The theory of Schauder hats is a beautiful and powerful tool for investigating, under several respects, the algebraic semantics of Łukasiewicz infinite-valued logic [CDM99],[MMM07], [Mun94], [P95]. As a notably application of the theory, the elements of the free n-generated MV-algebra, that constitutes the algebraic semantics of the n-variate fragment ofŁukasiewicz logic, are obtained as (t-conorm) monoidal combination of finitely many hats, which are in turn obtained through finitely many applications of an operation called starring, starting from a finite family of primitive hats. The aim of this paper is to extend this portion of the Schauder hats theory to the two-variable fragment of Hajek’s Basic logic. This step represents a non-trivial generalization of the one variable case studied in [AG05], [Mon00], and provides sufficient insight to capture the behaviour of the n-variable case for n ≥ 1.
Schauder hats for the two-variable fragment of BL / S. Aguzzoli, S. Bova - In: Proceedings [of the] 40th IEEE International Symposium on Multiple-Valued Logic —— ISMVL 2010 —— : 26–28 May 2010, Barcelona, SpainLos Alamitos : IEEE Computer Society, 2010. - ISBN 9781424467525. - pp. 27-32 (( Intervento presentato al 40th. convegno The 40th IEEE International Symposium On Multiple-Valued Logic tenutosi a Barcelona, Spain nel 2010 [10.1109/ISMVL.2010.14].
Schauder hats for the two-variable fragment of BL
S. AguzzoliPrimo
;
2010
Abstract
The theory of Schauder hats is a beautiful and powerful tool for investigating, under several respects, the algebraic semantics of Łukasiewicz infinite-valued logic [CDM99],[MMM07], [Mun94], [P95]. As a notably application of the theory, the elements of the free n-generated MV-algebra, that constitutes the algebraic semantics of the n-variate fragment ofŁukasiewicz logic, are obtained as (t-conorm) monoidal combination of finitely many hats, which are in turn obtained through finitely many applications of an operation called starring, starting from a finite family of primitive hats. The aim of this paper is to extend this portion of the Schauder hats theory to the two-variable fragment of Hajek’s Basic logic. This step represents a non-trivial generalization of the one variable case studied in [AG05], [Mon00], and provides sufficient insight to capture the behaviour of the n-variable case for n ≥ 1.Pubblicazioni consigliate
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