Abstract

In this paper I shall present some of the results I have obtained on modal theories which contain quantifiers for propositions. The paper is in two parts: in the first part I consider theories whose non-quantificational part is S5; in the second part I consider theories whose non-quantificational part is weaker than or not contained in S5. Unless otherwise stated, each theory has the same language L. This consists of a countable set V of propositional variables pl, pa, ... , the operators v (or), ~ (not) and □ (necessarily), the universal quantifier (p), p a propositional variable, and brackets ( and ). The formulas of L are then defined in the usual way