Contextual Query Using Bell Tests

Self Cite

Considering links between logic and physics is important because of the fast development of quantum information technologies in our everyday life. This paper discusses a new method in logic inspired from quantum theory using operators, named Eigenlogic. It expresses logical propositions using linear algebra. Logical functions are represented by operators and logical truth tables correspond to the eigenvalue structure. It extends the possibilities of classical logic by changing the semantics from the Boolean binary alphabet { 0 , 1 } using projection operators to the binary alphabet { + 1 , − 1 } employing reversible involution operators. Also, many-valued logical operators are synthesized, for whatever alphabet, using operator methods based on Lagrange interpolation and on the Cayley–Hamilton theorem. Considering a superposition of logical input states one gets a fuzzy logic representation where the fuzzy membership function is the quantum probability given by the Born rule. Historical parallels from Boole, Post, Poincaré and Combinatory Logic are presented in relation to probability theory, non-commutative quaternion algebra and Turing machines. An extension to first order logic is proposed inspired by Grover’s algorithm. Eigenlogic is essentially a logic of operators and its truth-table logical semantics is provided by the eigenvalue structure which is shown to be related to the universality of logical quantum gates, a fundamental role being played by non-commutativity and entanglement.

Section: Discussionmentioning

confidence: 99%

Section: Pauli and Weyl-heisenberg Operators And Their Semantic And Smentioning

confidence: 99%

Adapting Logic to Physics: The Quantum-Like Eigenlogic Program

Toffano

Dubois

2020

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“…Document relevance to the query could be measured as a document vector’s projection to the query plane built by two query words. In [ 9 , 10 ], Bell’s test was used to assess the entanglement of words from a query in English texts as a measure of document relevance.…”

Section: Introductionmentioning

confidence: 99%

Applying the Bell’s Test to Chinese Texts

Bessmertny

Huang

Platonov

et al. 2020

Search engines are able to find documents containing patterns from a query. This approach can be used for alphabetic languages such as English. However, Chinese is highly dependent on context. The significant problem of Chinese text processing is the missing blanks between words, so it is necessary to segment the text to words before any other action. Algorithms for Chinese text segmentation should consider context; that is, the word segmentation process depends on other ideograms. As the existing segmentation algorithms are imperfect, we have considered an approach to build the context from all possible n-grams surrounding the query words. This paper proposes a quantum-inspired approach to rank Chinese text documents by their relevancy to the query. Particularly, this approach uses Bell’s test, which measures the quantum entanglement of two words within the context. The contexts of words are built using the hyperspace analogue to language (HAL) algorithm. Experiments fulfilled in three domains demonstrated that the proposed approach provides acceptable results.

“…Nowadays, quantum-like modeling is widely used in mathematical modeling in cognitive science, psychology, decision-making, game theory, economics and finances, social and political sciences (see, for example, monographs [ 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 ] and a few representative papers [ 24 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 , 36 , 37 , 38 ]). These applications are typically based on the use of quantum probabilistic calculus, instead of the classical one.…”

Section: Introductionmentioning

confidence: 99%

“…For example, such data can violate the classical formula of total probability and this violation can be mathematically expressed in the form of quantum interference. Some cognitive experiments demonstrating violation of the Bell type inequalities have been performed [ 35 , 36 , 37 , 38 ]. The violation can be interpreted as contextuality of mental observables represented as questions or tasks.…”

Section: Introductionmentioning

confidence: 99%

On Interpretational Questions for Quantum-Like Modeling of Social Lasing

Khrennikov

Alodjants

Трофимова

et al. 2018

The recent years were characterized by increasing interest to applications of the quantum formalism outside physics, e.g., in psychology, decision-making, socio-political studies. To distinguish such approach from quantum physics, it is called quantum-like. It is applied to modeling socio-political processes on the basis of the social laser model describing stimulated amplification of social actions. The main aim of this paper is establishing the socio-psychological interpretations of the quantum notions playing the basic role in lasing modeling. By using the Copenhagen interpretation and the operational approach to the quantum formalism, we analyze the notion of the social energy. Quantum formalizations of such notions as a social atom, s-atom, and an information field are presented. The operational approach based on the creation and annihilation operators is used. We also introduce the notion of the social color of information excitations representing characteristics linked to lasing coherence of the type of collimation. The Bose–Einstein statistics of excitations is coupled with the bandwagon effect, one of the basic effects of social psychology. By using the operational interpretation of the social energy, we present the thermodynamical derivation of this quantum statistics. The crucial role of information overload generated by the modern mass-media is emphasized. In physics laser’s resonator, the optical cavity, plays the crucial role in amplification. We model the functioning of social laser’s resonator by “distilling” the physical scheme from connection with optics. As the mathematical basis, we use the master equation for the density operator for the quantum information field.