The use of situation theory in context modeling

At the heart of natural language processing is the understanding of context dependent meanings This paper presents a preliminary model of formal contexts based on situation theory. It also gives a worked-out example to show the use of contexts in lifting, i.e., how propositions holding in a particular context transform when they are moved to another context. This is useful in NLP applications where preserving meaning is a desideratum

Concepts and Their Dynamics: A Quantum-Theoretic Modeling of Human Thought

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.Comment: 31 pages, 5 figure

On the Foundations of the Brussels Operational-Realistic Approach to Cognition

The scientific community is becoming more and more interested in the research that applies the mathematical formalism of quantum theory to model human decision-making. In this paper, we provide the theoretical foundations of the quantum approach to cognition that we developed in Brussels. These foundations rest on the results of two decade studies on the axiomatic and operational-realistic approaches to the foundations of quantum physics. The deep analogies between the foundations of physics and cognition lead us to investigate the validity of quantum theory as a general and unitary framework for cognitive processes, and the empirical success of the Hilbert space models derived by such investigation provides a strong theoretical confirmation of this validity. However, two situations in the cognitive realm, 'question order effects' and 'response replicability', indicate that even the Hilbert space framework could be insufficient to reproduce the collected data. This does not mean that the mentioned operational-realistic approach would be incorrect, but simply that a larger class of measurements would be in force in human cognition, so that an extended quantum formalism may be needed to deal with all of them. As we will explain, the recently derived 'extended Bloch representation' of quantum theory (and the associated 'general tension-reduction' model) precisely provides such extended formalism, while remaining within the same unitary interpretative framework.Comment: 21 page

Contextual Risk and Its Relevance in Economics

Uncertainty in economics still poses some fundamental problems illustrated, e.g., by the Allais and Ellsberg paradoxes. To overcome these difficulties, economists have introduced an interesting distinction between 'risk' and 'ambiguity' depending on the existence of a (classical Kolmogorovian) probabilistic structure modeling these uncertainty situations. On the other hand, evidence of everyday life suggests that 'context' plays a fundamental role in human decisions under uncertainty. Moreover, it is well known from physics that any probabilistic structure modeling contextual interactions between entities structurally needs a non-Kolmogorovian quantum-like framework. In this paper we introduce the notion of 'contextual risk' with the aim of modeling a substantial part of the situations in which usually only 'ambiguity' is present. More precisely, we firstly introduce the essentials of an operational formalism called 'the hidden measurement approach' in which probability is introduced as a consequence of fluctuations in the interaction between entities and contexts. Within the hidden measurement approach we propose a 'sphere model' as a mathematical tool for situations in which contextual risk occurs. We show that a probabilistic model of this kind is necessarily non-Kolmogorovian, hence it requires either the formalism of quantum mechanics or a generalization of it. This insight is relevant, for it explains the presence of quantum or, better, quantum-like, structures in economics, as suggested by some authors, and can serve to solve the aforementioned paradoxes.Comment: 6 pages, 2 figure

Identifying Quantum Structures in the Ellsberg Paradox

Empirical evidence has confirmed that quantum effects occur frequently also outside the microscopic domain, while quantum structures satisfactorily model various situations in several areas of science, including biological, cognitive and social processes. In this paper, we elaborate a quantum mechanical model which faithfully describes the 'Ellsberg paradox' in economics, showing that the mathematical formalism of quantum mechanics is capable to represent the 'ambiguity' present in this kind of situations, because of the presence of 'contextuality'. Then, we analyze the data collected in a concrete experiment we performed on the Ellsberg paradox and work out a complete representation of them in complex Hilbert space. We prove that the presence of quantum structure is genuine, that is, 'interference' and 'superposition' in a complex Hilbert space are really necessary to describe the conceptual situation presented by Ellsberg. Moreover, our approach sheds light on 'ambiguity laden' decision processes in economics and decision theory, and allows to deal with different Ellsberg-type generalizations, e.g., the 'Machina paradox'.Comment: 16 pages, no figures. arXiv admin note: substantial text overlap with arXiv:1208.235

Supporting Student’s Thinking In Addition Of Fraction From Informal To More Formal Using Measuring Context

One of reasons why fractions are a topic which many students find difficult to learn is that there exist many rules calculating with fractions. In addition, students have been trained for the skills and should have mastered such procedures even they do not ‘understand’. Some previous researcher confirmed that the problem which students encounter in learning fraction operations is not firmly connected to concrete experiences. For this reason, a set of measuring context was designed to provide concrete experiences in supporting students’ reasoning in addition of fractions, because the concept of fractional number was derived from measuring. In the present study we used design research as a reference research to investigate students’ mathematical progress in addition of fractions. In particular, using retrospective analysis to analyze data of fourth graders’ performance on addition of fractions, we implemented some instructional activities by using measuring activities and contexts to provide opportunities students use students’ own strategies and models. The emergent modeling (i.e. a bar model) played an important role in the shift of students reasoning from concrete experiences (informal) in the situational level towards more formal mathematical concept of addition of fractions. We discuss these findings taking into consideration the context in which the study was conducted and we provide implications for the teaching of fractions and suggestions for further research. Key word: measuring context, addition of fractions, design research, emergent modelin