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.

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.

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