Foundations of Inquisitive Logic

Abstract

AbstractIn this chapter, we lay the foundations for our enterprise. In particular, we explain how an information-based semantics,inquisitive semantics, allows us to interpret statements and questions in a uniform way and to define a general notion of entailment in which questions can occur as premises and conclusions. We explore in detail the significance of this generalized notion of entailment, showing in particular that it captures as a special case an important logical notion that we calldependency. We explain how questions can be viewed as denotinginformation types and how inquisitive entailment can thus be seen as generalizing entailment from a notion relating pieces of informations to one relating information types. We also show how a logic based on inquisitive semantics can be equipped in a canonical way with an implication connective that internalizes, in a precise sense, the meta-language entailment relations into the object language. At the end of the section we motivate in more detail some of our setup choices and we relate our approach to previous work on questions in logic.