Nonmonotonic Logic

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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

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
• 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
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
Real life usage
• Used in artificial intelligent systems
• Adding, removing and modifying facts
• To reach appropriate conclusions for appropriate scenarios
Application
• Consider an example that can’t be handled by monotonic logic
• Birds can fly
• Seems logical, right?
Exceptions?
• Ostrich, Penguins
Exceptions
• Bird(x) → Flies(x)
• How to handle exceptions?
• Bird(x) Ù  Abnormal(x) → Flies(x)
• Through nonmonotonic logic, we handle exceptions
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
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.
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
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)
Inheritance Diagram

Flying Things

Ostriches

Birds

Alma

Jack

Comparison with Probability
• Nomonontonic logic isn’t compatible with probability
• The uncertainty and addition of facts disturb the probability model.
Comparison with Classical Logic
• Always results in a conclusion
• Classical logic might loop forever with incomplete information