We analyze different aspects of our quantum modeling approach of human concepts, and more specifically focus on the quantum effects of contextuality, interference, entanglement and emergence, illustrating how each of them makes its appearance in specific situations of the dynamics of human concepts and their combinations. We point out the relation of our approach, which is based on an ontology of a concept as an entity in a state changing under influence of a context, with the main traditional concept theories, i.e. prototype theory, exemplar theory and theory theory. We ponder about the question why quantum theory performs so well in its modeling of human concepts, and shed light on this question by analyzing the role of complex amplitudes, showing how they allow to describe interference in the statistics of measurement outcomes, while in the traditional theories statistics of outcomes originates in classical probability weights, without the possibility of interference. The relevance of complex numbers, the appearance of entanglement, and the role of Fock space in explaining contextual emergence, all as unique features of the quantum modeling, are explicitly revealed in this paper by analyzing human concepts and their dynamics.
In context of efforts of composing category-theoretic and logical methods in the area of knowledge representation we propose the notion of conceptory. We consider intersection/union and other constructions in conceptories as expressive alternative to category-theoretic (co)limits and show they have features similar to (pro-, in-)jections. Then we briefly discuss approaches to development of formal systems built on the base of conceptories and describe possible application of such system to the specific ontology.
CONICET-Universidad de Buenos Aires（国家科学技术研究委员会-布宜诺斯艾利斯大学）；Universidad de Buenos Aires（布宜诺斯艾利斯大学）；Universidad Torcuato di Tella（托库阿托·迪·特利亚大学）
Recent approaches to human concept learning have successfully combined the power of symbolic, infinitely productive rule systems and statistical learning to explain our ability to learn new concepts from just a few examples. The aim of most of these studies is to reveal the underlying language structuring these representations and providing a general substrate for thought. However, describing a model of thought that is fixed once trained is against the extensive literature that shows how experience shapes concept learning. Here, we ask about the plasticity of these symbolic descriptive languag…
Center Leo Apostel for Interdisciplinary Studies（利奥·阿波斯特尔跨学科研究中心）；Brussels Free University（布鲁塞尔自由大学）
We identify the presence of typically quantum effects, namely 'superposition' and 'interference', in what happens when human concepts are combined, and provide a quantum model in complex Hilbert space that represents faithfully experimental data measuring the situation of combining concepts. Our model shows how 'interference of concepts' explains the effects of underextension and overextension when two concepts combine to the disjunction of these two concepts. This result supports our earlier hypothesis that human thought has a superposed two-layered structure, one layer consisting of 'classic…
Center Leo Apostel for Interdisciplinary Studies（莱奥·阿波斯泰尔跨学科研究中心）；Brussels Free University（布鲁塞尔自由大学）
We present modeling for conceptual combinations which uses the mathematical formalism of quantum theory. Our model faithfully describes a large amount of experimental data collected by different scholars on concept conjunctions and disjunctions. Furthermore, our approach sheds a new light on long standing drawbacks connected with vagueness, or fuzziness, of concepts, and puts forward a completely novel possible solution to the 'combination problem' in concept theory. Additionally, we introduce an explanation for the occurrence of quantum structures in the mechanisms and dynamics of concepts an…
University of British Columbia（不列颠哥伦比亚大学）；Vrije Universiteit Brussel（布鲁塞尔自由大学）
The quantum inspired State Context Property (SCOP) theory of concepts is unique amongst theories of concepts in offering a means of incorporating that for each concept in each different context there are an unlimited number of exemplars, or states, of varying degrees of typicality. Working with data from a study in which participants were asked to rate the typicality of exemplars of a concept for different contexts, and introducing an exemplar typicality threshold, we built a SCOP model of how states of a concept arise differently in associative versus analytic (or divergent and convergent) mo…
Center Leo Apostel for Interdisciplinary Studies（利奥·阿波斯泰尔跨学科研究中心）；Brussels Free University（布鲁塞尔自由大学）；University of British Columbia（不列颠哥伦比亚大学）；Instituto de Filosofía y Ciencias de la Complejidad (IFICC)（哲学与复杂性研究所（IFICC））
