jats:titleAbstract</jats:title>jats:pIn this theoretical paper, we consider the notion of semantic competence and its relation to general language understanding—one of the most sough-after goals of Artificial Intelligence. We come back to three main accounts of competence involving (a) lexical knowledge; (b) truth-theoretic reference; and (c) causal chains in language use. We argue that all three are needed to reach a notion of meaning in artificial agents and suggest that they can be combined in a single formalisation, where competence develops from exposure to observable performance data. We introduce a theoretical framework which translates set theory into vector-space semantics by applying distributional techniques to a corpus of utterances associated with truth values. The resulting meaning space naturally satisfies the requirements of a causal theory of competence, but it can also be regarded as some ‘ideal’ model of the world, allowing for extensions and standard lexical relations to be retrieved.</jats:p>