Non-Monotonic Logic

This is maybe the source of Logic, which we use in our day-to-day Life, and we are using of it, unconsciously; non-monotonic logic.

 

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).

The term “non-monotonic logic” covers a family of formal frameworks devised to capture and represent defeasible inference, i.e., that kind of inference of everyday life in which reasoners draw conclusions tentatively, reserving the right to retract them in the light of further information. Such inferences are called “non-monotonic” because the set of conclusions warranted on the basis of a given knowledge base, given as a set of premises, does not increase (in fact, it can shrink) with the size of the knowledge base itself. This is in contrast to standard logical frameworks (e.g., classical first-order) logic, whose inferences, being deductively valid, can never be “undone” by new information.