STEAM-H: Science, Technology, Engineering,

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STEAM-H: Science, Technology, Engineering,

Agriculture, Mathematics & Health

Series Editor

Bourama Toni

Department of Mathematics

Howard University

Washington, DC, USA

This interdisciplinary series highlights the wealth of recent advances in the pure and applied sciences made by researchers collaborating between Þelds where mathematics is a core focus. As we continue to make fundamental advances in various scientiÞc disciplines, the most powerful applications will increasingly be revealed by an interdisciplinary approach. This series serves as a catalyst for these researchers to develop novel applications of, and approaches to, the mathematical sciences. As such, we expect this series to become a national and international reference in STEAM-H education and research.

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The series originated from the weekly yearlong STEAM-H Lecture series at Virginia State University featuring world-class experts in a dynamic forum. Contributions reßected the most recent advances in scientiÞc knowledge and were delivered in a standardized, self-contained and pedagogically-oriented manner to a multidisciplinary audience of faculty and students with the objective of fostering student interest and participation in the STEAM-H disciplines as well as fostering interdisciplinary collaborative research. The series strongly advocates multidisciplinary collaboration with the goal to generate new interdisciplinary holistic approaches, instruments and models, including new knowledge, and to transcend scientiÞc boundaries.

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Diederik Aerts ¥ Andrei Khrennikov

Massimo Melucci ¥ Bourama Toni

Editors

Quantum-Like Models for Information Retrieval and Decision-Making

123

https://doi.org/10.1007/978-3-030-25913-6

Mathematics Subject ClassiÞcation: 37-04, 46C99, 60B99, 37N, 81P45, 94A05, 94A17, 94A40, 81Q93, 81Q20, 81Q65, 81S05, 81S10, 81S22

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Preface

All of us are users of information access and retrieval (IAR) systems. Search engines for the World Wide Web (WWW), local or personal media repositories and mailbox search functions are some of the many examples that are becoming a preferred way of acquiring, aggregating, Þltering and interacting with multimodal information as well as of achieving certain information goals especially when interacting with people and companies.

The peculiar difÞculty of IAR is the fact that relevance cannot be precisely and exhaustively described by the data itself; for example, a relevant document may not be precisely and exhaustively described using text even if this text includes or considers all elements or aspects of a topic; a userÕs information need may not be precisely and exhaustively described using a query even if this query is a comprehensive description of the need.

Humans are adept at making reasonably robust and quick decisions about what information is relevant to them, despite the ever-increasing complexity and volume of their surrounding information environment. The literature on document relevance has identiÞed various dimensions of relevance (e.g. topicality, novelty, etc.) that evolve and interact with each other.

However, little is understood about how the dimensions of relevance may interact and how this interaction is contextual and uncertain in nature. The problem becomes more complex and challenging when processing and interacting with multimodal information (e.g. linking an image with a news article, identifying regions or objects of interest within images, tagging video and music clips, etc.), due to the semantic gap between low-level multimedia content features (e.g. pixels, colour histograms, texture, etc.) and high-level meanings as well as the interference on relevance judgements for a document caused by multimodal interactions. Therefore, the current state-of-the-art of IAR is insufÞcient to address the challenges of the dynamic, adaptive and multimodal nature of the information and user interaction context. A genuine theoretical breakthrough is on the contrary necessary.

The quantum mechanical framework may help give up the notions of unimodal features and classical ranking models disconnected from context, thus making the emergence of quantum-like modelling of IAR possible and potentially effective at

v

the same level of efÞciency of the traditional modelling. It is believed by the authors of this volume that the quantum theoretical framework can provide the breakthrough in IAR because it can integrate abstract vector spaces, probability spaces and query languages and extend and generalise the classical vector, probability and query languages utilised in IAR.

The chapters of this volume share the aim of Þnding novel ways to address foundational problems that a community of researchers is actively working to deÞne, investigate and evaluate new methods for information processing inspired by quantum theory. For many years, there exists an active research area where psychology, economy, mathematics, information science, computer science and others meet to provide and share methodological and experimental results obtained by the means of quantum theory when applied to disciplines other than physics.

In this context, the European Union funded the project ÒQuantum Information Access TheoryÓ (QUARTZ) which is an Innovative Training Network (ITN) within the Horizon 2020 Marie Sklodowska-Curie Action programme. QUARTZ started from the idea of transferring the scientiÞc research results and expertise from senior researchers in the utilisation of quantum theory in IAR to the junior researchers, thus stimulating the birth and growth of a networked European community of scholars with a larger, stronger and deeper expertise in IAR. We believe that this volume is providing an updated view of the current research in quantum-like modelling of IAR and in particular describes some of the research issues and the solutions thereof investigated within QUARTZ.

Contents

vii

Contributors

Diederik Aerts Center Leo Apostel for Interdisciplinary Studies, Brussels, Belgium

Department of Mathematics, Brussels Free University, Brussels, Belgium

Alexander P. Alodjants ITMO University, Saint Petersburg, Russia

Igor A. Bessmertny ITMO University, Saint Petersburg, Russia

Jerome Busemeyer Psychological and Brain Sciences, Indiana University, Bloomington, IN, USA

Emanuele Di Buccio Department of Information Engineering, University of Padova, Padova, Italy

Andrei Khrennikov Linnaeus University, International Center for Mathematical Modeling in Physics and Cognitive Sciences, VŠxjš, Sweden

Massimo Melucci Department of Information Engineering, University of Padova, Padova, Italy

Aleksey V. Platonov ITMO University, Saint Petersburg, Russia

Massimiliano Sassoli de Bianchi Center Leo Apostel for Interdisciplinary Studies, Brussels, Belgium

Laboratorio di Autoricerca di Base, Barbengo, Switzerland

Ingo Schmitt Brandenburg University of Technology Cottbus-Senftenberg,

Cottbus, Germany

Evgeny K. Semenenko ITMO University, Saint Petersburg, Russia

Sandro Sozzo School of Business and Centre IQSCS, University of Leicester, Leicester, UK

ix

Tomas Veloz Center Leo Apostel for Interdisciplinary Studies, Brussels, Belgium

Universidad Andres Bello, Departamento Ciencias Biol—gicas, Facultad Ciencias de la Vida, Santiago, Chile

Fundaci—n para el Desarrollo Interdisciplinario de la Ciencia la Tecnolog’a y las Artes, Santiago, Chile

Zheng Joyce Wang School of Communication, Center for Cognitive and Brain Sciences, The Ohio State University, Columbus, OH, USA

Benyou Wang Department of Information Engineering, University of Padova, Padova, Italy

Günther Wirsching Catholic University of EichstŠtt-Ingolstadt, EichstŠtt,

Germany

Matthias Wolff Brandenburg University of Technology Cottbus-Senftenberg,

Cottbus, Germany