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Monotonic and non-monotonic reasoning in AI

Introduction

  • Logic is the study of reasoning and a core element of AI.
  • Monotonic reasoning is a type of reasoning where the addition of new information can only increase the set of conclusions that can be drawn.  
  • Non-monotonic reasoning is a type of reasoning where the addition of new information can either increase or decrease the set of conclusions.  

Monotonic Reasoning

  • Example: If we know that “all birds have feathers” and that “Tweety is a bird,” then we can conclude that “Tweety has feathers.” Even if we add the premise that “Tweety is a penguin,” the conclusion that “Tweety has feathers” remains valid.
  • In monotonic reasoning, if a conclusion can be drawn from a set of premises, then that conclusion will still be valid even if more premises are added.
  • This is a fundamental property of classical logic, including propositional and first-order logic.  

Non-monotonic Reasoning

  • In non-monotonic reasoning, adding new information can invalidate previously drawn conclusions.
  • This type of reasoning is often used in commonsense reasoning, where knowledge is incomplete and subject to change.  
  • Example: If we know that “birds typically fly” and that “Tweety is a bird,” we might conclude that “Tweety can fly.” However, if we add the premise that “Tweety is a penguin,” we need to retract the conclusion that “Tweety can fly.”

Types of Non-monotonic Reasoning

  • Default reasoning: This type of reasoning uses default rules or assumptions that are assumed to be true unless there is evidence to the contrary.  
  • Circumscription: This is a formalism for specifying which predicates are assumed to be false unless they are explicitly stated to be true.  
  • Closed-world reasoning: This type of reasoning assumes that any fact not explicitly stated in the knowledge base is false.  

Applications of Non-monotonic Reasoning

  • Commonsense reasoning: Modeling how humans reason about everyday situations.  
  • Diagnosis: Reasoning about the possible causes of observed symptoms.  
  • Planning: Reasoning about the effects of actions in incompletely known environments.  

Conclusion

  • Monotonic and non-monotonic reasoning are fundamental concepts in AI.
  • Non-monotonic reasoning is particularly important for modeling human-like commonsense reasoning.
  • Understanding these concepts is important for building AI systems that can reason effectively in complex and uncertain environments.

References:

  • Russell, S., and Norvig, P. Artificial Intelligence: A Modern Approach, 4th Edition, 2020, Pearson.
  • Rich, E., Knight, K., & Nair, S. B. Artificial Intelligence. McGraw-Hill International.
  • Nilsson, N. J. Artificial Intelligence: A New Synthesis. Morgan Kaufmann.

Note: This content was generated with the assistance of Google’s Gemini AI.

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