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 phase cannot be accomplished in the incremental way that is instead typical of knowledge base management systems based on monotonic logics. As a result, some researchers have departed from orthodox non-monotonic formalisms and proposed languages for the representation of Multiple Inheritance Networks with Exceptions (MINEs). Such languages do not suffer from the problem of incrementality in knowledge acquisition, but are inadequate both from a formal and from an empirical point of view. In fact, they are not endowed with a formal semantics, and the intuitions that underlie their inferential mechanisms are far from being widely agreed upon. In this paper we discuss an approach to non-monotonic reasoning which does allow the phase of knowledge acquisition to be accomplished in an incremental and modular way, but 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.