We investigate the automorphism group of finite Gödel algebras, the algebraic counterpart of Gödel infinite-valued propositional logic with a finite number of variables. In logical terms, we look at the structure of substitution of terms that preserve logical equivalence in this logic. We obtain a characterisation of the arising automorphism groups in terms of semidirect and direct products of symmetric groups. Building on this, we establish an explicit closed formula for the cardinality of the automorphism group of the Lindenbaum algebra of Gödel logic over n propositional variables, for any integer n >= 1.
The automorphism group of finite Gödel algebras / S. Aguzzoli, B. Gerla, V. Marra - In: 40th IEEE International Symposium on Multiple-Valued Logic, ISMVL 2010, 26–28 May 2010, Barcelona, Spain : proceedingsLos Alamitos : IEEE computer society, 2010. - ISBN 9781424467525. - pp. 21-26 (( Intervento presentato al 40. convegno International Symposium on Multiple-Valued Logic tenutosi a Barcelona, Spain nel 2010 [10.1109/ISMVL.2010.13].
The automorphism group of finite Gödel algebras
S. AguzzoliPrimo
;V. MarraUltimo
2010
Abstract
We investigate the automorphism group of finite Gödel algebras, the algebraic counterpart of Gödel infinite-valued propositional logic with a finite number of variables. In logical terms, we look at the structure of substitution of terms that preserve logical equivalence in this logic. We obtain a characterisation of the arising automorphism groups in terms of semidirect and direct products of symmetric groups. Building on this, we establish an explicit closed formula for the cardinality of the automorphism group of the Lindenbaum algebra of Gödel logic over n propositional variables, for any integer n >= 1.
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