The algebraic semantics of propositional Gödel logic is given by the variety of Gödel algebras, that is, prelinear Heyting algebras, or, equivalently, idempotent BL (or MTL) algebras. In this work we provide a recurrence that allows to compute the number of homomorphisms between finite Gödel algebras. We then show that the same recurrence can be used to compute the cardinality of the hom-sets also for the finite members of other varieties of algebras related to many-valued logics.
Counting Homomorphisms Between Finite Gödel Algebras / S. Aguzzoli, M. Mordonini (LECTURE NOTES IN NETWORKS AND SYSTEMS). - In: Information Processing and Management of Uncertainty in Knowledge-Based Systems / [a cura di] M.-J. Lesot, S. Vieira, M.Z. Reformat, J.P. Carvalho, F. Batista, B. Bouchon-Meunier, R.R. Yager. - [s.l] : Springer, 2025. - ISBN 978-3-031-73999-6. - pp. 365-377 (( Intervento presentato al 20. convegno IPMU tenutosi a Lisbona nel 2024 [10.1007/978-3-031-74000-8_30].
Counting Homomorphisms Between Finite Gödel Algebras
S. Aguzzoli
Primo
;
2025
Abstract
The algebraic semantics of propositional Gödel logic is given by the variety of Gödel algebras, that is, prelinear Heyting algebras, or, equivalently, idempotent BL (or MTL) algebras. In this work we provide a recurrence that allows to compute the number of homomorphisms between finite Gödel algebras. We then show that the same recurrence can be used to compute the cardinality of the hom-sets also for the finite members of other varieties of algebras related to many-valued logics.
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