Information Systems and Complete Lattices
by
Michael Bukatin
Brandeis University

Among two approaches to the domain topology via logic - the covariant one (information systems) and the contravariant one (Stone duality) - information systems lead to easier treatment of lattice-like structures.

In [Hoofman R. Continuous information systems. Information and Computation, 105, #1, pp.42-71, 1993] information systems were generalized to continuous, bounded complete cpo's. The rule A \vdash A was replaced by the inverse cut rule:

A \vdash C ===> existsB. A \vdash B, B \vdash C .

We explain the intuition behind the inverse cut rule and further generalize information systems to bounded complete cpo's. We also explain why closure operations play an exclusive role to describe subdomains of algebraic, bounded complete cpo's (domains) and introduce the following condition for retractions of domains: a retraction R is finitary iff for the corresponding approximable mapping r

for allu, w in Con. (urw ===> existsv in Con. urv, vrv, vrw).

Supported by NSF Grant CCR-9216185 and Office of Naval Research Grant ONR N00014-93-1-1015

Date received: April 12, 1996