The PRIMUS family of systems

PRIMUS stands for Prime Implicate Uncovering System. It is a system for discovering intensional rules in first-order logic from extensional facts.

The most general clauses satisfied by a set of observations under the domain closure assumption are its prime implicates. There may be a large number of such clauses. In order to make the search more efficient and to reduce the results provided to the user, the approach of PRIMUS is to look first for sets of dependent literals, and then to construct clauses only for those literal sets that obtain a high interdependency estimate. This estimate is based on $\chi^2$ .

The PRIMUS approach is described in the report:

A full implementation of PRIMUS has not yet been released, but the following offspring is available:

Tertius is an implementation of PRIMUS restricted to signed literals.
1BC and 1BC2 are first-order naive Bayesian classifiers.