Kleene Algebras and Logic: Boolean and Rough Set Representations, 3-valued, Rough and Perp Semantics
Logic
2020-07-24 v1
Abstract
A structural theorem for Kleene algebras is proved, showing that an element of a Kleene algebra can be looked upon as an ordered pair of sets. Further, we show that negation with the Kleene property (called the `Kleene negation') always arises from the set theoretic complement. The corresponding propositional logic is then studied through a 3-valued and rough set semantics. It is also established that Kleene negation can be considered as a modal operator, and enables giving a perp semantics to the logic. One concludes with the observation that all the semantics for this logic are equivalent.
Cite
@article{arxiv.1511.07165,
title = {Kleene Algebras and Logic: Boolean and Rough Set Representations, 3-valued, Rough and Perp Semantics},
author = {Arun Kumar and Mohua Banerjee},
journal= {arXiv preprint arXiv:1511.07165},
year = {2020}
}