This paper approaches the question of how to describe the higher-level internal structures and representations of cognitive systems across various kinds of nonhuman (neuro)cognitive systems. While much research in cognitive (neuro)science and comparative cognition is dedicated to the exploration of the (neuro)cognitive mechanisms and processes with a focus on brain-behavior relations across different non-human species, not much has been done to connect (neuro)cognitive mechanisms and processes and the associated behaviors to plausible higher-level structures and representations of distinct kinds of cognitive systems in non-humans. Although the study of (neuro)cognitive mechanisms and processes can certainly be revealing, (neuro)cognitive mechanisms and processes are underspecified with respect to internal structures and representations of non-human cognitive systems because multiple such mechanisms can target, or be mapped onto, the same internal structure or vice versa. This paper outlines a biosemiotic approach to this linking problem in order to bridge the gap between functions of (neuro)cognitive systems in different species and the higher-level cognitive structures and representations. It is contended that the higher-level internal structures and representations of various cognitive systems are biosemiotic constraints on the (biological) functions of (neuro)cognitive systems that serve to restrict the range of functions (neuro)cognitive systems have or are selected for. This turns out to have implications for issues on the convergent evolution of cognitive traits. © 2020, Springer Nature B.V.