Pawlak, Belnap and the magical number seven

Salvatore Greco; Roman Slowinski

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arXiv · 2310.11483

Pawlak, Belnap and the magical number seven

Salvatore Greco·Roman Slowinski

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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.

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Salvatore Greco, Roman Slowinski. 2023-10-17. Pawlak, Belnap and the magical number seven. https://arxiv.org/abs/2310.11483

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