Towards a dynamical theory of observation

We introduce a model of classical and quantum observation based on contextuality and dynamically evolving apparatus. Power sets of classical bits model the four classical states of elementary detectors, viz. the two normal yes/no signal states, the faulty or decommissioned state and the non-existence state. Operators over power set registers are used to describe various physical scenarios such as the construction and decommissioning of physical devices in otherwise empty laboratories, the dynamics of signal states over those detectors, the extraction of information from those states, and multiple observers. We apply our quantum formalism to the Elitzur-Vaidman bomb-tester experiment and the Hardy paradox experiment.