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# Nonmonotonic Logic - PowerPoint PPT Presentation

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

Ahmed Salman Malik

• Monotonic Logic

• Nonmonotonic Logic

• Usage and Applications

• Comparison with other forms of logic

• Related Topics

• Summary

• 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

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

• 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

• Used in artificial intelligent systems

• Adding, removing and modifying facts

• To reach appropriate conclusions for appropriate scenarios

• Consider an example that can’t be handled by monotonic logic

• Birds can fly

• Seems logical, right?

• Ostrich, Penguins

• Bird(x) → Flies(x)

• How to handle exceptions?

• Bird(x) Ù  Abnormal(x) → Flies(x)

• Through nonmonotonic logic, we handle 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

• 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.

• 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

• 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)

Flying Things

Ostriches

Birds

Alma

Jack

• Nomonontonic logic isn’t compatible with probability

• The uncertainty and addition of facts disturb the probability model.

• Always results in a conclusion

• Classical logic might loop forever with incomplete information

• 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