An Epimorphism between Fine and Ferguson's Matrices for Angell's AC
Logic
2023-06-21 v3
Abstract
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.
Keywords
Cite
@article{arxiv.2105.15160,
title = {An Epimorphism between Fine and Ferguson's Matrices for Angell's AC},
author = {Richard Zach},
journal= {arXiv preprint arXiv:2105.15160},
year = {2023}
}