Human reasoning involving quantified statements is one area in which findings from cognitive psychology and linguistic pragmatics complement each other. This article shows how mental models theory provides a promising account of the mechanisms underlying peoples’ performance in three types of reasoning tasks involving quantified premises and conclusions. It further suggests that relevance theory can help to explain the way in which mental models are employed in the reasoning processes. Conversely, mental models theory suggests that human reasoning typically does not involve deductive rules, which in turn entails a modification to the nature of the deductive processes proposed by relevance theory. The mechanism proposed by mental models theory also helps to clarify the nature of the relevance theory distinction between conceptual and procedural information.