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Non-monotonic reasoning

  • Classical logic is monotonic in the following sense: whenever a sentence A is a logical consequence of a set of sentences T, then A is also a consequence of an arbitrary superset of T [13].

  • Non-monotonic reasoning:

    • Additional information may invalidate conclusions.

    • Non-monotonic reasoning is closer to (human) common-sense reasoning.

    • Most rules in common-sense reasoning only hold with exceptions (i.e. university_professors_teach)

  • Important approaches to formalise non-monotonic reasoning:

    • Default-Logics: Non-classical inference rules are use to represent defaults

    • The modale approach: Modal operators are used to explicitely declare if sth. is believed in or is consistent.

    • Circumscription: Validity can be restricted to specific models.

    • Conditional approaches: A conditional junctor is used to represent defaults in a logical language.

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