آیا شبکه های بیزی کوانتومی قوی تر از شبکه های بیزی کلاسیک هستند؟ Are quantum-like Bayesian networks more powerful than classical Bayesian networks?

1. Introduction The task of determining human judgments under uncertainty has got increasing attention in the scientific literature in the last decade (Moreira & Wichert, 2016b). More specifically, several models that are capable to predict or explain human decisions that are inconsistent with the laws of classical probability theory and logic (Crosson, 1999; Kuhberger, Komunska, & Josef, 2001; Lambdin & Burdsal, 2007; Tversky & Shafir, 1992) have been recently proposed. These models turn to quantum probability to explain human decision-making and are part of a new emerging discipline called Quantum Cognition (Busemeyer, 2015; Wang, Busemeyer, Atmanspacher, & Pothos, 2013). Recent research shows that quantum-based probabilistic models are able to explain and predict scenarios that cannot be explained by pure classical models (Bruza,Wang,&Busemeyer, 2015; Busemeyer & Wang, 2015). However, there is still a big resistance in the scientific literature to accept these quantum-based models. Many researchers believe that one can model scenarios that violate the laws of probability and logic through classical probabilistic decision models that are often used in machine learning (Murphy, 2012). These violations of the laws of probability theory are hard to explain through classical theory and can have different types: violations to the Sure Thing Principle (Savage, 1954), disjunction/conjunction errors (Tversky & Kahneman, 1983), Ellsberg (Ellsberg, 1961)/Allais (Allais, 1953) paradoxes, order effects (Sudman & Bradburn, 1974), etc. To accommodate these violations, several quantum-like models have been proposed in the literature. Note that, the term quantumlike is simply the designation that it is used to refer to any model that is applied in the domains outside of physics and that use the mathematical formalisms of quantum mechanics, abstracting them from any physical meaning and interpretations. Although, the quantum cognition field is recent in the literature, there have been several different quantum-like models proposed in the literature. These models range from dynamical models (Busemeyer, Wang, & Lambert-Mogiliansky, 2009; Busemeyer, Wang, & Townsend, 2006; Pothos & Busemeyer, 2009), which make use of unitary operators to describe the time evolution since a participant is given a problem (or asked a question), until he/she makes a decision, to models that are based on contextual probabilities (Aerts & Aerts, 1994; Khrennikov, 2009b; Yukalov & Sornette, 2011). Quantum-like dynamical models have also been proposed in the literature to accommodate violations to the Prisoner’s Dilemma Game (Pothos & Busemeyer, 2009), study the evolution of the interaction of economical agents in markets (Haven & Khrennikov, 2013; Khrennikov, 2009a) or even to specify a formal description of dynamics of epigenetic states of cells interacting with an environment (Asano et al., 2013). On the other hand, quantum-like models based on contextual probabilities, explore the application of complex probability amplitudes to define contexts that can interfere with the decision-maker (Khrennikov, 2005b, 2009b, 0000). For a survey about the applications of quantum-like models for the Sure Thing Principle, the reader can refer to Moreira and Wichert (2016b).