7. Model-theoretic semantics
Thomas Ede Zimmermann · 2019
Model-theoretic semantics is a special form of truth-conditional semantics. According to it, the truth-values of sentences depend on certain abstract objects called models. Understood in this way, models are mathematical structures that provide the interpretations of the (non-logical) lexical expressions of a language and determine the truth-values of its (declarative) sentences. Originally designed for the semantic analysis of mathematical logic, model-theoretic semantics has become a standard tool in linguistic semantics, mostly through the impact of Richard Montague’s seminal work on the analogy between formal and natural languages. As such, it is frequently (and loosely) identified with possible worlds semantics, which rests on an identification of sentence meanings with regions in Logical Space, the class of all possible worlds. In fact, the two approaches have much in common and are not always easy to keep apart. In a sense, (i) model-theoretic semantics can be thought of as a restricted form of possible worlds semantics, where models represent possible worlds; in another sense, (ii) model-theoretic semantics can be seen as a wild generalization of possible worlds semantics, treating Logical Space as variable rather than given. Consequently, the present introductory exposition of model-theoretic semantics also covers possible worlds semantics - hopefully helping to disentangle the relationship between the two approaches. It starts with a general discussion of truth-conditional semantics (section 1), the main purpose of which is to provide some motivation and background. Model- theoretic semantics is then approached from the possible worlds point of view (section 2), highlighting the similarities between the two approaches that give rise to perspective (i). The final section 3 turns to model theory as providing a mathematical reconstruction of possible worlds semantics, ultimately arriving at the more abstract perspective (ii).