Technical Group Charter
Uncertainty, like imprecision and vagueness, has gained considerable attention during the last decades. This is mainly due to the fact that information itself is sometimes inherently imprecise or vague, like the concepts of a “tall” person or a "partly cloudy" sky. In many applications, like information retrieval, multimedia information analysis, most facts are not true or false, they are rather a matter of similarities or ranking degrees.
Even though the combination of ontology and rule languages in the web results to the creation of a highly expressive knowledge representation framework, there are still many cases where the language fail to represent knowledge of our world. In particular these languages are not able to face the uncertainty introduced in real application knowledge and information (like multimedia processing [SST+05, KK92], information retrieval [LY93], pattern recognition [Kan82], decision making [Zim87] and many more).
The need for covering uncertainty in the Semantic Web context has been stressed out in literature many times the last years [STPH05, Mat05, Kif05]. It has been pointed out that dealing with such information would improve Semantic Web applications like, portals [ZYZ+05], multimedia application in the semantic web [BG96, SST+05], e-commerce applications [AL05], situation awareness and information fusion [Mat05], rule languages [Kif05, STPH05], medicine and diagnosis [GBDG05], geospatial applications [CFB05] and many more.
In Fuzzy RuleML, facts about the world can include a specification of a “degree” (a truth value between 0 and 1) of confidence with which one can assert that a combination of facts. For example, the following fuzzy rule asserts that being healthy is more important than being rich to determine if one is happy:
Rich(?p) 0.5 ^Healthy(?p) 0.9 -> Happy(?p),
where Rich, Healthy and Happy are unary predicates, and 0.5 and 0.9 are the weights for the atoms Rich(?p) and Healthy(?p), respectively. Predicates Rich, Healthy and Happy are represented by fuzzy predicates, since the degree to which someone is Rich is both subjective and varies according to the level that one is rich. The same property holds for the predicates “Happy” and “Healty”, where one cannot assign absolute degrees of membership of an individual to such predicates. Hence, it would be best for someone to be able to assign a degree to which a particular individual belongs to the above predicates (concepts).
A Use Case
In this section, we discuss a motivating use case from the production line of multimedia content. More specifically, a casting company, has a knowledge base of models used in the production of multimedia content used in advertisements or other activities. Each entry in the knowledge base contains photo(s) and/or video(s) of the model and metadata containing personal information, some body and face characteristics etc. The casting company has created a user interface for inserting the information of the models as instances of a predefined ontology. It also provides a query engine to search for models with specific characteristics. A user can query the knowledge base providing high-level information about the models (such as the name, the height, the type of the hair etc.). We suppose that we have only information about the following two models in the knowledge base:
- Mary has long good medium quality hair.
- Susan has medium long good quality.
Suppose now that an advertisement company requires a model for a hair dye commercial. From the view of the company the model should have long and good quality hair. Under such definitions, it is obvious that there are no female model in the knowledge base, that satisfy these restrictions. Although Susan satisfies the restrictions of good quality she fails to satisfy the restriction about the length of the hair. But the hair of Susan are medium long so they might be also considered long to some degree. Furthermore, since the casting company and the advertisement company might have different views on the definition of “long hair”, it might also be the case that Susan fulfils the needs of the advertisement company. Similar observations hold for Mary, too. The above problems can be solved if we use a fuzzy knowledge representation, instead of a crisp knowledge representation. In particular, we can define the concepts of “long hair” and “good quality hair” in a fuzzy way, i.e., by using degrees of confidence. For instance, based on the above data of the two models as well as the policy of the advertisement company, we can have the following fuzzy assertions.
- Mary has long hair with a degree no less than 0.8.
- Mary has medium quality hair with a degree no less than 0.7.
- Susan has medium long hair with a degree no less than 0.8.
- Susan has good quality with a degree no less than 1.
But, additionally, Mary can be classified as having good quality hair to a degree no less than 0.6. Furthermore, Susan can also be assigned as having long hair to a degree no less than 0.6. Note that the above membership degrees of the individuals Mary and Susan to the fuzzy concepts “long”, “good quality” have resulted by providing a fuzzy partition [KY95] of the space of the possible values that ones hair length and color can obtain. In addition to the fuzzy assertions, one can encode the knowledge about who qualifies for a hair dye commercial in the form of a rule. So one could say that models with long and good quality hair qualify for playing in a hair dye commercial. We will use this motivating example as a guide for the extension of the RuleML syntax. Moreover, after introducing the semantics of the extended language we will see how we can evaluate the above rule to get some valuable results.
This Technical Group is a part of RuleML and the Semantic Web Community. It will focus on the extension of the RuleML framework with fuzzy set theory and fuzzy logic aspects, called Fuzzy RuleML, in order to provide a rule language framework for representing both certain and uncertain information. More specifically, this working group is focused on syntactic and semantic changes that need to take place in order to make RuleML capable of representing vague (fuzzy) information.
The work will start from the syntax changes and the semantics of two fuzzy rule languages, the fuzzy FOL RuleML (Fuzzy FOL RuleML) and the fuzzy SWRL (Fuzzy SWRL).
The idea of adding fuzziness in logic programs is not new. In [Voj01] an extension to fuzzy logic programs without negation was provided. The semantics was based on Herbrand models. In [Ebr01] a foundation for fuzzy logic programming was also developed. This approach is based on Horn rules with negation as failure and the semantics presented include, declarative, fixed-point, minimal model and procedural semantics. Also in [ Ebr01] several equivalences between these types of semantics was proven. Furthermore, in [Cao00], annotated fuzzy logic programs where proposed as a formal logical base for fuzzy logic programming systems. Also in [Mat99], an approach towards uncertainty and disjunctive logic programs, with negation as failure and stable model semantics was presented. A general framework for monotonic residuated propositional logic programs was presented in [DP01b], and was later extended to non-monotonic programs [DP01a]. Results regarding covering uncertainty when ontologies and rules are combined together, where achieved recently. More precisely, in [Str04], a report on uncertainty and description logic programs, extended with disjunction in the head of the rules and negation as failure, was presented. Additionally, in [PSTH05] an extension of SWRL to fuzzy-SWRL (f-SWRL) was presented.
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