Grice (1957) defined
conventional implicatures as inferences that are simply attached by convention to particular lexical
items or expressions. Levinson (1983, 2000) outlined the distinctive properties of
conventional implicatures. However, both Grice and Levinson failed to pin down the way in which conventional implicatures are derived. This paper employs three types of mappings in Space Mapping Theory (Fauconnier 1985/1994, 1997) to uncover the cognitive processes in which conventional implicatures are calculated. Fauconnier's Access Principle delineates the interlocutor's cognitive strategy of using one concept in one mental space to refer to and consequently trigger another concept in a different mental space. The authors show that the Access Principle relies on the conventional ties between concepts whereby the hearer generates conventional implicatures in the mapping of one concept from one mental space to another associated mental space. This paper starts with the exploration of the theoretical sources of Space Mapping Theory, and proceeds to describe the roles three types of mappings play in triggering conventional implicatures.