We characterize the class of quantum measurements that matches the applications of quantum theory to cognition (and decision making) - quantum-like modeling. Projective measurements describe the canonical measurements of the basic observables of quantum physics. However, the combinations of the basic cognitive effects, such as the question order and response replicability effects, cannot be described by projective measurements. We motivate the use of the special class of quantum measurements, namely {\it sharp repeatable non-projective measurements} - ${\cal SR\bar{P}}. $ This class is practically unused in quantum physics. Thus, physics and cognition explore different parts of quantum measurement theory. Quantum-like modeling isn't automatic borrowing of the quantum formalism. Exploring the class ${\cal SR\bar{P}}$ highlights the role of {\it noncommutativity of the state update maps generated by measurement back action.} Thus, ``non-classicality'' in quantum physics as well as quantum-like modeling for cognition is based on two different types of noncommutativity, of operators (observables) and instruments (state update maps): {\it observable-noncommutativity} vs. {\it state update-noncommutativity}. We speculate that distinguishing quantum-like properties of the cognitive effects are the expressions of the latter, or possibly both.

The past few years have seen a surge in the application of quantum theory methodologies and quantum-like modeling in fields such as cognition, psychology, and decision-making. Despite the success of this approach in explaining various psychological phenomena such as order, conjunction, disjunction, and response replicability effects there remains a potential dissatisfaction due to its lack of clear connection to neurophysiological processes in the brain. Currently, it remains a phenomenological approach. In this paper, we develop a quantum-like representation of networks of communicating neurons. This representation is not based on standard quantum theory but on generalized probability theory (GPT), with a focus on the operational measurement framework. Specifically, we use a version of GPT that relies on ordered linear state spaces rather than the traditional complex Hilbert spaces. A network of communicating neurons is modeled as a weighted directed graph, which is encoded by its weight matrix. The state space of these weight matrices is embedded within the GPT framework, incorporating effect observables and state updates within the theory of measurement instruments a critical aspect of this model. This GPT based approach successfully reproduces key quantum-like effects, such as order, non-repeatability, and disjunction effects (commonly associated with decision interference). Moreover, this framework supports quantum-like modeling in medical diagnostics for neurological conditions such as depression and epilepsy. While this paper focuses primarily on cognition and neuronal networks, the proposed formalism and methodology can be directly applied to a wide range of biological and social networks.

In this work we initiate the study of the correspondence between p-adic statistical field theories (SFTs) and neural networks (NNs). In general quantum field theories over a p-adic spacetime can be formulated in a rigorous way. Nowadays these theories are considered just mathematical toy models for understanding the problems of the true theories. In this work we show these theories are deeply connected with the deep belief networks (DBNs). Hinton et al. constructed DBNs by stacking several restricted Boltzmann machines (RBMs). The purpose of this construction is to obtain a network with a hierarchical structure (a deep learning architecture). An RBM corresponds to a certain spin glass, we argue that a DBN should correspond to an ultrametric spin glass. A model of such a system can be easily constructed by using p-adic numbers. In our approach, a p-adic SFT corresponds to a p-adic continuous DBN, and a discretization of this theory corresponds to a p-adic discrete DBN. We show that these last machines are universal approximators. In the p-adic framework, the correspondence between SFTs and NNs is not fully developed. We point out several open problems.

We present a new experiment demonstrating destructive interference in customers' estimates of conditional probabilities of product failure. We take the perspective of a manufacturer of consumer products, and consider two situations of cause and effect. Whereas individually the effect of the causes is similar, it is observed that when combined, the two causes produce the opposite effect. Such negative interference of two or more reasons may be exploited for better modeling the cognitive processes taking place in the customers' mind. Doing so can enhance the likelihood that a manufacturer will be able to design a better product, or a feature within it. Quantum probability has been used to explain some commonly observed deviations such as question order and response replicability effects, as well as in explaining paradoxes such as violations of the sure-thing principle, and Machina and Ellsberg paradoxes. In this work, we present results from a survey conducted regarding the effect of multiple observed symptoms on the drivability of a vehicle. We demonstrate that the set of responses cannot be explained using classical probability, but quantum formulation easily models it, as it allows for both positive and negative "interference" between events. Since quantum formulism also accounts for classical probability's predictions, it serves as a richer paradigm for modeling decision making behavior in engineering design and behavioral economics.

