Overview

The data we tend to be interested in in semantics is inference judgment data. We can view an inference as being a pair of expressions of the language (or utterances of such expressions)—\(E_{1}\) and \(E_{2}\)—where \(E_{2}\) is generally a declarative sentence. In that case, we can ask if using \(E_{1}\) triggers an inference that \(E_{2}\) is true. If it does, then we say that \(E_{2}\) is an inference of \(E_{1}\) (or of an utterance of \(E_{1}\)).

There are four kinds of inference that we’d like to be able to classify. These are:

Each of these kinds of inference can itself be viewed as a relation between expressions, or utterances of expressions. For example, we can say that sentence 1 entails sentence 2, or that it conversationally implicates it. Strictly speaking, it is really an utterance of a sentence that would trigger a conversational implicature—one wherefrom it is assumed that the person making the utterance is following certain conversational principles—but linguists often say that a sentence triggers a conversational implicature as a shorthand to mean that utterances of the sentence tend to give rise to the implicature.

Likewise, expressions of different syntactic categories can presuppose certain sentences, or they can conventionally implicate them.