Increasing experimental evidence shows that humans combine concepts in a way that violates the rules of classical logic and probability theory. On the other hand, mathematical models inspired by the formalism of quantum theory are in accordance with data on concepts and their combinations. In this paper, we investigate a novel type of concept combination were a number is combined with a noun, e.g., `Eleven Animals. Our aim is to study 'conceptual identity' and the effects of 'indistinguishability' - in the combination 'Eleven Animals', the 'animals' are identical and indistinguishable - on the…
From Concept Alignment to Causal Grounding: An Intervention Test of Chain-of-Thought Faithfulness
German Research Center for Artificial Intelligence (DFKI)（德国人工智能研究中心（DFKI））；Saarland Informatics Campus（萨尔兰信息学园区）；Centre for European Research in Trusted AI (CERTAIN)（欧洲可信人工智能研究中心（CERTAIN））；Technische Universität Berlin（柏林工业大学）；IBM Research（IBM研究院）；University of Copenhagen（哥本哈根大学）；University of Groningen（格罗宁根大学）
Center Leo Apostel for Interdisciplinary Studies, Brussels Free University（布鲁塞尔自由大学列奥·阿波斯泰尔跨学科研究中心）；School of Management and IQSCS, University of Leicester（莱斯特大学管理学院和IQSCS）；Department of Mathematics, University of British Columbia, Okanagan Campus（不列颠哥伦比亚大学奥卡纳根校区数学系）；Instituto de Filosofía y Ciencias de la Complejidad (IFICC)（复杂性与哲学科学研究所）
We analyse in this paper the data collected in a set of experiments performed on human subjects on the combination of natural concepts. We investigate the mutual influence of conceptual conjunction and negation by measuring the membership weights of a list of exemplars with respect to two concepts, e.g., 'Fruits' and 'Vegetables', and their conjunction 'Fruits And Vegetables', but also their conjunction when one or both concepts are negated, namely, 'Fruits And Not Vegetables', 'Not Fruits And Vegetables' and 'Not Fruits And Not Vegetables'. Our findings sharpen existing analysis on conceptual…
University of British Columbia（不列颠哥伦比亚大学）；Queensland University of Technology（昆士兰科技大学）
At the core of our uniquely human cognitive abilities is the capacity to see things from different perspectives, or to place them in a new context. We propose that this was made possible by two cognitive transitions. First, the large brain of Homo erectus facilitated the onset of recursive recall: the ability to string thoughts together into a stream of potentially abstract or imaginative thought. This hypothesis is supported by a set of computational models where an artificial society of agents evolved to generate more diverse and valuable cultural outputs under conditions of recursive recall…
Brussels Free University（布鲁塞尔自由大学）；University of British Columbia（不列颠哥伦比亚大学）
Experiments in cognitive science and decision theory show that the ways in which people combine concepts and make decisions cannot be described by classical logic and probability theory. This has serious implications for applied disciplines such as information retrieval, artificial intelligence and robotics. Inspired by a mathematical formalism that generalizes quantum mechanics the authors have constructed a contextual framework for both concept representation and decision making, together with quantum models that are in strong alignment with experimental data. The results can be interpreted …
Symbolic Analysis of Grover Search Algorithm via Chain-of-Thought Reasoning and Quantum-Native Tokenization
Department of Computer Science, The University of Pittsburgh（匹兹堡大学计算机科学系）；Department of Computer Science, The University of North Carolina at Chapel Hill（北卡罗来纳大学教堂山分校计算机科学系）
Identifying, Evaluating, and Mitigating Risks of AI Thought Partnerships
Princeton University（普林斯顿大学）；University of Cambridge（剑桥大学）；Leverhulme Centre for Future Intelligence（勒沃胡姆未来智能中心）；Universitat Politècnica de València（瓦伦西亚理工大学）；The Alan Turing Institute（艾伦·图灵研究所）；NYU（纽约大学）
Laboratory for Computational Mathematics - LabMaC（计算数学实验室）；Embrapa Agriculture Informatics - CNPTIA（巴西农业信息研究所）；Brazilian Agricultural Research Corporation - Embrapa（巴西农业研究公司）
After more than sixty years, Shannon's research [1-3] continues to raise fundamental questions, such as the one formulated by Luce [4,5], which is still unanswered: "Why is information theory not very applicable to psychological problems, despite apparent similarities of concepts?" On this topic, Pinker [6], one of the foremost defenders of the computational theory of mind [6], has argued that thought is simply a type of computation, and that the gap between human cognition and computational models may be illusory. In this context, in his latest book, titled Thinking Fast and Slow [8], Kahnema…
