Rotations of Gödel algebras with modal operators
This work provides a theoretical characterization for a specific class of algebraic structures in mathematical logic, which is incremental as it builds on existing rotation constructions.
The paper tackled the problem of characterizing directly indecomposable nilpotent minimum algebras with modal operators by studying rotations of Gödel algebras, showing that these structures are fully characterized as connected and disconnected rotations of directly indecomposable Gödel algebras with modal operators.
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.