Quantum eigenlogic observables applied to the study of fuzzy behaviour of Braitenberg vehicle quantum robots

Abstract

Purpose The purpose of this paper is to apply the quantum “eigenlogic” formulation to behavioural analysis. Agents, represented by Braitenberg vehicles, are investigated in the context of the quantum robot paradigm. The agents are processed through quantum logical gates with fuzzy and multivalued inputs; this permits to enlarge the behavioural possibilities and the associated decisions for these simple vehicles. Design/methodology/approach In eigenlogic, the eigenvalues of the observables are the truth values and the associated eigenvectors are the logical interpretations of the propositional system. Logical observables belong to families of commuting observables for binary logic and many-valued logic. By extension, a fuzzy logic interpretation is proposed by using vectors outside the eigensystem of the logical connective observables. The fuzzy membership function is calculated by the quantum mean value (Born rule) of the logical projection operators and is associated to a quantum probability. The methodology of this paper is based on quantum measurement theory. Findings Fuzziness arises naturally when considering systems described by state vectors not in the considered logical eigensystem. These states correspond to incompatible and complementary systems outside the realm of classical logic. Considering these states allows the detection of new Braitenberg vehicle behaviours related to identified emotions; these are linked to quantum-like effects. Research limitations/implications The method does not deal at this stage with first-order logic and is limited to different families of commuting logical observables. An extension to families of logical non-commuting operators associated to predicate quantifiers could profit of the “quantum advantage” due to effects such as superposition, parallelism, non-commutativity and entanglement. This direction of research has a variety of applications, including robotics. Practical implications The goal of this research is to show the multiplicity of behaviours obtained by using fuzzy logic along with quantum logical gates in the control of simple Braitenberg vehicle agents. By changing and combining different quantum control gates, one can tune small changes in the vehicle’s behaviour and hence get specific features around the main basic robot’s emotions. Originality/value New mathematical formulation for propositional logic based on linear algebra. This methodology demonstrates the potentiality of this formalism for behavioural agent models (quantum robots).