Nonmonotonic Extensions for First Order Logic

First order logic was originally conceived to formalize the notion of mathematical proof. It should not be surprising that certain facets of human reasoning do not come under the realm of first order logic. These deficiencies have been the motivation for non classical logics (for instance modal logics [Lewis and Langford 1959] and relevance logic [Anderson and Belnap 1975]). In particular, nonmonotonic logics [Bobrow 1980] were introduced after it became apparent that default reasoning (its importance for Artificial Intelligence has been discussed in Section 1.1), violates a fundamental property of first order logic, namely monotonicity [Minsky 1975].