## Quantum Cognition

is a research field that applies ideas from quantum physics and quantum information science in order to develop radically new models of a variety of cognitive phenomena ranging from human memory, information retrieval, and human language to decision making, social interaction, personality psychology, and philosophy of mind.

The initial motivation for this new research field is quite simple and rather unmysterious. It has to do with the assumed algebraic structure of the inner world of ideas, concepts, and propositions. Boole and other great logicians of the 19th century assumed that thinking is like doing regular algebra in following strict rules exhibiting associative, distributive and commutative properties. These are the same rules we can observe when we consider the construction of sets by using union, intersection and complementation (Boolean algebra). However, modern cognitive psychology has challenged this view: natural concepts are based on prototypes. As such, natural concepts are geometrical concepts that best can be represented by convex sets (Gärdenfors). The algebra underlying the operation with convex sets is different from the traditional Boolean algebra and, surprisingly, it comes close to the orthoalgebra underlying quantum mechanics.

Based on work of the great Hungarian mathematician and philosopher John von Neumann it has become visible that the heart of quantum theory is a new kind of probability theory based on ortho-algebras rather than Boolean algebras. This theory is more general than the traditional (Boolean-based) probability theory. Interestingly, this approach seems to be powerful enough to solve some hard puzzles known from standard approaches to rationality, logical thinking, and probabilistic reasoning. This opens new horizons for cognitive modeling and their rational foundation.

In the present literature, there are several approaches that seek for
a general justification of quantum probabilities in the context of
cognitive science. For example, Kitto (2008) considers very complex
systems such as the growth and evolution of natural languages and other
cultural systems
and argues that the description of such systems cannot be separated from
their context of interaction. She argues that quantum interaction
formalisms provide a natural model of these systems “because a mechanism
for dealing with such contextual dependency is inbuilt into the quantum
formalism itself”. Hence, the question of why quantum interaction is

necessary in modelling cognitive phenomena is answered by referring to
its nature as a complex
epistemic system.

In their recent book, Busemeyer and Bruza (2012), give several arguments why quantum models are necessary for cognition. Some arguments relate to the cognitive mechanism of judgments. Judgments normally do not take place in definite situations. Rather, judgments create the context where they take place. This is the dynamic aspect of judgments also found in dynamic models of meaning. Another is the logical aspect. The logic of judgments does not obey classical logic. Rather, the underlying logic is very strange with asymmetric conjunction and disjunction operations. When it comes to considering probabilities and conditioned probabilities the principle of unicity is violated, i.e. it is impossible to assume a single sample space with a fixed probability distribution for judging all possible events.

Another line of argumentation seeks to answer the question of “why
quantum models of cognition” by speculating about implications for brain
neurophysiology. In the taken algebraic
approach, even classical dynamical systems such as neural networks,
could exhibit quantum-like properties in the case of coarse-graining
measurements, when testing a property cannot distinguish between
epistemically equivalent states (beim Graben 2004). In neuroscience,
most measurements, such as electroencephalography or magnetic resonance
imaging, are coarse-grainings in this sense. Thus, the quantum approach
to cognition has direct implications for brain neurophysiology, without
needing to refer to a “quantum
brain”. A novel application of this idea using
Hebbian neurodynamics as an underlying classical system to describe
emerging properties that exhibit quantum-like traits is given by de
Barros and Suppes (2009) and Blutner and beim Graben (2015).

In the themes section
several applications of the new approach may be
found. Most of these application exploit the close analogy between ideas from quantum theory and
crucial traits of the cognitive machinery.

last update: February 2015