ABSTRACT
In this part of the book we shall examine what happens when modal logic is combined with the Lower Predicate Calculus. We shall assume that readers are familiar with the ordinary non-modal LPC (as we shall refer to it) but we shall make our development self-contained, and explain all our terminology as we proceed.1 In essence the predicate calculus extends the propositional calculus by the addition of symbols which enable us to speak about 'all' or 'some' things which satisfy a certain condition. These symbols are called quantifiers. The symbol V is used to say that everything satisfies a certain condition and is called the universal quantifier, while the symbol 3 is used to say that there exists something which satisfies a certain condition and is called the existential quantifier. Each can be defined in terms of the other, and we shall set out a version of LPC which takes V as primitive.
