@article{FLAMINIO202266,
title = {Prelinearity in (quasi-)Nelson logic},
journal = {Fuzzy Sets and Systems},
volume = {445},
pages = {66-89},
year = {2022},
note = {Logic and Databases},
issn = {0165-0114},
doi = {https://doi.org/10.1016/j.fss.2022.03.021},
url = {https://www.sciencedirect.com/science/article/pii/S0165011422001257},
author = {Tommaso Flaminio and Umberto Rivieccio},
keywords = {(Quasi-)Nelson, Weak nilpotent minimum, Rotation logics, Non-involutive, Prelinear logics, Algebraic logic},
abstract = {The algebraic theory of quasi-Nelson logic, a non-involutive generalization of Nelson's constructive logic with strong negation, has been shown to be surprisingly rich in a series of recent papers. In the present paper we bring quasi-Nelson logic into the fuzzy setting by adding the prelinearity axiom to it. We observe that the resulting system is an extension of the well-known Weak Nilpotent Minimum logic, as well as a rotation logic in the sense of recent work by P. Aglianò and S. Ugolini. We characterize the algebraic models of prelinear quasi-Nelson logic as twist-structures over Gödel algebras endowed with a nucleus operator and use the insight thus gained to look at subvarieties corresponding to extensions of well-known fuzzy systems. Our study of the quasi-Nelson negation in a prelinear setting also allows us to show that the variety of prelinear quasi-Nelson algebras is generated by a single standard algebra, thus obtaining a single chain completeness theorem for the logic.}
}