.

Fuzzy OWL2 Ontology is an OWL ontology to represent fuzzy extensions of the OWL and OWL 2 languages. For more information on this subject, click the following link.

http://webdiis.unizar.es/~fbobillo/papers/ISMIS2009presentation.pdf


Vagueness, Logic, and Ontology

Some people are clearly bald (Picasso), some are clearly hairy (the count of Montecristo), and some are borderline cases. Achille C. Varzi, Department of Philosophy, Columbia University, New York, starts here and presents a very interesting discussion on Vagueness, Logic, and Ontology in an easy-to-read paper reached by clicking the following link.

http://www.columbia.edu/~av72/papers/Dialogue_2001.pdf


Studies in Fuzziness and Soft Computing

http://www.springer.com/engineering/book/978-3-540-71257-2?cm_mmc=Google-_-Book%20Search-_-Springer-_-0

"Bernstein at Harvard" -- Segue to Probability, Semantic Amiguity, etc.

My prior post was about Watson, a tool for accessing multiple and usually heterogeneous online ontologies, but never once mentioned the word "probability." However, the recognition of uncertainty in the real world is sometimes needed within description logics, the underpinning of ontologies like OWL. Because of its importance, I'll take up the topic of uncertain domain knowledge in my next post.

For the present, however, I've embed here the 4 1/2 minute video "Bernstein at Harvard," which includes many of the terms - e.g., probability, meaning, semantic ambiguity, meta, language, and knowledge - that I'll use in my upcoming rant. Hope you find this segue as relevant as I do.





Note: Semantic ambiguity arises when a word or concept has an inherently diffuse meaning based on widespread or informal usage. This is often the case, for example, with idiomatic expressions whose definitions are rarely or never well-defined, and are presented in the context of a larger argument that invites a conclusion.

For example, “You could do with a new automobile. How about a test drive?” The clause “You could do with” presents a statement with such wide possible interpretation as to be essentially meaningless. Lexical ambiguity is contrasted with semantic ambiguity. The former represents a choice between a finite number of known and meaningful context-dependent interpretations. The latter represents a choice between any number of possible interpretations, none of which may have a standard agreed-upon meaning. This form of ambiguity is closely related to vagueness.