Order effects occur when judgments about a hypothesis's probability given a sequence of information do not equal the probability of the same hypothesis when the information is reversed. Different experiments have been performed in the literature that supports evidence of order effects. We proposed a Bayesian update model for order effects where each question can be thought of as a mini-experiment where the respondents reflect on their beliefs. We showed that order effects appear, and they have a simple cognitive explanation: the respondent's prior belief that two questions are correlated. The proposed Bayesian model allows us to make several predictions: (1) we found certain conditions on the priors that limit the existence of order effects; (2) we show that, for our model, the QQ equality is not necessarily satisfied (due to symmetry assumptions); and (3) the proposed Bayesian model has the advantage of possessing fewer parameters than its quantum counterpart.

The concepts developed by Chilean psychoanalyst Ignacio Matte Blanco in his books (Matte Blanco, 1980, 1988) represent the first attempt to formalize ideas that Sigmund Freud introduced in his book'The Interpretation of Dreams' (2011) and then elaborated on his later paper'The Unconscious'(1915). Matte Blanco's work presents the basis of a scientific discipline that takes a mathematical approach to psychoanalysis-Computational Psychoanalysis. Previous work on this topic has mainly dealt with the application of the p-adic model (Khrennikov, 2002), ultrametric topology (Murtagh, 2012; Lauro-Grotto, 2008), and the utilization of grupoid theory to Bi-logic concepts (Iurato, 2014). The author intends to present a new mathematical (logical) model that could formally describe phenomena that represent the fundamental characteristics of the unconscious psyche. In the first part of this paper, we give a short overview of the most important concepts and conclusions of Matte Blanco. The second part of the paper is designed to present the fundamental concepts of quantum logic and to explain the concept of Hilbert space which represents the'basis' for the quantum-logical system. Eventually, in the third part of the paper, we deal with the interpretation of the phenomena and concepts from Bi-logic in the context of quantum logic.

Formalisms inspired by Quantum theory have been used in Cognitive Science for decades. Indeed, Quantum-Like (QL) approaches provide descriptive features that are inherently suitable for perception, cognition, and decision processing. A preliminary study on the feasibility of a QL robot perception model has been carried out for a robot with limited sensing capabilities. In this paper, we generalize such a model for multi-sensory inputs, creating a multidimensional world representation directly based on sensor readings. Given a 3-dimensional case study, we highlight how this model provides a compact and elegant representation, embodying features that are extremely useful for modeling uncertainty and decision. Moreover, the model enables to naturally define query operators to inspect any world state, which answers quantifies the robot's degree of belief on that state.

The paper describes an algorithm for cognitive representation of triples of related behavioral contexts two of which correspond to mutually exclusive states of some binary situational factor while uncertainty of this factor is the third context. The contexts are mapped to vector states in the two-dimensional quantum Hilbert space describing a dichotomic decision alternative in relation to which the contexts are subjectively recognized. The obtained triad of quantum cognitive representations functions as a minimal carrier of semantic relations between the contexts, which are quantified by phase relations between the corresponding quantum representation states. The described quantum model of subjective semantics supports interpretable vector calculus which is geometrically visualized in the Bloch sphere view of quantum cognitive states.

We mathematically model Ignacio Matte Blanco's principles of symmetric and asymmetric being through use of an ultrametric topology. We use for this the highly regarded 1975 book of this Chilean psychiatrist and pyschoanalyst (born 1908, died 1995). Such an ultrametric model corresponds to hierarchical clustering in the empirical data, e.g. text. We show how an ultrametric topology can be used as a mathematical model for the structure of the logic that reflects or expresses Matte Blanco's symmetric being, and hence of the reasoning and thought processes involved in conscious reasoning or in reasoning that is lacking, perhaps entirely, in consciousness or awareness of itself. In a companion paper we study how symmetric (in the sense of Matte Blanco's) reasoning can be demarcated in a context of symmetric and asymmetric reasoning provided by narrative text.

We try to perform geometrization of psychology by representing mental states, <>, by points of a metric space, <>. Evolution of ideas is described by dynamical systems in metric mental space. We apply the mental space approach for modeling of flows of unconscious and conscious information in the human brain. In a series of models, Models 1-4, we consider cognitive systems with increasing complexity of psychological behavior determined by structure of flows of ideas. Since our models are in fact models of the AI-type, one immediately recognizes that they can be used for creation of AI-systems, which we call psycho-robots, exhibiting important elements of human psyche. Creation of such psycho-robots may be useful improvement of domestic robots. At the moment domestic robots are merely simple working devices (e.g. vacuum cleaners or lawn mowers) . However, in future one can expect demand in systems which be able not only perform simple work tasks, but would have elements of human self-developing psyche. Such AI-psyche could play an important role both in relations between psycho-robots and their owners as well as between psycho-robots. Since the presence of a huge numbers of psycho-complexes is an essential characteristic of human psychology, it would be interesting to model them in the AI-framework.