  This paper establishes a purely syntactic representation for the category of
algebraic L-domains with Scott-continuous functions as morphisms. The central
tool used here is the notion of logical states, which builds a bridge between
disjunctive sequent calculi and algebraic L-domains. To capture
Scott-continuous functions between algebraic L-domains, the notion of
consequence relations between disjunctive sequent calculi is also introduced.
It is shown that the category of disjunctive sequent calculi with consequence
relations as morphisms is categorical equivalent to that of algebraic L-domains
with Scott-continuous functions as morphisms.
