Slide trí tuệ nhân tạo propositional logic

Introduction to
Artificial Intelligence
Chapter 3: Knowledge
Representation and Reasoning
(2) Propositional Logic (cont)
Nguyễn Hải Minh, Ph.D


07/09/2018

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Outline
❑Horn Clauses
❑Forward and Backward Chaining
❑DPLL Algorithm

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Horn Clauses
❑KB:

Clause 1

Disjuctions of literals
(𝑙1 ∨ 𝑙2 ∨ ⋯ ∨ 𝑙𝑚)

∧

Clause 2

∧…∧

Clause n

Conjunction Normal Form (CNF)
Disjunctions of literals of which at most one is positive
(¬𝑙1 ∨ ¬𝑙2 ∨ ⋯ ∨ 𝑙𝑚)

Restricted form

Horn Clause
E.g., ¬B1,2 ∨ ¬B2,1 ∨ P2,2
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B1,2 ∧ B2,1 ⇒ P2,2

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Horn Clauses
B ⇒ A ,B

❑Modus Ponens for Horn Form:

A

❑More general version of the rule:
B1 ∧ B2 ∧ … ∧ Bk ⇒ A ,

B1, B2, … , Bk

A

❑Why do we need Horn Clauses?

o Horn clauses are closed under resolution
o In the implication form, the sentence is easier to
understand
o Can be used with forward chaining or backward
chaining.
o These algorithms are very natural and run in linear time.

07/09/2018

Nguyễn Hải Minh @ FIT - HCMUS
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A grammar for CNF, Horn Clauses

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Forward chaining
❑Idea:
o fire any rule whose premises are satisfied in the KB,
o add its conclusion to the KB, until query is found
query →

KB →
AND
OR

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Forward chaining algorithm

❑Forward chaining is sound and complete for Horn KB
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Forward chaining example

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Forward chaining example

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Forward chaining example

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Forward chaining example

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Forward chaining example

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Forward chaining example

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Forward chaining example

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Forward chaining example

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Backward chaining
❑Idea: work backwards from the query q:
o to prove q by BC,
•
•

check if q is known already, or
prove by BC all premises of some rule
concluding q

❑Avoid loops: check if new subgoal is already on
the goal stack
❑Avoid repeated work: check if new subgoal
o
o

has already been proved true, or
has already failed

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Backward chaining example

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Backward chaining example

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Backward chaining example

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Backward chaining example

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Backward chaining example

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Backward chaining example

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Backward chaining example

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Backward chaining example

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Backward chaining example

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