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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

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nonmonotonic logic

Nonmonotonic Logic

Ahmed Salman Malik

overview
Overview
  • Monotonic Logic
  • Nonmonotonic Logic
  • Usage and Applications
  • Comparison with other forms of logic
  • Related Topics
  • Summary
monotonic logic
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 logic1
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
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
Real life usage
  • Used in artificial intelligent systems
    • For its adaptability
    • Adding, removing and modifying facts
    • To reach appropriate conclusions for appropriate scenarios
application
Application
  • Consider an example that can’t be handled by monotonic logic
    • Birds can fly
  • Seems logical, right?
exceptions
Exceptions?
  • What about exceptions?
    • Ostrich, Penguins
exceptions1
Exceptions
  • Bird(x) → Flies(x)
  • How to handle exceptions?
    • Bird(x) Ù  Abnormal(x) → Flies(x)
  • Through nonmonotonic logic, we handle exceptions
handling 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
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
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
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
Inheritance Diagram

Flying Things

Ostriches

Birds

Alma

Jack

comparison with probability
Comparison with Probability
  • Nomonontonic logic isn’t compatible with probability
  • The uncertainty and addition of facts disturb the probability model.
comparison with classical logic
Comparison with Classical Logic
  • Always results in a conclusion
  • Classical logic might loop forever with incomplete information
  • Would return wrong answer, instead of none.
related topics
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
summary
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
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