A representation theorem for finite Gödel algebras with operators

LLUIS GODO; RICARDO O. RODRIGUEZ; TOMMASO FLAMINIO

International Workshop on Logic, Language, Information, and Computation

Springer

Lugar: Berlin; Año: 2019; p. 223 - 235

In this paper, we introduce and study finite Godel algebras with operators (GAOs for short) and their dual frames. Taking into account that the category of finite Godel algebras is dually equivalent to the category of finite forests, the dual relational frames of GAOs are forest frames: finite forests endowed with two binary (crisp) relations satisfying suitable properties. Our main result is a Jonsson-Tarski like representation theorem for these structures. In particular, we show that every finite Godel algebra with operators determines a unique forest frame whose set of subforests, endowed with suitably defined algebraic and modal operators, is a GAO isomorphic to the original one.