Modality-free pre-rough logic

Abstract

In this paper, we present a modality-free pre-rough algebra. Łukasiewicz Moisil algebra and Wajsberg algebra are equivalent under a transformation. A similar type of equivalence exists in our proposed definition and standard definition of pre-rough algebra. We obtain a few modality-free algebras weaker than pre-rough algebra. Furthermore, it is also established that modality-free versions for other analogous structures weaker than pre-rough algebra do not exist. Both Hilbert-type axiomatization and sequent calculi for all proposed algebras are presented.

Keywords:

• Pre-rough algebra
• system algebra
• pre-rough logic
• modality-free logic

Acknowledgments

We are grateful to the reviewers for their important remarks and suggestions.

Disclosure statement

No potential conflict of interest was reported by the author(s).