Knowledge Representation and Reasoning
Knowledge Representation and Reasoning
Knowledge Representation and Reasoning
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Resolution<br />
Conjunctive Normal Form (CNF—universal)<br />
conjunction of disjunctions of literals<br />
} {{ }<br />
clauses<br />
E.g., (A ∨ ¬B) ∧ (B ∨ ¬C ∨ ¬D)<br />
Resolution inference rule (for CNF): complete for propositional<br />
logic<br />
l 1 ∨ · · · ∨ l k ,<br />
m 1 ∨ · · · ∨ m n<br />
l 1 ∨ · · · ∨ l i−1 ∨ l i+1 ∨ · · · ∨ l k ∨ m 1 ∨ · · · ∨ m j−1 ∨ m j+1 ∨ · · · ∨ m n<br />
where l i <strong>and</strong> m j are complementary literals. E.g.,<br />
P 1,3 ∨ P 2,2 , ¬P 2,2<br />
P 1,3<br />
Resolution is sound <strong>and</strong> complete for propositional logic<br />
<strong>Knowledge</strong> <strong>Representation</strong> <strong>and</strong> <strong>Reasoning</strong> – 29