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Artificial Intelligence Knowledge Representation Propositional Representation

Lecture 5. Artificial Intelligence Knowledge Representation Propositional Representation. Reasoning method of resolution. Reasoning methods of Resolution. Forward Reasoning Backward Reasoning. Backward Reasoning. The steps required to prove propositional with Backward Reasoning method:-

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Artificial Intelligence Knowledge Representation Propositional Representation

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  1. Lecture 5 Artificial IntelligenceKnowledge RepresentationPropositional Representation

  2. Reasoning method of resolution

  3. Reasoning methods of Resolution • Forward Reasoning • Backward Reasoning

  4. Backward Reasoning • The steps required to prove propositional with Backward Reasoning method:- 1- Convert all propositional sentences to CNF and Clauses Form. 2-Negate the Goal and constructs clauses for this proposal. 3-Select the proposed clauses and one of the other clauses as parents.

  5. Backward Reasoning 4-Solve the parents with each other and put the result in new clause. 5-Solve the new clauses with one of the other clauses. 6-Reapet step(5) until reach to the empty. A- if you reach to the empty clauses then the goal is proved. B- if you does not reach to the empty clauses then the goal is not proved.

  6. Forward Reasoning • The steps required to prove propositional with Forward Reasoning method:- 1- Convert all propositional sentences to CNF and Clauses Form. 2-Select two clauses to solve them with each other. 3-Solve the two selected clauses and put the result in new clause.

  7. Forward Reasoning 4-Solve the new clauses with one of the other clauses. 6-Reapet step(4) until reach to the Goal. A- if you reach to the clauses Goal then the goal is proved. B- if you does not reach to the clauses Goal then the goal is not proved.

  8. Forward Reasoning • From facts to conclusions • Given • s1: p • s2: q, • s3: p  q  r Rewrite in clausal form: Goal: r ; s3 =( p  q  r) • s1 resolve with s3 =  q  r (s4) • s2 resolve with s4 = r • Generally used for processing sensory information.

  9. Backwards Reasoning: • From Negative of Goal to data • Given • s1: p, • s2: q, • s3: p  q  r • Goal: r ; negate the goal s4 =  r • Rewrite s3 in clausal form: s3 = ( p  q  r) • Resolve s4 with s3 =  p  q (s5) • Resolve s5 with s2 =  p (s6) • Resolve s6 with s1 = empty. r is true. • From Negative of Goal to data • Given • s1: p, • s2: q, • s3: p  q  r • Goal: s4 = r Rewrite in clausal form: s3 = ( p  q  r) • Resolve s4 with s3 =  p  q (s5) • Resolve s5 with s2 =  p (s6) • Resolve s6 with s1 = empty. r is true. state1

  10. Example Suppose our knowledge base consists of the rules S  T  (P  R) And the facts S T R And I need to prove P 1.Using resolution

  11. S1 S2 S5S3 S6S4 P Forward chaining or Forward Reasoning • S1=S  T  (P  R) • S2=S • S3=T • S4=R • And I need to prove P Convert to CNF (S1) (S  T )(P  R) S   T (P  R) S   T   P   R S1= S   T  P   R (CNF) S1 with S2 S5=  T  P   R S5 resolve with S3 S6=P   R S6 resolve with S4 P Then P is proved

  12. S1 S5 S6S2 S7S3 S8S4 empty Backward chaining or Backward Reasoning S1=S  T  (P  R) S2=S S3=T S4=R And I need to prove P Convert to CNF S1= S   T  P   R (CNF) Add S5= P S5 with S1 S6= S   T   R S6 with S2 S7=  T   R S7 with S3 S8=  R S8 with S4 Infer empty Thenpis proved

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