Concept Formation and Quantum-like Probability from Nonlocality in Cognition

Human decision-making is relevant for concept formation and cognitive illusions. Cognitive illusions can be explained by quantum probability, while the reason for introducing quantum mechanics is based on ad hoc bounded rationality (BR). Concept formation can be explained in a set-theoretic way, although such explanations have not been extended to cognitive illusions. We naturally expand the idea of BR to incomplete BR and introduce the key notion of nonlocality in cognition without any attempts on quantum theory. We define incomplete bounded rationality and nonlocality as a binary relation, construct a lattice from the relation by using a rough-set technique, and define probability in concept formation. By using probability defined in concept formation, we describe various cognitive illusions, such as the guppy effect, conjunction fallacy, order effect, and so on. It implies that cognitive illusions can be explained by changes in the probability space relevant to concept formation.