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Unit 5: Knowledge Representation

predicates is: mega_star(sachin)  m: mega_star(m)  rich(m)  c:car(car_of(m),m).  c,m: car(c,m)  Notes

rich(m)  fast(c).  c: [fast(c)  m:car(c,m)  consume(c)]. Provided this we could conclude:

consume(car_of(sachin)).
5.3.1 Isa and Instance Relationships

Two traits isa and instance play an imperative role in many facets of knowledge representation.
The cause for this is that they maintain property inheritance.
isa

— used to demonstrate class inclusion, such as isa(mega_star,rich).
instance
— used to demonstrate class membership, such as instance (prince,mega_star).

Thus, now it should be easy to observe how to represent these in predicate logic.
Isa is used to demonstrate class inclusion, such as isa(mega_star,rich).
Instance is used to demonstrate class membership, such as instance (prince,mega_star).

Self Assessment

Fill in the blanks:
9. Predicate logic contains various standard logic symbols to represent ........................... .

10. Isa is used to demonstrate class ........................... .
11. Instance is used to demonstrate class ........................... .

5.4 Resolution

This is another type of proof system based on refutation. Better suited to computer
implementation than systems of axioms and rules (can give correct answers). Generalizes to
first order logic. This is the basis of Prologs inference method.

!
Caution To apply resolution, all formulae in the knowledge base and the query must be in
clausal form (c.f. Prolog clauses).

5.4.1 Normal Forms

A literal is a propositional letter or the negation of a propositional letter and a clause is a
disjunction of literals.
Conjunctive Normal Form (CNF): a conjunction of clauses, e.g., (P Q  R) (S  R).
Disjunctive Normal Form (DNF): a disjunction of conjunctions of literals, e.g., (P  Q  R) 
(S  R).
Every propositional logic formula can be converted to CNF and DNF.

Conversion to Conjunctive Normal Form
Eliminate rewriting P Q as (P  Q) (Q  P)

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