CS621 : Artificial Intelligence Pushpak Bhattacharyya CSE Dept., IIT Bombay Lecture 16 Description Logic

Brief on Knowledge Representation

KR: primary aim of AI facilitate inferencing Inferencing often involves making classes of objects, defining a hierarchy, giving attributes to objects and specifying constraints.

Predicate Calculus: foundational KR Uses (i) Predicates for describing relationships and (ii) Rules for inferencing A special kind of inferencing is Inheritance where all properties of a super class are passed onto its subclasses For example, it can be inferred that bulldogs- being dogs- have 4 legs by virtue of their inheriting dog-properties.

Structured Knowledge Representation Components and their interrelationships have to be expressed Semantic Nets and Frames prove more effective than predicate calculus Reminiscent of calculus where using differentiation to find the rate of change of one quantity with respect to another is more convenient than using the more foundational

Example Semantic Net

Frames (example from medical entities dictionary, Columbia University) Have slots and fillers

A more common example of frame Student Frame with the left column representing slots and the right column representing fillers

Description Logic

Motivation to study Structure of the knowledge may not be visible, and obvious inferences may be difficult to draw Expressive power is too high for obtaining decidable and efficient inference Inference power may be too low for expressing interesting, but still decidable theories

Wikipedia Definition “Description logics (DL) are a family of knowledge representation languages which can be used to represent the terminological knowledge of an application domain in a structured and formally well- understood way. The name description logic refers, on the one hand, to concept descriptions used to describe a domain and, on the other hand, to the logic-based semantics which can be given by a translation into first-order predicate logic. Description logic was designed as an extension to frames and semantic networks, which were not equipped with formal logic-based semantics.”knowledge representation logicfirst-order predicate logicframes semantic networks

Constituents of DL Individuals (such as Jack and Jill) Concepts (such as Man and Woman) Roles (such as isStudent) Individuals are like constants in predicate calculus, while Concepts are like Unary predicates and Roles are like Binary Predicates.

Constructors of DL and their meaning

Examples For example the set of all those parents having a male child who is a doctor or a lawyer is expressed as Has-child.Male ∩ ( Doctor U Lawyer)

Quantifiers and ‘Dots’  HasChild.Girl is interpreted as the set {x |  (y)( HasChild(x,y)  Girl(y))} and  isEmployedBy.Farmer is interpreted as {x |  (y)( isEmployedBy(x,y) Farmer(y))}

Inference in DL Main mechanism: Inheritance via subsumption DL suitable for ontology engineering A concept C subsumes a concept D iff I(D)  I(C) on every interpretation I For example: Person subsumes Male, Parent subsumes Father etc. Every attribute of a concept is also present in the subsumed concepts