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)  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) 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)  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
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