Institute of Information Theories and Applications FOI ITHEA
Abstract:
Reflective Logic and Default Logic are both generalized so as to allow universally quantified
variables to cross modal scopes whereby the Barcan formula and its converse hold. This is done by
representing both the fixed-point equation for Reflective Logic and the fixed-point equation for Default both as
necessary equivalences in the Modal Quantificational Logic Z. and then inserting universal quantifiers before
the defaults. The two resulting systems, called Quantified Reflective Logic and Quantified Default Logic, are
then compared by deriving metatheorems of Z that express their relationships. The main result is to show that
every solution to the equivalence for Quantified Default Logic is a strongly grounded solution to the
equivalence for Quantified Reflective Logic. It is further shown that Quantified Reflective Logic and
Quantified Default Logic have exactly the same solutions when no default has an entailment condition.