Much of our understanding of human thinking is based on probabilistic models. This innovative book by Jerome R. Busemeyer and Peter D. Bruza argues that, actually, the underlying mathematical structures from quantum theory provide a much better account of human thinking than traditional models. They introduce the foundations for modelling probabilistic-dynamic systems using two aspects of quantum theory. The first, 'contextuality', is a way to understand interference effects found with inferences and decisions under conditions of uncertainty. The second, 'quantum entanglement', (...) allows cognitive phenomena to be modeled in non-reductionist ways. Employing these principles drawn from quantum theory allows us to view human cognition and decision in a totally new light. Introducing the basic principles in an easy-to-follow way, this book does not assume a physics background or a quantum brain and comes complete with a tutorial and fully worked-out applications in important areas of cognition and decision. (shrink)

Conceptual combination performs a fundamental role in creating the broad range of compound phrases utilised in everyday language. This article provides a novel probabilistic framework for assessing whether the semantics of conceptual combinations are compositional, and so can be considered as a function of the semantics of the constituent concepts, or not. While the systematicity and productivity of language provide a strong argument in favor of assuming compositionality, this very assumption is still regularly questioned in both cognitive science and philosophy. (...) Additionally, the principle of semantic compositionality is underspecifi ed, which means that notions of both "strong" and "weak" compositionality appear in the literature. Rather than adjudicating between different grades of compositionality, the framework presented here contributes formal methods for determining a clear dividing line between compositional and non-compositional semantics. In addition, we suggest that the distinction between these is contextually sensitive. Compositionality is equated with a joint probability distribution modeling how the constituent concepts in the combination are interpreted. Marginal selectivity is introduced as a pivotal probabilistic constraint for the application of the Bell/CH and CHSH systems of inequalities. Non-compositionality is equated with a failure of marginal selectivity, or violation of either system of inequalities in the presence of marginal selectivity. This means that the conceptual combination cannot be modeled in a joint probability distribution, the variables of which correspond to how the constituent concepts are being interpreted. The formal analysis methods are demonstrated by applying them to an empirical illustration of twenty-four non-lexicalised conceptual combinations. (shrink)

The term “vagueness” describes a property of natural concepts, which normally have fuzzy boundaries, admit borderline cases, and are susceptible to Zeno's sorites paradox. We will discuss the psychology of vagueness, especially experiments investigating the judgment of borderline cases and contradictions. In the theoretical part, we will propose a probabilistic model that describes the quantitative characteristics of the experimental finding and extends Alxatib's and Pelletier's () theoretical analysis. The model is based on a Hopfield network for predicting truth values. Powerful (...) as this classical perspective is, we show that it falls short of providing an adequate coverage of the relevant empirical results. In the final part, we will argue that a substantial modification of the analysis put forward by Alxatib and Pelletier and its probabilistic pendant is needed. The proposed modification replaces the standard notion of probabilities by quantum probabilities. The crucial phenomenon of borderline contradictions can be explained then as a quantum interference phenomenon. (shrink)

Measures and theories of information abound, but there are few formalised methods for treating the contextuality that can manifest in different information systems. Quantum theory provides one possible formalism for treating information in context. This paper introduces a quantum inspired model of the human mental lexicon. This model is currently being experimentally investigated and we present a preliminary set of pilot data suggesting that concept combinations can indeed behave non-separably.

This chapter is offered as a contribution to the logic of down below. We attempt to demonstrate that the nature of human agency necessitates that there actually be such a logic. The ensuing sections develop the suggestion that cognition down below has a structure strikingly similar to the physical structure of quantum states. In its general form, this is not an idea that originates with the present authors. It is known that there exist mathematical models from the cognitive science of (...) cognition down below that have certain formal similarities to quantum mechanics. We want to take this idea seriously. We will propose that the subspaces of von Neumann-Birkhoff lattices are too crisp for modelling requisite cognitive aspects in relation to subsymbolic logic. Instead, we adopt an approach which relies on projections into nonorthogonal density states. The projection operator is motivated from cues which probe human memory. (shrink)

