Non-Monotonic Reasoning Task

A Non-Monotonic Reasoning Task is a reasoning task that allows conclusion retraction when new information is added, unlike monotonic reasoning tasks where new knowledge can only expand but never reduce the set of conclusions.

• AKA: Defeasible Reasoning Task, Revisable Reasoning Task, Common-Sense Reasoning Task, Assumption-Based Reasoning Task.
• Context:
  • It can typically employ Non-Monotonic Logic to formalize reasoning patterns where conclusions can be invalidated by new information.
  • It can typically handle incomplete knowledge through default assumption generation and tentative conclusion drawing.
  • It can typically support belief revision by allowing previously accepted conclusions to be withdrawn when contradictory evidence emerges.
  • It can typically model real-world reasoning more accurately than monotonic reasoning tasks when dealing with uncertain information.
  • It can typically formalize exception handling in knowledge representation systems.
  • ...
  • It can often employ default rules of the form "typical members of class A have property B unless there is evidence to the contrary."
  • It can often use closed-world assumption to infer the negation of propositions that are not explicitly stated as true.
  • It can often implement circumscription to minimize the extension of certain predicates to formalize the commonsense assumption that things are as expected unless otherwise specified.
  • It can often involve truth maintenance systems to track justifications for beliefs and manage belief revision.
  • It can often rely on preference ordering among possible worlds or interpretations to select the most plausible ones.
  • ...
  • It can range from being a Simple Non-Monotonic Reasoning Task to being a Complex Non-Monotonic Reasoning Task, depending on its non-monotonic reasoning computational complexity.
  • It can range from being a Domain-Specific Non-Monotonic Reasoning Task to being a General-Purpose Non-Monotonic Reasoning Task, depending on its non-monotonic reasoning application scope.
  • It can range from being a Purely Symbolic Non-Monotonic Reasoning Task to being a Hybrid Non-Monotonic Reasoning Task, depending on its non-monotonic reasoning representation formalism.
  • It can range from being a Classical Non-Monotonic Reasoning Task to being a Probabilistic Non-Monotonic Reasoning Task, depending on its non-monotonic reasoning uncertainty handling approach.
  • ...
  • It can support artificial intelligence systems for non-monotonic reasoning common-sense reasoning.
  • It can connect to machine learning systems for non-monotonic reasoning knowledge acquisition.
  • It can implement automated planning for non-monotonic reasoning action consequence prediction.
  • It can integrate with natural language understanding for non-monotonic reasoning default interpretation.
  • It can combine with knowledge graphs for non-monotonic reasoning fact verification.
  • ...
• Examples:
  • Non-Monotonic Reasoning Task Formal Systems, such as:
    • Default Logic Non-Monotonic Reasoning Tasks, such as:
      • Reiter's Default Logic Non-Monotonic Reasoning Task for non-monotonic reasoning default rule application.
      • Justified Default Logic Non-Monotonic Reasoning Task for non-monotonic reasoning justification tracking.
    • Autoepistemic Logic Non-Monotonic Reasoning Tasks, such as:
      • Moore's Autoepistemic Logic Non-Monotonic Reasoning Task for non-monotonic reasoning introspective knowledge modeling.
      • Stable Autoepistemic Theory Non-Monotonic Reasoning Task for non-monotonic reasoning belief fixpoint computation.
    • Circumscription Non-Monotonic Reasoning Tasks, such as:
      • McCarthy's Circumscription Non-Monotonic Reasoning Task for non-monotonic reasoning abnormality minimization.
      • Prioritized Circumscription Non-Monotonic Reasoning Task for non-monotonic reasoning preference-based minimization.
  • Non-Monotonic Reasoning Task Types, such as:
    • Abductive Reasoning Task for non-monotonic reasoning best explanation inference.
    • Belief Revision Task for non-monotonic reasoning knowledge update.
    • Defeasible Reasoning Task for non-monotonic reasoning tentative conclusion management.
    • Truth Maintenance Task for non-monotonic reasoning dependency tracking.
  • Non-Monotonic Reasoning Task Application Domains, such as:
    • Medical Diagnosis Non-Monotonic Reasoning Task for non-monotonic reasoning clinical decision support.
    • Legal Reasoning Non-Monotonic Reasoning Task for non-monotonic reasoning case-based argumentation.
    • Commonsense Reasoning Non-Monotonic Reasoning Task for non-monotonic reasoning everyday situation understanding.
    • Robot Planning Non-Monotonic Reasoning Task for non-monotonic reasoning action execution in dynamic environments.
  • ...
• Counter-Examples:
  • Monotonic Reasoning Task, which ensures that adding new premises never invalidates previously derived conclusions.
  • Deductive Logic Task, which requires complete information and derives only conclusions that necessarily follow from the premises.
  • Mathematical Proof Task, which builds on absolute certainty rather than defeasible inference.
  • Classical First-Order Logic Task, which maintains monotonicity of entailment as a core property.
  • Formal Verification Task, which typically relies on monotonic formal systems to ensure program correctness.
• See: Formal Logic System, Logical Consequence Relation, Relation (Mathematics) Theory, Monotonicity of Entailment Property, Default Logic System, Abductive Reasoning Task, Belief Revision Task, Inductive Reasoning Task, Approximate Reasoning Task, Defeasible Logic System, Answer Set Programming System, Closed World Assumption Principle.

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References

2014

• (Wikipedia, 2014) ⇒ http://en.wikipedia.org/wiki/Non-monotonic_logic Retrieved:2014-10-9.
  • A non-monotonic logic is a formal logic whose consequence relation is not monotonic. Most studied formal logics have a monotonic consequence relation, meaning that adding a formula to a theory never produces a reduction of its set of consequences. Intuitively, monotonicity indicates that learning a new piece of knowledge cannot reduce the set of what is known. A monotonic logic cannot handle various reasoning tasks such as reasoning by default (consequences may be derived only because of lack of evidence of the contrary), abductive reasoning (consequences are only deduced as most likely explanations), some important approaches to reasoning about knowledge (the ignorance of a consequence must be retracted when the consequence becomes known), and similarly, belief revision (new knowledge may contradict old beliefs).

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