Propositional Gödel Logic and Delannoy Paths
Pietro Codara, Ottavio M. D’Antona, Vincenzo Marra · 2007
Gödel propositional logic is the logic of the minimum triangular norm, and can be axiomatized as propositional intuitionistic logic augmented by the prelinearity axiom(α → β) V (β → α). Its algebraic counterpart is the subvariety of Heyting algebras satisfying prelinearity, known as Gödel algebras. A Delannoy path is a lattice path in 𝕫2that only uses northward, eastward, and northeastward steps. We establish a representation theorem for free n-generated Gödel algebras in terms of the Boolean 𝓃-cube {0,1}𝓃, enriched by suitably generalized Delannoy paths.