Genealogy of FOL and LP

A diagram summarizing the genealogy of First-order Logic (FOL), Description Logic (DL), and Logic Programming (LP) as a basis for (an) open-source, enterprise-scale EvaluationSemantics4RETE which outperforms tableau-based algorithms and implements the restricted intersection of Description Logics (OWL-DL primarily) and Horn Logic (RIF Basic Logic Dialect @@WORKINPROGRESS): DescriptionLogicPrograms

The diagram is also available in its original SVG format

Notes

Cardinality (see: owl:cardinality) and Disjoint semantics (see: DisjointClasses(d1 … dn)) cannot be expressed in DLP!:

"These constructors cannot, in general, be mapped into def-Horn. The case of negation is obvious as negation is not allowed in either the head or body of a def-Horn rule. As can be seen in Figure 4, cardinality restrictions correspond to assertions of variable equality and inequality in FOL, and this is again outside of the def-Horn framework."