Institute of Information Theories and Applications FOI ITHEA
Abstract:
The nonmonotonic logic called Default Logic is shown to be representable in a monotonic Modal
Quantificational Logic whose modal laws are stronger than S5. Specifically, it is proven that a set of
sentences of First Order Logic is a fixed-point of the fixed-point equation of Default Logic with an initial set of
axioms and defaults if and only if the meaning or rather disquotation of that set of sentences is logically
equivalent to a particular modal functor of the meanings of that initial set of sentences and of the sentences in
those defaults. This result is important because the modal representation allows the use of powerful
automatic deduction systems for Modal Logic and because unlike the original Default Logic, it is easily
generalized to the case where quantified variables may be shared across the scope of the components of the
defaults thus allowing such defaults to produce quantified consequences. Furthermore, this generalization
properly treats such quantifiers since both the Barcan Formula and its converse hold.