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

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

A Novel Graph-Based Modelling Approach for Reducing Complexity in Model-Based Systems Engineering Environment

Field of systems engineering (SE) is developing rapidly and becoming more complex, where multiple issues arise such as overcomplexity, lack of communication or understanding of the design process on different stages of its lifecycle. Model-based systems engineering (MBSE) has been introduced to overcome the communication issues and reduce systems complexity. A novel approach for modelling interactions is proposed to enhance the existing MBSE methodologies and further address the identified challenges. The approach is based on graph theory, where pre-defined rules and relationships are substituted and reorganised dynamically with graphical constructs. A framework for reducing complexity and improving logic modelling in MBSE with metagraph object-oriented approach is presented. This framework is tested in use cases from literature, where the model-based systems approach is applied to design an automobile system to match the acceleration requirements, and to improve a CubeSat nanosatellite communication subsystem. Through the use case scenarios, it has been proven that the methodology framework meets all the identified functional and design requirements and achieves the aim of the research. This work may be viewed as a step forward towards more consistent and automatic modelling of interactions among subsystems and components in MBSE. Automation techniques have multiple applications in systems engineering field as engineers always aim to produce higher quality and cost-effective products in less time and that is achieved by integrating knowledge on every stage of a development lifecycle. In addition to those advantages for SE field, the research provides basis for potential research proposals for future work in various engineering fields such as knowledge based engineering or virtual engineering