We consider several puzzles of bounded rationality. These include the Allais- and Ellsberg paradox, the disjunction effect, and related puzzles. 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 treatments in the traditional frameworks of bounded rationality. Unfortunately, the quantum probabilistic treatment does not always provide a deeper understanding and a true explanation of these puzzles. One reason is that quantum approaches introduce additional (...) parameters which possibly can be fitted to empirical data but which do not necessarily explain them. Hence, the phenomenological research has to be augmented by responding to deeper foundational issues. In this article, we make the general distinction between foundational and phenomenological research programs, explaining the foundational issue of quantum cognition from the perspective of operational realism. This framework is motivated by assuming partial Boolean algebras. They are combined into a uniform system via a mechanism preventing the simultaneous realization of perspectives. Gleason’s theorem then automatically leads to a distinction between probabilities that are defined by pure states and probabilities arising from the statistical mixture of pure states. This formal distinction relates to the conceptual distinction between risk and ignorance. Another outcome identifies quantum aspects in dynamic macro-systems using the framework of symbolic dynamics. Finally, we discuss several ideas that are useful for justifying complementarity in cognitive systems. (shrink)

Classical cognitive science assumes that intelligently behaving systems must be symbol processors that are implemented in physical systems such as brains or digital computers. By contrast, connectionists suppose that symbol manipulating systems could be approximations of neural networks dynamics. Both classicists and connectionists argue that symbolic computation and subsymbolic dynamics are incompatible, though on different grounds. While classicists say that connectionist architectures and symbol processors are either incompatible or the former are mere implementations of the latter, connectionists reply that neural (...) networks might be incompatible with symbol processors because the latter cannot be implementations of the former. In this contribution, the notions of 'incompatibility' and 'implementation' will be criticized to show that they must be revised in the context of the dynamical system approach to cognitive science. Examples for implementations of symbol processors that are incompatible with respect to contextual topologies will be discussed. (shrink)

By means of an intriguing physical example, magnetic surface swimmers, that can be described in terms of Dennett's intentional stance, I reconstruct a hierarchy of necessary and sufficient conditions for the applicability of the intentional strategy. It turns out that the different levels of the intentional hierarchy are contextually emergent from their respective subjacent levels by imposing stability constraints upon them. At the lowest level of the hierarchy, phenomenal physical laws emerge for the coarse-grained description of open, nonlinear, and dissipative (...) non-equilibrium systems in critical states. One level higher, dynamic patterns, such as, for example, magnetic surface swimmers, are contextually emergent as they are invariant under certain symmetry operations. Again one level up, these patterns behave apparently rationally by selecting optimal pathways for the dissipation of energy that is delivered by external gradients. This is in accordance with the restated Second Law of thermodynamics as a stability criterion. At the highest level, true believers are intentional systems that are stable under exchanging their observation conditions. (shrink)

In their target article, Wang and Busemeyer (2013) discuss question order effects in terms of incompatible projectors on a Hilbert space. In a similar vein, Blutner recently presented an orthoalgebraic query language essentially relying on dynamic update semantics. Here, I shall comment on some interesting analogies between the different variants of dynamic semantics and generalized quantum theory to illustrate other kinds of order effects in human cognition, such as belief revision, the resolution of anaphors, and default reasoning that result from (...) the crucial non-commutativity of mental operations upon the belief state of a cognitive agent. (shrink)

In 1972,Ernst Ulrich and Christine von Weizs ¨acker introduced the concept of pragmatic information with three desiderata: Pragmatic information should assess the impact of a message upon its receiver;Pragmatic information should vanish in the limits of complete 'novelty 'and complete 'confirmation';Pragmatic information should exhibit non-classical properties since novelty and confirmation behave similarly to Fourier pairs of complementary operators in quantum mechanics. It will be shown how these three desiderata can be naturally fulfilled within the framework of Gardenfors' dynamic semantics of (...) Bayesian belief models.The meaning of a message is its impact upon the epistemic states of a cognitive agent. A pragmatic information measure can then be quanti .ed by the average information gain for the transition from a prior to a posterior state.Total novelty can be represented by the identical proposition, total con- .rmation by the logical consequence of propositions. In both cases, pragmatic information vanishes.For operators that are neither idempotent nor commuting, novelty and confirmation relative to a message sequence can be defined within Gardenfors' theory of belief revisions.The proposed approach is consistent with measures of relevance derived from statistical decision theory and it contains Bar-Hillel 's and Carnap's theory of semantic information as a special case. (shrink)