Simulating Basic Logic with Tensors

Can we simulate basic logic operations, i.e. the operations of first-order predicate logic, using tensors? In his 2013 paper “Towards a Formal Distributional Semantics: Simulating Logical Calculi with Tensors”, Edward Grefenstette made some suggestions for such simulation. The paper’s motivation was to take a step towards combining distributional with formal semantics. I’ve explored this paper in a Jupyter Notebook, which I put on github.

At the moment, the github notebook viewer breaks some of the LaTex formulas, but you can see it in the Jupyter notebook viewer here.