##  [Nonmonotonic Reasoning](/nonmonotonic-reasoning-0) 

 Definition

A class of inferential processes in which adding new premises can invalidate previously drawn conclusions; inference is defeasible rather than strictly monotonic.

 

 

 

 

 

 





## Principle

Principle

Inference is guided by defeasible rules and preferences so that conclusions may be withdrawn when additional information conflicts with earlier assumptions; minimal change and specificity often govern which conclusions survive.

 

 

 

 

 





## Demonstration

Demonstration

An agent assumes "birds fly" by default and concludes that a particular bird b can fly; after learning b is a penguin (an exception to the default), the agent withdraws the earlier conclusion that b flies.

 

 

 

 

## Misapplication

Misapplication

Treating nonmonotonic reasoning as mere uncertainty quantification and using it to justify persistent contradictions, or applying default withdrawals without respecting priorities and context, producing unstable or oscillating conclusions.

 

 

 

 

 





## Consequence

Consequence

Supports flexible, context-sensitive inference appropriate for common-sense reasoning and many AI applications, enabling systems to make tentative conclusions that are retractable when new facts arrive.

 

 

 

 

## Reversal

Reversal

Monotonic reasoning: conclusions accumulate monotonically and are never invalidated by adding further premises; once entailed, a conclusion remains entailed.

 

 

 

 

 





## Boundary

Boundary

Applies to logics and systems that permit defeasible entailment (default logic, defeasible logics, circumscription etc.); does not cover purely monotonic deductive systems, though it may interact with probabilistic update mechanisms.

 

 

 

 

 





## Semantic Tension

Semantic Tension

Tension with probabilistic or Bayesian reasoning: both handle uncertain knowledge but differ in mechanism (defeasible logical rules versus degrees of belief); tension also with belief revision which focuses on change of an agent's belief set rather than local defeasible inferences.

 

 

 

 

 





## Synthesis

Synthesis

Nonmonotonic reasoning is the family of rule-based, defeasible inference procedures that permit provisional conclusions to be withdrawn under new information, organized by priorities, specificity, and minimal-change principles to model commonsense defeasible inference.