Pawlak, Belnap and the magical number seven
Logic
2023-10-19 v1
Abstract
We are considering the algebraic structure of the Pawlak-Brouwer-Zadeh lattice to distinguish vagueness due to imprecision from ambiguity due to coarseness. We show that a general class of many-valued logics useful for reasoning about data emerges from this context. All these logics can be obtained from a very general seven-valued logic which, interestingly enough, corresponds to a reasoning system developed by Jaina philosophers four centuries BC. In particular, we show how the celebrated Belnap four-valued logic can be obtained from the very general seven-valued logic based on the Pawlak-Brouwer-Zadeh lattice.
Cite
@article{arxiv.2310.11483,
title = {Pawlak, Belnap and the magical number seven},
author = {Salvatore Greco and Roman Slowinski},
journal= {arXiv preprint arXiv:2310.11483},
year = {2023}
}