Erwin Schrödinger holds a prominent place in the history of science primarily due to his crucial role in the development of quantum physics. What is perhaps lesser known are his insights into subject-object duality, consciousness and mind. He documented himself that these were influenced by the Upanishads, a collection of ancient Hindu spiritual texts. Central to his thoughts in this area is that Mind is only One and there is no separation between subject and object. This chapter aims to bridge (...) Schrödinger’s view on One Mind with the teachings of Dōgen, a twelfth century Zen master. This bridge is formed by addressing the question of how time relates to One Mind, and subject-object duality. Schrödinger describes the experience of One Mind to be like a timeless now, whereas subject-object duality involves a linear continuum of time. We show how these differing positions are unified in the notion of ‘absolute present’, which was put forward in the philosophy of Nishida Kitarō (1871–1945). In addition, we argue that it is in this notion of absolute present that the views of Schrödinger, Dōgen and Nishida meet. (shrink)

Diminishing awareness is a consequence of the information explosion: disciplines are becoming increasingly specialized; individuals and groups are becoming ever more insular. This paper considers how awareness can be enhanced via abductive knowledge discovery the goal of which is to produce suggestions which can span disparate islands of knowledge. Knowledge representation is motivated from a cognitive perspective. Words and concepts are represented as vectors in a high dimensional semantic space automatically derived from a text corpus. Information flow computation between vectors (...) is proposed as a means of suggesting potentially interesting implicit associations between concepts. Information flow is applied to computational scientific discovery by attempting to simulate Swanson's Raynaud-fish oil discovery in medical texts. Both automatic and semi-automatic attempts were studied and compared against suggestions computed via semantic association. Even though this work is preliminary and speculative in nature, there is some justification to believe that appropriate suggestions can be “abduced” from semantic space. (shrink)

Diminishing awareness is a consequence of the information explosion: disciplines are becoming increasingly specialized; individuals and groups are becoming ever more insular. This article considers how awareness can be enhanced via operational abductive systems. The goal is to generate and justify suggestions which can span disparate islands of knowledge. Knowledge representation is motivated from a cognitive perspective. Words and concepts are represented as vectors in a high dimensional semantic space automatically derived from a text corpus. Various mechanisms will be presented (...) for computing suggestions from semantic space: information flow, semantic similarity, pre-inductive generalization. The overall goal of this article is to introduce semantic space to the model-based reasoning and abduction community and to illustrate its potential for principled, operational abduction by semi-automatically replicating the Swanson Raynaud/fish oil discovery in medical text. (shrink)

The expressive power of logic is believed to be able to model most of the fundamental aspects of information retrieval. However, it is also understood that classical logic is ineffective for handling partiality and uncertainty in IR. Applying non-classical logics such as the AGM belief revision logic and the possibilistic logic to adaptive information retrieval is appealing since they provide a powerful and rigorous framework to model partiality and uncertainty inherent in any IR processes. The maxi-adjustment method, which is an (...) effective computational apparatus of the AGM paradigm, is applied to develop the learning components of the adaptive information agents. Essentially, maxi-adjustment allows the partial representation K of a user's information needs N to be refined gradually based on the user's relevance feedback t. Generally speaking, learning in adaptive information agents is characterised by the AGM belief revision Kt*. On the other hand, possibilistic logic supports a gradated assessment of the uncertainty arising from matching K with the imperfect characterisation d of an information object D. Information matching in adaptive information agents is underpinned by K ƕ d, where ƕ is the possibilistic inference relation. This paper illustrates how maxi-adjustment and possibilistic deduction can be applied to develop the adaptive information agents. Their impact on the agents learning autonomy and explanatory power is also discussed. (shrink)

This article extends the combinatorial approach to support the determination of contextuality amidst causal influences. Contextuality is an active field of study in Quantum Cognition, in systems relating to mental phenomena, such as concepts in human memory. In the cognitive field of study, a contemporary challenge facing the determination of whether a phenomenon is contextual has been the identification and management of disturbances. Whether or not said disturbances are identified through the modeling approach, constitute causal influences, or are disregardableas as (...) noise is important, as contextuality cannot be adequately determined in the presence of causal influences. To address this challenge, we first provide a formalization of necessary elements of the combinatorial approach within the language of canonical causal models. Through this formalization, we extend the combinatorial approach to support a measurement and treatment of disturbance, and offer techniques to separately distinguish noise and causal influences. Thereafter, we develop a protocol through which these elements may be represented within a cognitive experiment. As human cognition seems rife with causal influences, cognitive modelers may apply the extended combinatorial approach to practically determine the contextuality of cognitive phenomena. (shrink)