Discovering information flow using a high dimensional conceptual space

This paper presents an informational inference mechanism realized via the use of a high dimensional conceptual space. More specifically, we claim to have operationalized important aspects of G?rdenforss recent three-level cognitive model. The connectionist level is primed with the Hyperspace Analogue to Language (HAL) algorithm which produces vector representations for use at the conceptual level. We show how inference at the symbolic level can be implemented by employing Barwise and Seligmans theory of information flow. This article also features heuristics for enhancing HAL-based representations via the use of quality properties, determining concept inclusion and computing concept composition. The worth of these heuristics in underpinning informational inference are demonstrated via a series of experiments. These experiments, though small in scale, show that informational inference proposed in this article has a very different character to the semantic associations produced by the Minkowski distance metric and concept similarity computed via the cosine coefficient. In short, informational inference generally uncovers concepts that are carried, or, in some cases, implied by another concept, (or combination of concepts)

Quantum Information Dynamics and Open World Science

One of the fundamental insights of quantum mechanics is that complete knowledge of the state of a quantum system is not possible. Such incomplete knowledge of a physical system is the norm rather than the exception. This is becoming increasingly apparent as we apply scientific methods to increasingly complex situations. Empirically intensive disciplines in the biological, human, and geosciences all operate in situations where valid conclusions must be drawn, but deductive completeness is impossible. This paper argues that such situations are emerging examples of {it Open World} Science. In this paradigm, scientific models are known to be acting with incomplete information. Open World models acknowledge their incompleteness, and respond positively when new information becomes available. Many methods for creating Open World models have been explored analytically in quantitative disciplines such as statistics, and the increasingly mature area of machine learning. This paper examines the role of quantum theory and quantum logic in the underpinnings of Open World models, examining the importance of structural features of such as non-commutativity, degrees of similarity, induction, and the impact of observation. Quantum mechanics is not a problem around the edges of classical theory, but is rather a secure bridgehead in the world of science to come

Evaluating probabilistic programming languages for simulating quantum correlations

This article explores how probabilistic programming can be used to simulate quantum correlations in an EPR experimental setting. Probabilistic programs are based on standard probability which cannot produce quantum correlations. In order to address this limitation, a hypergraph formalism was programmed which both expresses the measurement contexts of the EPR experimental design as well as associated constraints. Four contemporary open source probabilistic programming frameworks were used to simulate an EPR experiment in order to shed light on their relative effectiveness from both qualitative and quantitative dimensions. We found that all four probabilistic languages successfully simulated quantum correlations. Detailed analysis revealed that no language was clearly superior across all dimensions, however, the comparison does highlight aspects that can be considered when using probabilistic programs to simulate experiments in quantum physics.Comment: 24 pages, 8 figures, code is available at https://github.com/askoj/bell-ppl

Modelling contextuality by probabilistic programs with hypergraph semantics

Models of a phenomenon are often developed by examining it under different experimental conditions, or measurement contexts. The resultant probabilistic models assume that the underlying random variables, which define a measurable set of outcomes, can be defined independent of the measurement context. The phenomenon is deemed contextual when this assumption fails. Contextuality is an important issue in quantum physics. However, there has been growing speculation that it manifests outside the quantum realm with human cognition being a particularly prominent area of investigation. This article contributes the foundations of a probabilistic programming language that allows convenient exploration of contextuality in wide range of applications relevant to cognitive science and artificial intelligence. Specific syntax is proposed to allow the specification of "measurement contexts". Each such context delivers a partial model of the phenomenon based on the associated experimental condition described by the measurement context. The probabilistic program is translated into a hypergraph in a modular way. Recent theoretical results from the field of quantum physics show that contextuality can be equated with the possibility of constructing a probabilistic model on the resulting hypergraph. The use of hypergraphs opens the door for a theoretically succinct and efficient computational semantics sensitive to modelling both contextual and non-contextual phenomena. Finally, this article raises awareness of contextuality beyond quantum physics and to contribute formal methods to detect its presence by means of hypergraph semantics.Comment: Accepted for "Theoretical Computer Science

Modelling word meaning using efficient tensor representations

Models of word meaning, built from a corpus of text, have demonstrated success in emulating human performance on a number of cognitive tasks. Many of these models use geometric representations of words to store semantic associations between words. Often word order information is not captured in these models. The lack of structural information used by these models has been raised as a weakness when performing cognitive tasks. This paper presents an efficient tensor based approach to modelling word meaning that builds on recent attempts to encode word order information, while providing flexible methods for extracting task specific semantic information

A probabilistic framework for analysing the compositionality of conceptual combinations

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 underspecified, 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

Nonseparability of Shared Intentionality

According to recent studies in developmental psychology and neuroscience, symbolic language is essentially intersubjective. Empathetically relating to others renders possible the acquisition of linguistic constructs. Intersubjectivity develops in early ontogenetic life when interactions between mother and infant mutually shape their relatedness. Empirical findings suggest that the shared attention and intention involved in those interactions is sustained as it becomes internalized and embodied. Symbolic language is derivative and emerges from shared intentionality. In this paper, we present a formalization of shared intentionality based upon a quantum approach. From a phenomenological viewpoint, we investigate the nonseparable, dynamic and sustainable nature of social cognition and evaluate the appropriateness of quantum interaction for modelling intersubjectivity

Towards a Quantum-Like Cognitive Architecture for Decision-Making

We propose an alternative and unifying framework for decision-making that, by using quantum mechanics, provides more generalised cognitive and decision models with the ability to represent more information than classical models. This framework can accommodate and predict several cognitive biases reported in Lieder & Griffiths without heavy reliance on heuristics nor on assumptions of the computational resources of the mind