Virtual Joins With Nonexistent Links

Many approaches to multi-relational learning require the computation of database frequencies in the presence of nonexistent links. The corresponding ILP problem is to compute the number of groundings that satisfy a given conjunction of literals in a relational database, where one or more of the literals is negated. We present a fast new dynamic programming algorithm for this problem. The database table joins performed by our algorithm are restricted to joins of tables already existing in the database. Evaluation on three data sets confirms the efficiency of our algorithm; computing frequencies for negated literals added about 15% to the cost of computing frequencies for positive literals only.