Concept

Non-monotonic logic

Overview

A non-monotonic logic is a formal logic whose entailment relation is not monotonic. In other words, non-monotonic logics are devised to capture and represent defeasible inferences, i.e., a kind of inference in which reasoners draw tentative conclusions, enabling reasoners to retract their conclusion(s) based on further evidence.

Most studied formal logics have a monotonic entailment relation, meaning that adding a formula to the hypotheses never produces a pruning of its set of conclusions. Intuitively, monotonicity indicates that learning a new piece of knowledge cannot reduce the set of what is known. Monotonic logics cannot handle various reasoning tasks such as reasoning by default (conclusions may be derived only because of lack of evidence of the contrary), abductive reasoning (conclusions are only deduced as most likely explanations), some important approaches to reasoning about knowledge (the ignorance of a conclusion must be retracted when the conclusion becomes known), and similarly, belief revision (new knowledge may contradict old beliefs).

Overview adapted from Wikipedia (CC BY-SA 4.0; see the article history for authors).

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Or, finally, the premises, of whichever kind they are, may never have been conceived in so distinct a manner as to produce any clear consciousness by what means they were arrived at; as in the case of what is called reasoning in a circle; and then the fallacy is one of Confusion.
John Stuart Mill, A System of Logic, Ratiocinative and Inductive
States what Non-monotonic logic is.
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Hence (3) the judgment suffers disruption into one of two forms. It is either (a) the Identical judgment, an empty identical relation stating that the individual is the individual; or it is (b) what is called the Infinite judgment, in which we are presented with the total incompatibility of subject and predicate. Examples of the latter are: 'The mind is no elephant:' 'A lion is no table;' propositions which are…
Georg Wilhelm Friedrich Hegel, The Logic of Hegel
States what Non-monotonic logic is.
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Any such select set is called the set of postulates, or premises, from which the reasoning proceeds. The reasoning is nothing else than the exhibition of the whole pattern of general conditions involved in the pattern derived from the selected postulates.
Alfred North Whitehead, Science and the modern world
States what Non-monotonic logic is.
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Related ideas

Opposing perspectives

Non-classical logic

Place in the tradition

Part of Deontic logic.

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