Knowledge Representation

• Keywords quick way for agents to locate potentially useful information

• Thesauri more structured approach than keywords, arranging descriptive terms into broader, narrower, and related classification categories

• Taxonomies classification structurespractice and science of classification grouping

• Ontologies richer way of structural and non-structural relationships than taxonomies. Ontologies provide more complete and precise domain

Relations• Generalization & Inheritance

– Generalization is the relationship between a class and a more refined class.

– Inheritance is transferring properties to subclass.– Anti symmetric

• Aggregation– part-whole or part-of relationship, in which classes

representing the components of something are associated with the class representing the entire assembly.

– Transitive and anti symmetric

• Instantiation– Relationship b/w a class and each of the individuals that

constitute that class

Frames vs. Descriptions

• Frames Directly express knowledge in terms of graphs.

• Description family of languages that

logic formally express certain constrains on KR. Precise semantic and axiomatization. concepts are computed from

these descrptions

Ontology Language Features

• RDF• DAML• OIL (DAML + OIL)• OWL• UML

Elementary Algebra: Relations

• Two important hierarchies:– isA (generalization, inheritance)– isPartOf (aggregation)

• Relationships in ontologies are modeled as binary relations

• A binary relation R b/w a set Sd and a set Sr relates zero or more members of Sd with zero or more members of Sr

• i.e. R can be modeled as a set of pairs, each of which consists of a member of Sd and a member of Sr.

• Since Sd * Sr refers to the Cartesian product of Sd and Sr, meaning the set of all possible pairs whose first component is drawn from Sd and second from Sr. i.e. R Sd X Sr

• Properties that indicate binary relationships occur in pairs, also indicate polarity of relationship. – If c1 is subclass of c2, then c2 is superclass of c1– Students take courses. Courses are taken by

students.

• Formally a binary relation R-1 Sr X Sd is defined as an inverse of R if and only ifd Sd, r Sr : (d,r) R(r,d) R-1

• Anti Symmetry: If xy and yx, then x=y. – In other words, we cannot have two distinct

objects such that each precedes the other.

• Transitivity: if xy and yz, then xz. – If x precedes y and y precedes z, then x precedes

z.

• Asymmetry: if xy, then yx. – Asymmetry is stronger from of anti symmetry,

because it forbids two objects from preceding each other. Also an object cannot precede each other.

• Irreflexivity: xx– This simply states that an object cannot precede it

self.

• Linearity: if xy and yx, then x=y.– This states that for any two distinct objects, one

must precede the other. That is, for any two objects, the ordering relation must hold one way or the other.

Hierarchies

• Taxonomy– isA relationship

• Meronomy– isPartOf relationship

Structure of an OntologyOntologies typically have two distinct components:

• Names for important concepts in the domain– Elephant is a concept whose members are a kind of animal– Herbivore is a concept whose members are exactly those animals who

eat only plants or parts of plants – Adult_Elephant is a concept whose members are exactly those

elephants whose age is greater than 20 years

• Background knowledge/constraints on the domain– Adult_Elephants weigh at least 2,000 kg– All Elephants are either African_Elephants or Indian_Elephants– No individual can be both a Herbivore and a Carnivore

Ontology Design and Deployment

• Given key role of ontologies in the Semantic Web, it will be essential to provide tools and services to help users:– Design and maintain high quality ontologies, e.g.:

• Meaningful — all named classes can have instances• Correct — captured intuitions of domain experts• Minimally redundant — no unintended synonyms• Richly axiomatised — (sufficiently) detailed descriptions

– Store (large numbers) of instances of ontology classes, e.g.:• Annotations from web pages

– Answer queries over ontology classes and instances, e.g.:• Find more general/specific classes• Retrieve annotations/pages matching a given description

– Integrate and align multiple ontologies