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.
