Recursive Definition of Default Logic Modal Logic Nonmonotonic Logic
Issue Date:
2004
Publisher:
Institute of Information Theories and Applications FOI ITHEA
Abstract:
The "recursive" definition of 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 "recursive" fixed-point equation of Default Logic with an initial set of
axioms and defaults if and only if the meaning of the fixed-point 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 is important
because the modal representation allows the use of powerful automatic deduction systems for Modal Logic and
because unlike the original "recursive" definition of Default Logic, it is easily generalized to the case where
quantified variables may be shared across the scope of the components of the defaults.