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Nonmonotonic Logic

Nonmonotonic Logic. Ahmed Salman Malik. Overview. Monotonic Logic Nonmonotonic Logic Usage and Applications Comparison with other forms of logic Related Topics Summary . Monotonic Logic. Standard type of logic If proven true, will be true forever Facts provided can’t be modified

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Nonmonotonic Logic

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  1. Nonmonotonic Logic Ahmed Salman Malik

  2. Overview • Monotonic Logic • Nonmonotonic Logic • Usage and Applications • Comparison with other forms of logic • Related Topics • Summary

  3. Monotonic Logic • Standard type of logic • If proven true, will be true forever • Facts provided can’t be modified • Doesn’t always fit in real life. • Sidra is in Doha and Doha is in Qatar, so Sidra is in Qatar. • Sidra can always take a trip to United States

  4. Nonmonotonic Logic • New facts can be added • Current facts can be modified • Conclusion can change • If A → B before new fact • Conclusion might change after new fact

  5. Example • Consider the following example • All balls bounce • Football is a ball • Does football bounce • Of course? • What about a football with no air filled in? • Conclusions change with new facts

  6. Real life usage • Used in artificial intelligent systems • For its adaptability • Adding, removing and modifying facts • To reach appropriate conclusions for appropriate scenarios

  7. Application • Consider an example that can’t be handled by monotonic logic • Birds can fly • Seems logical, right?

  8. Exceptions? • What about exceptions? • Ostrich, Penguins

  9. Exceptions • Bird(x) → Flies(x) • How to handle exceptions? • Bird(x) Ù  Abnormal(x) → Flies(x) • Through nonmonotonic logic, we handle exceptions

  10. Handling Exceptions • We know • Ostrich(x) → Abnormal(x) • Ostrich is not a normal bird We conclude • Ostrich(x) → Bird(x) Ù Flies(x) • We make all exceptions this way

  11. Specifying Defaults • Monotonic logic has formal systems to handle defaults • Defaults: Known facts and rules • Nonmonotoniclogic uses incomplete and uncertain information to form patterns for decision making • Abduction: Interpretation of the rules and facts.

  12. Reasoning • Default logic • The predicate logic used as set of inferences • Modal Operator - consistent with known facts • x,y: A(x,y) Ù B(x,y)  C (x,y) • Here B(x,y) is the Modal Operator

  13. Abduction • For a given fact • A(x) → B(x) and • A(x) is sufficient for B(x) • Although, A(x) is not required for B(x)

  14. Inheritance Diagram Flying Things Ostriches Birds Alma Jack

  15. Comparison with Probability • Nomonontonic logic isn’t compatible with probability • The uncertainty and addition of facts disturb the probability model.

  16. Comparison with Classical Logic • Always results in a conclusion • Classical logic might loop forever with incomplete information • Would return wrong answer, instead of none.

  17. Related Topics • Modal Logic • Modelling reasoning about knowledge, actions or time • Epistemic Logic • Uses modal logic to reason about knowledge • Deontic Logic • The representation of normative knowledge

  18. Summary • Adapts with addition, removal and modification of new facts. • Handling exceptions • Used in artificial intelligence for decision making purposes • Helpful where predicate or classic logic falls short

  19. QUESTIONS?

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