Материал: искусственный интеллект

is the conditional probability of having the QWebÕs state being successfully tested as being a Òstate of B,Ó when it has been successfully tested to be a Òstate of A.Ó Indeed, if the QWeb state |ψ was successfully tested to be a Òstate of A,Ó according to the projection postulate the state immediately following the test is |ψA = , which is now a Òstate of A.Ó And we have pψ (B|A) = ψA|MB |ψA , hence (38) possesses a sound interpretation as a conditional probability.

The ψ-meaning bond Mψ (A|B) of A towards B can be similarly obtained by interchanging in (37) the roles of A and B, and since in general [MA, MB ] = 0, Mψ (A|B) = Mψ (B|A), which means that the meaning bond of A towards B will not in general coincide with the meaning bond of B towards A. So, if pψA (B) and pψ (B) are interpreted as measuring how much of the meaning of B is present in the QWeb, when the latter is in state |ψA and |ψ , respectively, it is clear that

increase or decrease of the meaning presence of B when the QWeb state |ψ is further contextualized by a concept A. In that respect, we can also say that if B is more (resp., less) meaning present in the QWeb, when its state is further contextualized by a concept A, then for such state there is an attractive (resp., repulsive) meaning bond of B towards A, whereas if pψA (B) = pψ (B) the meaning bond can be said to be neutral. Also, since we have pψB (B) = 1, the meaning bond of B towards itself is Mψ (B|B) = pψ−1(B), so that there will be self-neutrality when pψ (B) = 1, and self-attraction if pψ (B) < 1 (but there cannot be self-repulsion).

We now observe that: pψ (Wj )Mψ (Wj |A) = pψ (Wj |A) = ψA|Pj |ψA = aj2, where Pj = |ej ej | is the projection operator onto the one-dimensional subspace

generated by the Ôground state of Wj ,Ó i.e., of the story-concept indicated by the speciÞc combination of words contained in the webpage Wj . Thus, we have that the

and therefore are given by (the square root of) the Òψ-meaning bond of Wj towards A,Ó normalized by the probability pψ (Wj ), and in that sense we can say that they express a meaning connection between A and the Wj . Note also that in the case

which corresponds to the more speciÞc notion of meaning bond introduced in [3] (see also [5]).

Acknowledgement This work was supported by the Marie Skłodowska-Curie Innovative Training Network 721321ÑÒQUARTZ.Ó

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Non-separability Effects in Cognitive

Semantic Retrieving

Aleksey V. Platonov, Igor A. Bessmertny, Evgeny K. Semenenko, and Alexander P. Alodjants

Abstract This paper discusses a Bell test analogue known in quantum physics, which allows determining the presence of non-separability features by using semantic search of information and document ranking for articles in Russian. The model of Bell test in semantics is based on hyperspace analogue to language (HAL) algorithm provides to obtain vector representation of words (in Hilbert space) using the dictionary index and considering the word order. We show the existence of certain quantum-like correlations between two words of the userÕs query; these correlations cannot be taken into account in the classical probabilistic description. We predict that the contextuality revealed can be regarded as human cognitive level both while writing of certain texts and queries to them.

Keywords Information retrieval systems á Decision-making á Quantum cognitive science á Quantum entanglement á Contextuality á Machine learning

1 Introduction

Over the past decade, the rapid growth of information resources in terms of information transmission and processing has led to an exponential growth of data, most of which are poorly structured or have no structure at all. The need to proceed and analyze such data in real time is a serious problem, which is directly related to the safety of society itself in various areas of economics, Þnances, and social sphere. Thematic modeling as one of the machine learning paradigms is an important tool for modern text and document analysis and has a direct application to the problems of information retrieval. On the other hand, quantum approach for information retrieving allows to take into account some peculiarities (disturbances) occurring during the ÒinteractionÓ of the user and ÒsmartÓ search system similarly to

A. V. Platonov á I. A. Bessmertny á E. K. Semenenko á A. P. Alodjants ( ) ITMO University, Saint Petersburg, Russia

D. Aerts et al. (eds.), Quantum-Like Models for Information Retrieval and Decision-Making, STEAM-H: Science, Technology, Engineering, Agriculture, Mathematics & Health, https://doi.org/10.1007/978-3-030-25913-6_2

quantum measurement paradigm [10]. As a result, it should lead to a more accurate formulation of requests context and, hence, to Þnding higher relevance of issued documents. In this regard, the model of semantic space looks very limited, as it is based on the so-called bag-of-words approach without word order consideration, when the meaning is coded by the counters of words included in the context of the object.

Quantum cognition represents one of the modern approaches taking into account the contextuality of interaction of the user and smart information system [2, 5]. Interestingly, in Ref. [4] there were the Þrst attempts to describe psychological aspects in decision-making via quantum probabilistic methods and quantum measurement theory approaches.

Nowadays, there is an increased interest in the application of quantum formalism to information retrieval problems, see, e.g., [6, 8, 9, 12, 13]. In particular, it is shown that information retrieval models such as logical, probabilistic, and vector ones, can be described with quantum formalism in Hilbert space. As a result, it is possible to take into account the contextuality of queries [8]. Notably, in [13] the authors formulate the quantum probability ranking principle, which is a generalization of a well-known probability ranking principle used to assess the criteria for ranking of issued documents considering links between documents. At the same time, to obtain the best overall search efÞciency, the information system ranks documents not only in descending order of the probability of their relevance to the user, but also considering the effects of Òquantum interference.Ó As shown in [11, 12], the analogies with quantum measurement of photon polarization considering in the framework of quantum optics paradigm are relevant here, cf. [1].

The aim of this paper is to demonstrate a quantum-like ranking algorithm using a Bell test performed with text samples given in Russian taking into account the contextuality and compatibility of different queries.

2Bell Test in the Problem of Cognitive Semantic Information Retrieval

2.1 Bell Inequality and Its Interpretation

In the problem under consideration, the most suitable toolkit is quantum theory, which originally aimed to simulate incompatible physical experiments. In such experiments a speciÞc experimental conÞguration (context) allows to consistently determine a certain set of physical quantities, which become undeÞned in another experimental conÞguration (context). In quantum cognitive science, such incompatible experimental situations correspond to incompatible cognitive contexts, the use of which in decision-making leads to violations of classical (Boolean) logic. A consequence of quantum theory is the possible occurrence of correlations between measurement results (conducted in physics over remote systems), which are stronger than allowed by classical theories with hidden parameters [7, 10].