1. Fuzzy Description Logics
Javad Abdollahi
Department of Computer Science
Wayne State University

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Motivation
As the vision of the Semantic Web (SW) is approached, ontologies are playing a major role for representing inherently imprecise and complex knowledge and making it machine readable. Practical solutions must be found for managing this complexity.
Semantic Web is mainly a searchable repository of world knowledge. Current search engines merely collect answers rather than synthesize and process this information.
Search engines are evolving into question-answering systems (by definition a system which has deduction capability).
The problem is that much of world knowledge consists of perceptions, which can not be represented by traditional logic-based approaches.
Bivalent-logic based methods (i.e., the methods that govern today’s ontology based web technology) have (by their nature) limited capability to address complex problems arising in deduction from information. This is due to information, being perceptions, pervasively ill-structured, uncertain and imprecise.
Javad A. Abdollahi - Fuzzy Description Logics

3. Web-based Information Systems
Today’s web is designed more for humans consumption rather than agents and machines.
Semantic web is:
To add a machine-readable meaning to Web pages
To use ontologies to impose consistent definitions of shared terms across various resources
To use KR technology for representing knowledge and for automated reasoning from Web resources, and to apply cooperative software agent systems for processing this knowledge.
Javad A. Abdollahi - Fuzzy Description Logics

4. Description logics Description logics: What are they?
Approaches to knowledge representation are sometimes divided roughly into two categories:
-logic-based formalisms, which evolved out of the intuition that predicate calculus could be used unambiguously to capture facts about the world
-non-logic-based representations, which developed by building on more cognitive notions
Description Logics (DLs) are approaches and general purpose languages to Knowledge Representation and Reasoning (KR&R)
Being a minimal requirement on adequate ontology-based systems, DLs are an important family of formalisms for reasoning about ontologies, especially for the Semantic Web
DLs are essentially the theoretical counterpart of the Web Ontology Language OWL DL (OWL consists of 3 species: OWL Lite, OWL DL, and OWL Full)

5. Description Logics, contd.
DLs are well-suited for the representation of and reasoning about
terminological knowledge
Configurations (Applications that support the design of complex systems created by combining multiple components)
ontologies
database schemata
DL reasoners can reveal inconsistencies, hidden dependencies, redundancies, and misclassifications, when building and maintaining sharable ontologies over the SW
Javad A. Abdollahi - Fuzzy Description Logics

6. Description Logics, contd.
DLs started with systems such as Back, Classic, Loom, etc. and reached mature implementations with mainstream applications and tools such as:
Databases
Consistency of conceptual schemata (EER, UML etc.) EER: Extended Entity Relationship
Schema integration
Query subsumption (w.r.t. a conceptual schema)
Ontologies and Semantic Web (and Grid)
Ontology engineering (design, maintenance, integration)
Reasoning with ontology-based markup (meta-data)
Service description and discovery
Commercial implementations
Cerebra system from Network Inference Ltd
Javad A. Abdollahi - Fuzzy Description Logics

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DL Ontologies
DL ontologies may become complex and very large.
DL ontologies contain many cross-links among classes, properties, individuals, and even among ontologies.
Javad A. Abdollahi - Fuzzy Description Logics

8. Web Ontology language (OWL)
In the SW, the layer of Web Ontology Language (OWL) provides the expressive means to connect knowledge (data) to the world
OWL has its roots in an earlier language DAML+OIL which included description logic
OWL from the World Wide Web Consortium (W3C) is the most recent development in standard ontology languages (Key SW ontology languages: RDF Schema and OWL)
Javad A. Abdollahi - Fuzzy Description Logics

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OWL
OWL consists of three species (i.e., increasingly expressive sublanguages) : OWL Lite, OWL DL (Descriptions logic), and OWL Full.
OWL Lite and OWL DL are essentially very expressive description logics with an RDF syntax. (RDF: Resource Description Framework uses a graph based structure connecting objects -web resources- as nodes)
Javad A. Abdollahi - Fuzzy Description Logics

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An Ontology for a University
Javad A. Abdollahi - Fuzzy Description Logics

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An Ontology for a University

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OWL
OWL goes beyond DL:
uses the linking provided by RDF to give structure to concepts and terminology. This allows ontologies to be distributed across systems, compatible with Web standards, open, extensible and scalable.
Ontologies can become distributed as OWL allows ontologies to refer to terms in other ontologies. In this way OWL is specifically engineered for the Web and Semantic Web, and of many languages sharing symbols
Javad A. Abdollahi - Fuzzy Description Logics

