Modelling contextuality by probabilistic programs with hypergraph semantics

TL;DR

This paper introduces a probabilistic programming language with hypergraph semantics to model and detect contextuality across various fields, including quantum physics and cognitive science.

Contribution

It proposes a novel syntax for specifying measurement contexts and translates probabilistic programs into hypergraphs, enabling efficient detection of contextuality.

Findings

Hypergraph semantics can represent contextual and non-contextual phenomena.

Probabilistic models on hypergraphs can detect contextuality.

The approach is applicable beyond quantum physics, including cognitive science.

Abstract

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.