A comparison of autoepistemic logic and default logic both generalized so as to allow quantified variables to cross modal scopes

Default logic and autoepistemic 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 the fixed point equation for default logic and the fixed point equation for the kernel of autepistemic logic both as reflective equivalences of the modal quantificational Logic Z. The two resulting systems, called quantified default logic and quantified autepistemic logic, are then compared by deriving metatheorems of Z that express their relationships. The main result is to show that every solution to the reflective equivalence for quantified default logic is a strongly grounded solution to the reflective equivalence for quantified autepistemic logic. This generalizes previous work relating default logic and autepistemic logic to the case where universally quantified variables cross modal scopes. It is further shown that quantified default logic and quantified autepistemic logic have exactly the same solutions when no default has an entailment condition. Finally it is noted that quantified default logic and quantified autepistemic logic are particularly powerful logics since the disjunction of all the solutions of a particular subcase of each is equivalent to parallel circumscription with circumscribed, variable, and fixed predicates.