Toward an Infinitary Logic of Domains: Abramsky Logic for Transition Systems

We give a new characterization of sober spaces in terms of their completely distributive lattice of saturated sets. This characterization is used to extend Abramsky’s results about a domain logic for transition systems. The Lindenbaum algebra generated by the Abramsky finitary logic is a distributive lattice dual to an SFP-domain obtained as a solution of a recursive domain equation. We prove that the Lindenbaum algebra generated by the infinitary logic is a completely distributive lattice dual to the same SFP-domain. As a consequence soundness and completeness of the infinitary logic is obtained for a class of transition systems that is computational interesting. 1991 Mathematics Subject Classification: 03B45, 03B70, 03C75, 03G10, 06D10, 55M05, 68Q55 1991 ACM Computing Classification System: D.3.1, F.3.1, F.4.1