Introduction

14.1.1 In this chapter we will start to look at quantified normal modal logics. These come in two varieties: constant domain (where the domain of quantification is the same in all worlds), and variable domain (where the domain may vary from world to world).

14.1.2 Where it is necessary to distinguish between the two, I will use the following notation. If S is any system of propositional modal logic, CS will denote the constant domain quantified version, and VS will denote the variable domain quantified version.

14.1.3 In this chapter we will look at the semantics and tableaux for constant domain logics, saving variable domains for the next.

14.1.4 For these two chapters we will take it that identity is not part of the language. We will turn to the topic of identity in modal logic in chapter 16.

14.1.5 We will also take a quick look at one of the major philosophical issues to which quantified modal logic gives rise: the issue of essentialism.

14.1.6 The chapter ends by showing how the semantic and tableau techniques of normal modal logic extend to tense logic.

Constant Domain K

14.2.1 The syntax of quantified modal logic augments the language of first order classical logic (12.2) with the operators □ and ◇, as propositional modal logic extends classical propositional logic (2.3.1, 2.3.2).