An Introduction to Formal Semantics

When people talk, they generally talk about things, events, and situations in the world. They are able to do this because they represent connections between the expressions of their language and extra-linguistic phenomena in a fully systematic way. The meaning of a sentence in a language is, to a large extent, dependent upon the ways in which the words and phrases from which it is constructed can be related to situations in the world. Speakers of a language are able to communicate effectively with each other because they have internalized the same rules for pairing the lexical items of the language with non-linguistic elements, and they use the same procedures for computing the meaning of a syntactically complex phrase from the meanings of its parts. Therefore, speakers will, in general, converge on the same sets of possible language–world connections which they assign to the sentences in their discourse. Formal semanticists seek to understand this aspect of linguistic meaning by constructing precise mathematical models of the principles that speakers use to define those relations between expressions in a natural language and the world which support meaningful discourse. Consider an example. Assume that two students in a class are discussing the class’s progress on a term paper. One student asserts (1a) and the second responds with (1b).