NONMONOTONIC

LOGIC

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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 For its adaptability 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?

What about 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

Nonmonotonic logic 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

BirdsOstriches

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

Would return wrong answer, instead of none.

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

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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