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CNF_Horn 4

# CNF_Horn 4 - York University CSE-CNF& Horn Example...

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Example P: { p:-q. , q:-.} If we want to know about p, we will ask the query: :-p. Note that the set { p:-q., q:-., :-p.} is inconsistent. (Reminder: truth table for above clauses does not have even one row where all the clauses are true) Therefore p is provable and your theorem proving program (e.g. Prolog) will return true . York University- CSE 3401 16 02-CNF & Horn

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‘Predicate Logic’ Clauses Same definition for literals, clauses, and CNF except now each literal is more complicated since an atomic formula is more complicated in predicate logic We need to deal with quantifiers and their object variables when converting to CNF York University- CSE 3401 17 02-CNF & Horn
Conversion to CNF in Predicate Logic 1. Remove implication and equivalence 2. Move negations inwards 3. Rename variables so that variables of each quantifier are unique 4. Move all quantifiers to the front (conversion to Prenex Normal Form or PNF) 5. Skolemize (get rid of existential quantifiers) 6. Distribute OR over AND 7. Remove all universal quantifiers

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Unformatted text preview: York University- CSE 3401 18 02-CNF & Horn Example Example: Convert the following formula to CNF: Step 1. Remove implication and equivalence Step 2. Move negations inwards Note Step 3. Rename variables so that variables of each quantifier are unique Step 4. Move all quantifiers to the front (PNF) York University- CSE 3401 19 ) ( ) ( ) ( ) ( x p x x p x ) ( ) , ( ) )( ( ) ( ) , ( ) ( ) ( ) ( ) , ( ) ( ) ( ) ( ) , ( ) ( ) ( X n Y X m Y X X n Y X m Y X X n Y X m Y X X n Y X m Y X 02-CNF & Horn Example- cont. Step 5. Skolemizing (get rid of existential quantifiers) Step 6. Distribute OR over AND to have conjunctions of disjunctions as the body of the formula Step 7. Remove all universal quantifiers Logic Programming notation: York University- CSE 3401 20 ). , ( : ) ( ) ( ) , ( ) ( ) , ( ) )( ( Y X m X n X n Y X m X n Y X m Y X 02-CNF & Horn...
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CNF_Horn 4 - York University CSE-CNF& Horn Example...

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