Abstract
We propose and discuss a formal semantics for predicative languages in terms of cognitively meaningful structures, that is, in terms of the framework of conceptual spaces introduced by Gärdenfors. The motivation of this paper is twofold: on the one hand, we associate predicative languages, a fundamental tool in logic and knowledge representation, to a cognitive semantics to investigate logical inferences on a cognitive base; on the other hand, by investigating conceptual spaces as a semantic framework for predicative languages, we highlight and approach a number of issues that are problematic for the theory of conceptual spaces. These issues emerge from the attempt of providing the basic elements of a predicative language - such as individual constants, unary predicates, relations, and logical connectives - with a conceptual counterpart.