Godel propositional logic is the logic of the minimum triangular norm, and can be axiomatized as propositional intuitionistic logic augmented by the prelinearity axiom (alpha ->beta) V (beta ->alpha). Its algebraic counterpart is the subvariety of Heyting algebras satisfying prelinearity, known as Godel algebras. A Delannoy path is a lattice path in Z^2 that only uses northward, eastward, and northeastward steps. We establish a representation theorem for free n-generated Godel algebras in terms of the Boolean n-cube {0,1}^n, enriched by suitably generalized Delannoy paths.

Propositional Gödel logic and Delannoy paths / P. Codara, O.M. D'Antona, V. Marra - In: IEEE International Conference on Fuzzy Systems : 23-26 july 2007, London, UK : proceedingsPiscataway : Institute of electrical and electronics engineers, 2007. - ISBN 9781424412099. - pp. 1233-1237 (( convegno IEEE International Conference on Fuzzy Systems tenutosi a London nel 2007.

Propositional Gödel logic and Delannoy paths

P. Codara
Primo
;
O.M. D'Antona
Secondo
;
V. Marra
Ultimo
2007

Abstract

Godel propositional logic is the logic of the minimum triangular norm, and can be axiomatized as propositional intuitionistic logic augmented by the prelinearity axiom (alpha ->beta) V (beta ->alpha). Its algebraic counterpart is the subvariety of Heyting algebras satisfying prelinearity, known as Godel algebras. A Delannoy path is a lattice path in Z^2 that only uses northward, eastward, and northeastward steps. We establish a representation theorem for free n-generated Godel algebras in terms of the Boolean n-cube {0,1}^n, enriched by suitably generalized Delannoy paths.
Gödel logic; Delannoy paths
Settore INF/01 - Informatica
Settore MAT/01 - Logica Matematica
http://air.unimi.it/handle/2434/41851
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2434/209248
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