chaining in first order logic
DESCRIPTION
Chaining in First Order Logic. CS 171/271 (Chapter 9, continued) Some text and images in these slides were drawn from Russel & Norvig’s published material. Forward Chaining. Forward Chaining in PL extends to FOL A similar restriction applies to the KB Implications Atomic sentences - PowerPoint PPT PresentationTRANSCRIPT
1
Chaining in First Order Logic
CS 171/271(Chapter 9, continued)
Some text and images in these slides were drawn fromRussel & Norvig’s published material
2
Forward Chaining Forward Chaining in PL extends to FOL A similar restriction applies to the KB
Implications Atomic sentences
KB can contain quantifiers Apply EI for existentially quantified sentences Allow variables for universally quantified
sentences (omit quantifier in such sentences)
3
Knowledge Base Example The law says that it is a crime for an
American to sell weapons to hostile nations. The country Nono, an enemy of America, has some missiles, and all of its missiles were sold to it by Colonel West, who is American.
Prove that Colonel West is a criminal
4
Knowledge Base Example... it is a crime for an American to sell weapons to hostile
nations:American(x) Weapon(y) Sells(x,y,z) Hostile(z) Criminal(x)
Nono … has some missiles, i.e., x Owns(Nono,x) Missile(x):Owns(Nono,M1) and Missile(M1)
… all of its missiles were sold to it by Colonel WestMissile(x) Owns(Nono,x) Sells(West,x,Nono)
Missiles are weapons:Missile(x) Weapon(x)
An enemy of America counts as "hostile“:Enemy(x,America) Hostile(x)
West, who is American …American(West)
The country Nono, an enemy of America …Enemy(Nono,America)
5
Forward Chaining Algorithm
6
Forward Chaining Example
7
Forward Chaining Example
Missile(x) Weapon(x)
Missile(x) Owns(Nono,x) Sells(West,x,Nono)
Enemy(x,America) Hostile(x)
8
Forward Chaining Example
American(x) Weapon(y) Sells(x,y,z) Hostile(z) Criminal(x)
9
About Forward Chaining Matching rules against known facts Incremental forward chaining Irrelevant facts
10
Backward Chaining Begin with goal (query) Recursively build a set of
substitutions that satisfy the premises necessary to conclude goal
11
Backward Chaining Algorithm
SUBST(COMPOSE(θ1, θ2), p) = SUBST(θ2, SUBST(θ1, p))
12
Backward Chaining Example
13
Backward Chaining Example
14
Backward Chaining Example
15
Backward Chaining Example
16
Backward Chaining Example
17
Backward Chaining Example
18
Backward Chaining Example
19
Backward Chaining Example
20
About Backward Chaining Uses composition of substitutions A DFS algorithm
Linear time Repeated states and incompleteness