Propositional Gödel Logic and Delannoy Paths

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 rarr beta) V (beta rarr alpha). Its algebraic counterpart is the subvariety of Heyting algebras satisfying prelinearity, known as Godel algebras. A Delannoy path is a lattice path in Z2 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.