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arXiv · 2606.31277

Recovery operators in quasi-Nelson logic: the prelinear case

Tommaso Flaminio·Lluis Godo·Umberto Rivieccio
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Abstract

This paper investigates recovery operators in quasi-Nelson logic, the algebraizable logical counterpart of quasi-Nelson algebras. These form a variety of three-potent, distributive, but not necessarily involutive residuated lattices that may be regarded as a common generalization of Nelson and Heyting algebras. We consider both consistency and determinedness operators, with a particular focus on logics and algebras that satisfy the prelinearity condition, which is well-known in the area of mathematical fuzzy logics. We show that, essentially, all algebraic and logical results already proved for (prelinear, distributive) involutive residuated lattice-based LFIs/LFUs can be recovered in the quasi-Nelson setting, where one dispenses with the involutivity assumption. In this setting, consistency and undeterminedness operators are no longer duals of one another, and hence call for a more fine-grained algebraic and logical formalization.

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Tommaso Flaminio, Lluis Godo, Umberto Rivieccio. 2026-06-30. Recovery operators in quasi-Nelson logic: the prelinear case. https://doi.org/10.1093/logcom%2Fexag020

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