not - Winter 2006 COSC-6490B Issues in Information...

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Unformatted text preview: Winter 2006 COSC-6490B: Issues in Information Integration —Godfrey p. 1 Negation Datalog with Negation Okay. Let us add “ not ” to the Datalog language (Datalog ¬ ). E.g., cousin ( X, Y ) ← grandparent ( P, X ), grandparent ( P, Y ), X negationslash = Y , not sibling ( X, Y ). We only allow use of “ not ” on the right-hand side of the ‘ ← ’. The intuitive meaning of “ not ” is quite clear. How to handle it formally is far from clear. • What are the models of a Datalog ¬ database? • What should the proof procedure be for Datalog ¬ ? This “ not ” is not logical negation (‘ ¬ ’)! Winter 2006 COSC-6490B: Issues in Information Integration —Godfrey p. 2 Safeness Extended for Datalog ¬ We require that Datalog ¬ programs be safe . We need to extend the definition of safeness for Datalog ¬ : Any variable that appears either in the head atom of the rule (on the left-hand side) or in a negated atom must also appear in a non-negated atom in the body (on the right-hand side). Thus, h ( X 1 , . . . , X k ) ← b 1 ( Y 1 , . . . , Y j 1 ) , . . . , b m ( Y j m − 1 , . . . , Y j m ) , not d 1 ( Z 1 , . . . , Z j 1 ) , . . . , not d n ( Z j n − 1 , . . . , Z j n ). is safe if ( { X 1 , . . ., X k } ∪ { Z 1 , . . . , Z j n } ) ⊆ { Y 1 , . . . , Y j m } Winter 2006 COSC-6490B: Issues in Information Integration —Godfrey p. 3 Non-Monotonicity...
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not - Winter 2006 COSC-6490B Issues in Information...

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