Logical Optimality of Groundness Analysis

In the context of the abstract interpretation theory, we study the relations among various abstract domains for groundness analysis of logic programs. We reconstruct the well-known domain Pos as a logical domain in a fully automatic way and we prove that it is the best abstract domain which can be set up from the property of groundness by applying logic operators only. We propose a new notion of optimality which precisely captures the relation between Pos and its natural concrete domain. This notion enables us to discriminate between the various abstract domains for groundness analysis from a computational point of view and to compare their relative precision. Finally, we propose a new domain for groundness analysis which has the advantage of being independent from the speciic program and we show its optimality.