Editing Non-monotonic logic (section)

{{Short description|Formal logic whose entailment relation is not monotonic}}
{{more footnotes needed|date=June 2008}}
A '''non-monotonic logic''' is a [[formal logic]] whose [[entailment]] relation is not [[Monotonicity of entailment|monotonic]]. In other words, non-monotonic logics are devised to capture and represent [[defeasible reasoning|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.<ref>{{cite web|last1=Strasser|first1=Christian|last2=Antonelli|first2=G. Aldo|title=Non-Monotonic Logic|url=http://plato.stanford.edu/entries/logic-nonmonotonic/|website=plato.stanford.edu/index.html|publisher=Stanford Encyclopedia of Philosophy|access-date=19 March 2015}}</ref>
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 [[Default logic|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).