Alternatives in Montague grammar

The type theoretic framework for natural language semantics laid out by Montague (1973) forms the cornerstone of formal semantics. Hamblin (1973) proposed an extension of Montague’s basic framework, referred to as alternative semantics. In this framework, the meaning of a sentence is not taken to be a single proposition, but rather a set of propositions—a set of alternatives. While this more fine-grained view on meaning has led to improved analyses of a wide range of linguistic phenomena, it also faces a number of problems. We focus here on two of these, in our view the most fundamental ones. The first has to do with how meanings are composed, i.e., with the type-theoretic operations of function application and abstraction; the second has to do with how meanings are compared, i.e., the notion of entailment. Our aim is to reconcile what we take to be the essence of Hamblin’s proposal with the solid type-theoretic foundations of Montague grammar, in such a way that the observed problems evaporate. Our proposal partly builds on insights from recent work on inquisitive semantics (Ciardelli et al. 2013), and it also further advances this line of work, specifying how the inquisitive meaning of a sentence, as well as the set of alternatives that it introduces, may be built up compositionally.