Nonmonotonic 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) and 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).
Search
The notion of "aboutness" is fundamental to information search and retrieval. The relevance of a specific document to a query is determined by the collection itself through ranking. The retrieval problem is to determine the relevance or aboutness between the query and the records in the collection.
