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19-PredCalcResolution

# 19-PredCalcResolution - Discussion#19 Resolution with...

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Discussion #19 Chapter 11, Section 3 1/17 Discussion #19 Resolution with Predicate Calculus

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Discussion #19 Chapter 11, Section 3 2/17 Topics Horn Clauses Dropping Quantifiers Unification Resolution
Discussion #19 Chapter 11, Section 3 3/17 Horn Clause For resolution, the premises are in CNF. CNF: (… …) (… …) (… …) Each (… …) is a clause. A horn clause is a disjunction of literals that contains at most one positive (non-negative) literal. Horn clause: P ¬ Q ¬ R Horn clause: P Horn clause: ¬ P Not a horn clause: P Q ¬ R too many positive literals Note that, in general, a horn clause is an implication with a conjunction of all positive literals on the lhs and one positive (non- negated) literal on the rhs. Horn clause: P ¬ Q ¬ R ¬ Q ¬ R P ¬ (Q R) P (Q R) P Degenerate cases: Horn clause: P F P ¬ T P T P Horn clause: ¬ P ¬ P F P F Horn clause: ¬ P 1 ¬ P 2 ¬ P n ¬ (P 1 P 2 P n ) F P 1 P 2 P n F Not a horn clause: P Q ¬ R ¬ R P Q R (P Q)

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Discussion #19 Chapter 11, Section 3 4/17 Horn Clauses Appear in 3 Forms 1. One positive literal and one or more negative literals. e.g. P ¬ Q ¬ R (Q R) P These are the Datalog rules. 2. One positive literal and no negative literals. i.e. P T P “We see P by itself as being true.” These are the Datalog facts. 3. No positive literal. ¬ P P F or ¬ P 1 ¬ P 2 ¬ P n P 1 P 2 P n F “When the consequent is false, we wonder what’s going on.” These are the Datalog queries either one query or several.
Discussion #19 Chapter 11, Section 3 5/17 Horn Clauses with Variables and Quantifiers For horn clauses in Datalog, we put all clauses in Prenex Normal Form.

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