Contextual Semantics Machinery

Topological field theory of data, a programme recently proposed by Rasetti and Merelli, is a theoretical framework to extract hidden relations, the emerging correlation patterns, existing among the data which are part of the global data space; as well as, provides potential semantics, for instance as a variational machinery, based on physical field theories to express these emerging patterns. The theory is based on three inter-connected layers that work in synergy; the topological data analysis followed by the topological field theoretic modelisation and finally its formal language description; invoking influxes between physical theories and computation using mathematical structures to act as a connecting bridge for the ever increasing dichotomy between the physical and the digital. This work is an instance of the physical genesis of computation based on the topological field theory of data. The thesis explores a way to discover directly from the space of observations; collection of data from a physical experiment, a specific emerging high degree correlation patterns among the data known as quantum contextuality, as well as, formalises a mathematical model of computation which provides semantics to these emerging patterns; the contextual semantics machinery, based on field theoretic description. As a result, establishes a formal connection between quantum contextuality and interactive computation advocating a next step forward for the theory as a whole. The phenomenon of quantum contextuality mathematically corresponds to a class of novel patterns known to be locally consistent and globally inconsis- tent which has been recently shown by Abramsky and Branderburger using mathematical structure of sheaves; arising from the impossibility of an observer to visualise all contexts of a model simultaneously. The central feature of sheaves is the failure of local solutions to glue together to form a global solution which advocates an irreducible holistic doctrine. We explore these patterns in the interactive computation by a mathematical model, whose expressive- ness generalises the empirical models in the foundation of quantum physics, introducing the concept of openness unlike Turing-like interactive models. The computing synthesis of algebraic interpretation of quantum contextuality is that the computation doesn’t depend only on the context but also on their collective structure. The results could encourage a deeper investigation into the foundations of computability.