19-PredCalcResolution

# Further to be a valid horn clause all variables must

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Further, to be a valid horn clause, all variables must be universally quantified. Sample horn clauses with variables and quantifiers: 2200 x 2200 y 2200 z( ¬ P(x,y) ¬ Q(x,z) R(z)) 2200 x( ¬ R(x)) Now we discard the universal quantifiers but don’t forget them. One consequence is that variables are local to their own horn clause (i.e. the x’s in P and Q are the same x, but the x’s in P and R are different). ¬ P(x,y) ¬ Q(x,z) R(z) ¬ R(x) We then convert the horn clauses to implications with all positive literals. P(x,y) Q(x,z) R(z) R(x) F Finally, we modify the syntax so that it corresponds to Datalog. R(z) :- P(x,y),Q(x,z) R(x)?

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Discussion #19 Chapter 11, Section 3 6/17 Because every variable is universally quantified, we can instantiate it to any (and every) constant in the domain. (We are in context of a derivation, so all statements are true either by assumption, premise, or by a rule of inference.) R(a) :- P(x,y),Q(x,a) S z a R(a)? S x a So, we’re asking if R(a) is true, but the rule says that R(a) is true if P(x,y) Q(x,a) is true. Formally, we are doing resolution ¬

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• Winter '12
• MichaelGoodrich
• Ann, Conjunctive normal form, sister, Horn clause

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