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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Acknowledgments
The authors thank the anonymous referees for their comments. Authors acknowledge partial support by the MOSAIC project (EU H2020-MSCA-RISE-2020 Project 101007627). Flaminio and Godo also acknowledge partial support by the Spanish project PID2019-111544GB-C21 funded by MCIN/AEI/10.13039/501100011033. Menchon acknowledge partial support by argentinean projects PIP 112-20200101301CO (CONICET) and PICT-2019-2019-00882 (ANPCyT). The fourth author wants to acknowledge partial support by the following argentinean projects: PIP 112-20150100412CO (CONICET) and UBA-CyT-20020190100021BA.
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Flaminio, T., Godo, L., Menchón, P., Rodriguez, R.O. (2022). Rotations of Gödel Algebras with Modal Operators. In: Ciucci, D., et al. Information Processing and Management of Uncertainty in Knowledge-Based Systems. IPMU 2022. Communications in Computer and Information Science, vol 1601. Springer, Cham. https://doi.org/10.1007/978-3-031-08971-8_55
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DOI: https://doi.org/10.1007/978-3-031-08971-8_55
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