Cohomology of Contextuality and Logical Paradoxes

Kohei Kishida

Contextuality is a key feature of quantum mechanics that provides distinct computational resource for quantum computation. Contextual phenomena are, however, found in many other fields as well, and the sheaf-theoretic framework of Abramsky and Brandenburger (2011) gives a unifying treatment of contextuality in various subjects. In this talk, I will introduce a kind of logic that may be called "contextual logic", and show that an equational theory in this logic (that generalizes a type of argument used in quantum foundations) characterizes the same class of contextual models as characterized by cohomology in the sheaf framework. I will moreover show that this framework can also be applied to a logical phenomenon that has not previously been considered to be of contextual nature --- namely, logical paradoxes.