CS621 : Artificial Intelligence

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CS621 Artificial Intelligence

• Pushpak BhattacharyyaCSE Dept., IIT Bombay
• Lecture 16
• Description Logic

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Brief on Knowledge Representation
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KR primary aim of AI

• facilitate inferencing
• Inferencing often involves making classes of
  objects, defining a hierarchy, giving attributes
  to objects and specifying constraints.

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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.

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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

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Example Semantic Net
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Frames (example from medical entities dictionary,
Columbia University)
Have slots and fillers
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A more common example of frame
Student Frame with the left column representing
slots and the right column representing fillers
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Description Logic
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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

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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.

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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.
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Constructors of DL and their meaning
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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 n( Doctor U Lawyer)

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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))

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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