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. CodaraPrimo
;O.M. D'AntonaSecondo
;V. MarraUltimo
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.
Pubblicazioni consigliate
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
