Institute of Information Theories and Applications FOI ITHEA
Abstract:
The nonmonotonic logic called Reflective 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 Reflective Logic with an initial set
of axioms and defaults if and only if the meaning 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 Reflective 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 all the laws of First Order Logic hold and since both the Barcan Formula and its converse
hold.