Incremental knowledge acquisition for non-monotonic reasoning

The use of conventional non-monotonic reasoning tools in real-sized knowledge-based applications is hindered by the fact that the knowledge acquisition (KA) phase cannot be accomplished in the incremental way that is instead typical of knowledge base management systems based on monotonic logics. Some researchers have proposed (non-monotonic) languages for the representation of Multiple Inheritance Networks with Exceptions (MINEs) that do not suffer from incrementality problems. However, such languages are formally inadequate, as their semantic status is somewhat questionable. In this paper we discuss an approach to non-monotonic reasoning which does allow the phase of KA to be accomplished incrementally, and at the same time relies on a solid and widely acknowledged formal apparatus such as First Order Logic (FOL). We have obtained this by specifying a (non-monotonic) function that maps MINEs into sets of FOL formulae. We have shown that the mapping function we discuss is sound and complete, in the sense that each conclusion that can be derived from a MINE is also derivable from the set of FOL formulae resulting from its translation via the mapping function, and vice-versa.