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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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