Generalised information systems capture L-domains

A generalisation of Scott's information systems \cite{sco82} is presented that captures exactly all L-domains. The global consistency predicate in definition relativised such a way there for each atomic proposition (token) saying which finite sets statements express consistent with the given statement. It shown states generalised form an L-domain, and L-domain can be generated this way, up to isomorphism. Moreover, equivalence category L-domains derived. In addition, it will seen from every system capturing algebraic bounded-complete domain corresponding Scott obtained easy natural vice versa; similarly Hoofman's continuous \cite{ho93} domains captured by them; Chen Jung's disjunctive propositional logic \cite{cj06} (as well as Wang Li's \cite{wll20} finitary version Lawson-compact L-domains); conjunctive sequent calculi \cite{wlbc20} proper domains. proofs always contain syntactic translations between logical involved.