Information systems for continuous semi-lattices

We consider two problems on representation theory for domains by information systems. The first problem is how to represent continuous semi-lattices as information systems, and the second one is which subclass of the continuous information systems designed by Spreen et al. for continuous domains can be used to represent bounded complete domains. We solve the first problem by defining a notion of SL-information systems. This is a special case of the continuous information systems. We also discuss the morphism part of SL-information systems, which corresponds to Scott-continuous functions between continuous semi-lattices. Noting that each bounded complete domain is a special continuous semi-lattices, we provide a correct solution to the second problem by properly strengthening the conditions of SL-information systems. (c) 2022 Elsevier B.V. All rights reserved.