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arXiv · 2405.19354

Rotations of Gödel algebras with modal operators

Tommaso Flaminio·Lluis Godo·Paula Menchón·Ricardo O. Rodriguez
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Abstract

The present paper is devoted to study the effect of connected and disconnected rotations of Gödel algebras with operators grounded on directly indecomposable structures. The structures resulting from this construction we will present are nilpotent minimum (with or without negation fixpoint, depending on whether the rotation is connected or disconnected) with special modal operators defined on a directly indecomposable algebra. In this paper we will present a (quasi-)equational definition of these latter structures. Our main results show that directly indecomposable nilpotent minimum algebras (with or without negation fixpoint) with modal operators are fully characterized as connected and disconnected rotations of directly indecomposable Gödel algebras endowed with modal operators.

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Tommaso Flaminio, Lluis Godo, Paula Menchón, Ricardo O. Rodriguez. 2024-05-23. Rotations of Gödel algebras with modal operators. https://doi.org/10.1007/978-3-031-08971-8_55

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