Classical logic with n truth values as a symmetric many-valued logic
Ledda, Antonio;Paoli, Francesco;Salibra, Antonino
2023-01-01
Abstract
We introduce Boolean-like algebras of dimension n (nBA s) having n constants e1, … , en, and an (n+ 1) -ary operation q (a “generalised if-then-else”) that induces a decomposition of the algebra into n factors through the so-called n-central elements. Varieties of nBA s share many remarkable properties with the variety of Boolean algebras and with primal varieties. The nBA s provide the algebraic framework for generalising the classical propositional calculus to the case of n–perfectly symmetric–truth-values. Every finite-valued tabular logic can be embedded into such a n-valued propositional logic, nCL , and this embedding preserves validity. We define a confluent and terminating first-order rewriting system for deciding validity in nCL , and, via the embeddings, in all the finite tabular logics.File | Size | Format | |
---|---|---|---|
Articolo versione stampa.pdf open access
Type: versione editoriale
Size 2.12 MB
Format Adobe PDF
|
2.12 MB | Adobe PDF | View/Open |
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.