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Resolution Proof Example

Resolution Proof Example. Prateek Tandon, John Dickerson. “Robot Doom” Domain. Jack owns a roomba Every roomba owner is a robot enthusiast. No robot enthusiast breaks a robot. Either Jack or SENSOR MALFUNCTION broke my roomba . Question: Did SENSOR MALFUNCTION break my roomba ?.

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Resolution Proof Example

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  1. Resolution Proof Example Prateek Tandon, John Dickerson

  2. “Robot Doom” Domain • Jack owns a roomba • Every roomba owner is a robot enthusiast. • No robot enthusiast breaks a robot. • Either Jack or SENSOR MALFUNCTION broke my roomba. Question: Did SENSOR MALFUNCTION break my roomba?

  3. Write in First Order Logic • Jack owns a roomba • Every roomba owner is a robot enthusiast. • No robot enthusiast breaks a robot. • Either Jack or SENSOR MALFUNCTION broke my roomba. Some Additional Facts:

  4. Algorithm for Converting FOL to CNF • Eliminate Implications • Move negation inward • Standardize variables • Skolemization • Drop universal quantifiers • Apply distributivity

  5. Convert to CNFStep 1: Eliminate Implications Replace pq with not p or q

  6. Convert to CNFStep 2: Move Negation Inward Apply Demorgan’s Laws, change quantifiers, etc.

  7. Convert to CNFStep 3: Standardize Variables If two variables have the same name, then change the name of one of the variables (no modification in this example)

  8. Convert to CNFStep 4: Skolemization “Skolemization” – the process of removing existential quantifiers by elimination. General Rule: Arguments of the skolem function are all the universally quantified variables in whose scope the existential quantifier appears.

  9. Convert to CNFStep 5: Drop Universal Quantifiers Pretty Easy…

  10. Convert to CNFStep 6: Apply Distributivity Nothing much to do in this example…but you know how to do this well after problem 1.

  11. Assert Negation of Conclusion What we want to conclude: Negation of conclusion:

  12. Resolution Rule(simplified)

  13. Apply Resolution

  14. Apply Resolution (continued) FALSE …So negated conclusion is wrong. …So original statement must be right.

  15. Practical Aspects of Logic • Jess Rule-Based System for Java (http://herzberg.ca.sandia.gov) • Wolfram-Alpha Logic Engine • MATLAB toolbox

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