Investigations in modal logic, with attention to relations between quantifiers and modal operators

Abstract

I have used, where available the standard Russellian symbolism and unless otherwise stated I intend it to have its normal interpretation. The following symbols require explanation; '@' is to be interpreted as a symbol for any number of any propositional variables.It is not a metasymbol however and is uninterpreted in a pure calculus. '(@)' is a symbol for a string of universal quantifiers. 'f'' is to be interpreted as a variable for a truth functor of n argument places. When followed by a string of variables, n is equal to the number of distict variables.When followed by @ the number of argument places is left indeterminate.