1. Knowledge Representation (Introduction)
Information
Data
Knowledge representation:
Information representation with support for inference
CSE (c) S. Tanimoto, Knowledge Representation- Intro

2. Procedural vs Declarative
Knowledge can be operational:
“When you see a grizzly bear, run away fast!”
if Condition is true then do Action
e.g., production rules.
Knowledge can be declarative:
“A grizzly bear is a dangerous animal.”
predicate(object)
e.g., logical statements or relations
CSE (c) S. Tanimoto, Knowledge Representation- Intro

3. Example of Declarative Representation: An “Isa” Hierarchy
Living-thing
Plant
Animal
Fish
Bird
Aquatic-bird
Land-bird
Great-blue-heron
CSE (c) S. Tanimoto, Knowledge Representation- Intro

4. Inference with Isa Hierarchies
(A great-blue-heron is an aquatic-bird)
Isa(great-blue-heron, aquatic-bird).
(An aquatic-bird is a bird)
Isa(acquatic-bird, bird).
(Is a great-blue-heron a bird)
Isa(great-blue-heron, bird)?
“Isa” represents a relation which has certain properties that support types of inference.
CSE (c) S. Tanimoto, Knowledge Representation- Intro

5. CSE 415 -- (c) S. Tanimoto, 2002 Knowledge Representation- Intro
Binary Relations
A binary relation R over a domain D is a set of ordered pairs (x,y) where x and y are in D.
For example, we could have,
D = {a,b,c,d} R = {(a, b), (c, a), (d, a)}
If (x, y) is in R, then we write R(x, y) or x R y.
CSE (c) S. Tanimoto, Knowledge Representation- Intro

6. CSE 415 -- (c) S. Tanimoto, 2002 Knowledge Representation- Intro
Partial Orders
If for each x in D we have x R x, then R is reflexive.
If for each x in D and y in D we have
x R y and y R x imply x = y,
then R is antisymmetric.
If for each x in D, y in D, and z in D we have
x R y and y R z imply x R z,
then R is transitive.
If R has all 3 properties, R is a partial order.
CSE (c) S. Tanimoto, Knowledge Representation- Intro

7. Examples of the Partial Order Properties
Isa is reflexive:
A bear is a bear.
-> Isa(bear, bear)
Isa is antisymmetric:
A bear is a wowie, and a wowie is a bear.
Therefore, bear and wowie represent the same things.
Isa(bear, wowie) & Isa(wowie, bear) -> bear = wowie
Isa is transitive:
A grizzly is a bear, and a bear is a mammal.
Therefore, a grizzly is a mammal.
Isa(grizzly, bear) & Isa(bear, mammal) -> Isa(grizzly, mammal)
CSE (c) S. Tanimoto, Knowledge Representation- Intro

8. CSE 415 -- (c) S. Tanimoto, 2002 Knowledge Representation- Intro
Redundant Facts
Any fact implied by others via the reflexive, antisymmetric, or transitive properties of a partial order can be considered redundant.
Suppose
a <= b
b <= c
c <= b
Then
a <= c is redundant.
a <= a is redundant.
b and c could be represented by one name.
CSE (c) S. Tanimoto, Knowledge Representation- Intro

9. Inheritance of Properties via Isa
A fox is a mammal.
A mammal bears live young
Therefore a fox bears live young.
CSE (c) S. Tanimoto, Knowledge Representation- Intro

10. Non-inheritance of Certain Properties
A neutron is an atomic particle.
There are three types of atomic particles.
Therefore there are three types of neutrons (??)
CSE (c) S. Tanimoto, Knowledge Representation- Intro

11. CSE 415 -- (c) S. Tanimoto, 2002 Knowledge Representation- Intro
Propositional Logic
The propositional calculus is a mathematical system for reasoning about the truth or falsity of statements.
The statements are made up from atomic statements using AND, OR, NOT, and their variations.
A more powerful representation system is the predicate calculus. It’s an extension of the propositional calculus.
CSE (c) S. Tanimoto, Knowledge Representation- Intro

12. Propositional Logic Examples
P: a grizzly is a bear.
Q: a bear is a mammal.
R: a grizzly is a mammal.
P & Q -> R
Each proposition symbol represents an atomic statement.
Atomic statements can be combined with logical connectives to form compound statements.
~P, P & Q, P v Q, P = Q, P -> Q
CSE (c) S. Tanimoto, Knowledge Representation- Intro