Propositional Gödel logic, Delannoy paths and ordered partitions
Pietro Codara · 2006
Godel propositional logic is the logic of the minimum t-norm, and can be axiomatised as propositional intuitionistic logic augmented by the prelinearity axiom (α → β) ∨ (β → α). Thus, its Tarski-Lindenbaum algebras are Heyting algebras satisfying prelinearity; we shall call them Godel algebras. A Delannoy path is a lattice path in Z that only uses northward, westward, and northwestward steps. We give a representation theorem for n-generated free Godel algebras based upon the boolean unit n-cube {0, 1}n enriched by families of Delannoy paths (more precisely, their straightforward multidimensional generalisation). If time allows, we report on work in progress that, using ordered partitions of finite sets, aims at building a new combinatorial semantics for Godel propositional logic. Parts of this talk are joint work with O. M. D’Antona and V. Marra.