An epimorphism Between Fine and Ferguson’s matrices for Angell’s AC

Zach, Richard. 2022. “An Epimorphism Between Fine and Ferguson’s Matrices for Angell’s AC.” Logic and Logical Philosophy, Forthcoming, 1–19. https://doi.org/10.12775/LLP.2022.025.

Angell’s logic of analytic containment AC has been shown to be characterized by a 9-valued matrix NC by Ferguson, and by a 16-valued matrix by Fine. It is shown that the former is the image of a surjective homomorphism from the latter, i.e., an epimorphic image. Some candidate 7-valued matrices are ruled out as characteristic of AC. Whether matrices with fewer than 9 values exist remains an open question. The results were obtained with the help of the MUltlog system for investigating finite-valued logics; the results serve as an example of the usefulness of techniques from computational algebra in logic. A tableau proof system for NC is also provided.