We discuss quantum non-locality and contextuality, emphasising logical and structural aspects. We also show how the same mathematical structures arise in various areas of classical computation.

Learning systems focused on collaborative learning are often described in terms of formal and informal learning, however definitions of formal and informal learning vary, which makes it difficult to compare systems that may have been described using different perspectives. In this paper we present a framework for describing formality in e-learning systems, which can account for the most common ...

In quantum physics, the notion of contextuality has a variety interpretations, which are typically associated with names their inventors, say, Bohr, Bell, Kochen, Specker, and recently Dzhafarov. fact, Bohr was first who pointed to measurements as part formulation his principle complementarity. (Instead “contextuality,” he considered dependence on “experimental conditions.”) Unfortunately, coun...

Testing the validity of knowledge requires formal expression of that knowledge. Formality of an expression is defined as the invariance, under changes of context, of the expression’s meaning, i.e. the distinction which the expression represents. This encompasses both mathematical formalism and operational determination. The main advantages of formal expression are storability, universal communi...

In this paper, we prove that, given appropriate hypotheses, n-formality of a differential graded algebraic structure is equivalent to the existence chain-level automorphism lifting degree twisting isomorphism relative unit order greater than n. A similar result with slightly different hypothesis was proved by Joana Cirici and second author. We use homotopy transfer theorem an explicit inductive...

We present a proof for a conjecture previously formulated by Dzhafarov, Kujala, and Larsson (Foundations of Physics, in press, arXiv:1411.2244). The conjecture specifies a measure for the degree of contextuality and a criterion (necessary and sufficient condition) for contextuality in a broad class of quantum systems. This class includes Leggett-Garg, EPR/Bell, and Klyachko-Can-Binicioglu-Shumo...

We present a simple proof of quantum contextuality for a spinless particle with a one dimensional configuration space. We then discuss how the maximally realistic deterministic quantum mechanics recently constructed by this author and V. Singh can be applied to different contexts.