13. OWL ontologies, Frame based ontologies - comparison
OWL ontologies and Protege frame based ontologies have similar components with slightly different names.
OWL ontology components: Individuals, Properties, and Classes, roughly corresponding to Protege frame based: Instances, Slots and Classes.
Javad A. Abdollahi - Fuzzy Description Logics

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Reasoning
OWL uses DLs for reasoning
Reasoning: the process of deriving valid deductions from an ontology.
“compute subsumption relationships between classes, and detect inconsistent classes”
Deduction: the capability to draw on bodies of knowledge from various parts of the Knowledge Base (KB), in order to synthesize an answer to a query.
A list of deductions (inferences):
Class membership
Classification
Equivalence of classes
Example of a reasoner: A DIG (Description Logic Implementers Group) compliant reasoner like RACER
Javad A. Abdollahi - Fuzzy Description Logics

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Fuzzy DLs
DLs are based on bivalent – logic (i.e., yes-no, 0-1, on-off …) and have limited capability to tackle complex deduction problems when information is imprecise.
DLs suffer from the drawback that information to be
captured is supposed to be perfect (well defined, unambiguous, and certain)
To make DLs (e.g. OWL DL) suitable for representing imprecise concepts, DLs can be extended to fuzzy-DLs.
Although a wide range of fuzzy description logics have been introduced for encoding vague knowledge in ontologies, research is still in its infancy in this direction.
Javad A. Abdollahi - Fuzzy Description Logics

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Fuzzy Logic
Introduced by Zadeh, fuzzy sets have been devised as a means to address fuzzy and imprecise concepts such as tall man, hot water, …
A fuzzy set A with respect to a universe X is formally characterized by a membership function μ: X  [0, 1]. An estimation of the belonging of element x to A is assigned to x by μA(x).
μA(x).= 1: x definitely belongs to A, μA(x) = 0.2: x is unlikely to belong to A
Javad A. Abdollahi - Fuzzy Description Logics

17. Example of fuzzy DL & its benefits
Work had been done to transform OWL-DL into a Fuzzy-DL
This has been done by taking corresponding DLs to OWL and converting them to fuzzy-DLs (alternatively fuzzyness can be encoded into concrete domains)
Representation and reasoning capabilities of fuzzy-DLs go beyond classical DLs
Crisp DLs only return queries where every term fits, but fuzzy-DLs can return some or all queries based on the degree of membership.
Degree of membership also provides a natural way rank results, which is a very desirable property.
In domains which are inherently imprecise, such as the information found on the web, fuzzy-DLs provide a more robust and practicable KR than the alternative.
Javad A. Abdollahi - Fuzzy Description Logics

18. Applications (continued)
Biomedical field
Medical Libraries: More robust information retrieval. Nicely suited to the vagueness of disease classification.
Medical trials: Allows for efficient selection of candidates for trials when medical conditions are vague (better model). Quickly identifies invalid definitions. Similar tasks would take multiple queries in standard DLs with less accurate results.
Degree of membership can offer qualitative results which are appropriate for these fields.
Data mining: In data mining, DLs’ inferences can be of use in the process of analyzing large volumes of data
Web Information Systems:
Provides efficient way to check consistency of ontologies
Build an OWL-DL ontology
Use a Description Logic Reasoner to check the consistency of the ontology
Automatically compute the ontology class hierarchy
Javad A. Abdollahi - Fuzzy Description Logics

19. Future Direction of Research
Verification of computational models of fuzzy-DL
Using reductions
reasoners
Creation of a new class of reasoners better suited for fuzzy-DLs: current reasoners are geared toward bivalent logic and thus might be inefficient for fuzzy-reasoning/deductions.
Continuing to investigate the alternative ways of making traditional DL systems fuzzy (which works best and in what domains)
Javad A. Abdollahi - Fuzzy Description Logics

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Conclusion
Imprecise and vague information abound in many practical domains. While traditional techniques are powerful and efficient, they are insufficient for managing complex systems or uncertainty.
Description logics coupled with fuzzy systems provide a balance between maximal expressive power and computional tractability, thus making them useful tools for current applications as well as attractive targets for further research aimed at managing complexity.
Javad A. Abdollahi - Fuzzy Description Logics

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Questions?
Javad A. Abdollahi - Fuzzy Description Logics