Institute for Mathematical Behavioral Sciences

Instances of non-commutativity are pervasive in human behavior. In this paper, we suggest that psychological properties such as attitudes, values, preferences and beliefs may be suitably described in terms of the mathematical formalism of quantum mechanics i.e., non-classical or quantum logic. We expose the foundations of non-classical measurement theory building on a simple notion of orthospace and ortholattice (logic). Two axioms are formulated and the characteristic state-property duality is derived. A last axiom concerned with the impact of measurement on the state takes us with a leap toward the Hilbert space model of Quantum Mechanics. An application to social sciences is then proposed. First we suggest an interpretation of the basic axioms and properties for human behavior. We next develop a decision theoretical example and indicate how non-classical measurement theory could be used to formulate a theory of actualized preferences.