  Quantum mechanics emerged as the result of a successful resolution of
stringent empirical and profound conceptual conflicts within the development of
atomic physics at the beginning of the last century. At first glance, it seems
to be bizarre and even ridiculous to apply ideas of quantum physics in order to
improve current psychological and linguistic or semantic ideas. However, a
closer look shows that there are some parallels in the development of quantum
physics and advanced theories of cognitive science. In psychology, geometric
models of meaning have a long tradition. However, they suffer from many
shortcomings which are illustrated by discussing several puzzles of bounded
rationality. In the first part of this article, we argue that the present
account of quantum cognition - taking quantum probabilities rather than
classical probabilities - can give a more systematic description of these
puzzles than the alternate and rather eclectic treatments in the traditional
framework of bounded rationality. Unfortunately, the quantum probabilistic
treatment does not always and does not automatically provide a deeper
understanding and a true explanation of these puzzles. In the second part of
this article, we explain the foundational issue from the perspective of Piron,
Foulis, Randall, and others, and we apply it to the foundation of quantum
cognition. In this connection, we show that quantum probabilities are of
(virtual) conceptual necessity if grounded in an abstract algebraic framework
of orthomodular lattices. This framework is motivated by assuming partial
Boolean algebras (describing particular perspectives) that are combined into a
uniform system while considering certain capacity restrictions. It is at this
point that one important aspect of the whole idea of bounded rationality
directly enters the theoretical scenery of quantum cognition: resource
limitation.
