Questions in Propositional Logic

Abstract

In the previous chapter we introduced the fundamental ideas of inquisitive logic. These ideas are general, and can be used to build many specific logical systems in which we can formalize both statements and questions. One way to build such systems is to start with a system of classical logic and extend it to an inquisitive system in two steps. In the first step, we re-implement the classical system by giving it a support semantics. In executing this step, we make sure our semantics satisfies the Truth-Support Bridge: as we discussed in Sect. 2.2, this guarantees that the original logic of statements is preserved. In the second step, we extend the language with question-forming operators, which can be interpreted naturally in the context of a support semantics. The result is an inquisitive system which is conservative over the original logic. The strategy is illustrated in Fig. 3.1.