Grammar theory based on lattice-ordered monoid

Motivated by Li and Pedrycz's work on fuzzy finite automata and fuzzy regular expressions with membership values in lattice-ordered monoids and inspired by the close relationship between the automata theory and the theory of formal grammars, we have established a fundamental framework of L-valued grammar. It is shown that the set of L-valued regular languages coincides with the set of L-languages recognized by nondeterministic L-fuzzy finite automata and every L-language recognized by a deterministic L-fuzzy finite automaton is an L-valued regular language.