A mathematical theory of sign-mediated concept formation

Cognitive theories of concept formation have usually ignored the fact that, as a natural part of their cognitive development, people form concepts through the linguistic mediation of signs. In this paper, we propose a mathematical theory of sign-mediated concept formation (SMCF). This theory relies heavily on ideas from category theory, specifically the ideas of pushout and pullback. The theory addresses some of the major problems in modeling concept formation, including family resemblance and contextuality, and has potential applications for a wide variety of tasks involving concept computation.