Systems of Logical Systems: Neuroscience and Quantum Logic

Sisir Roy

Robert W. Baloh

Henry Pierce Stapp

Subhash C. Kak

Quantum mechanics and neuroscience come together in the problem of observation. Quantum mechanics is a nonlocal theory but the expectations of our cognitive systems are local. The principle of veiled nonlocality appears to direct not only logic and design of experiments but also the manner in which experimental data is analyzed. The principle preserves the naive classical view of the universe that is consistent with locally realistic models; it also sees underlying similitude between biological and physical processes. One idea belonging to the set of similitudes is that of quantum Darwinism according to which stable states proliferate in an interaction between quantum systems in analogy with the survival of the fittest of biological evolution. This idea is investigated.

Pier Luigi Gentili

Human interaction with the world is dominated by uncertainty. Probability theory is a valuable tool to face such uncertainty. According to the Bayesian definition, probabilities are personal beliefs. Experimental evidence supports the notion that human behavior is highly consistent with Bayesian probabilistic inference in both the sensory and motor and cognitive domain. All the higher-level psychophysical functions of our brain are believed to take the activities of interconnected and distributed networks of neurons in the neocortex as their physiological substrate. Neurons in the neocortex are organized in cortical columns that behave as fuzzy sets. Fuzzy sets theory has embraced uncertainty modeling when membership functions have been reinterpreted as possibility distributions. The terms of Bayes' formula are conceivable as fuzzy sets and Bayes' inference becomes a fuzzy inference. According to the QBism, quantum probabilities are also Bayesian. They are logical constructs rather than physical realities. It derives that the Born rule is nothing but a kind of Quantum Law of Total Probability. Wavefunctions and measurement operators are viewed epistemically. Both of them are similar to fuzzy sets. The new link that is established between fuzzy logic, neuroscience, and quantum mechanics through Bayesian probability could spark new ideas for the development of artificial intelligence and unconventional computing.