Zese et al. present Prolog implementations of some reasoning algorithms for description logics (DL). They describe two principal algorithms, TRILL and TRILL^p; each implements the tableau algorithm. TRILL is able to return explanations for query results, and TRILL^p “is able to compute a Boolean formula representing the set of explanations for a query.” Furthermore, both algorithms are capable of computing the probabilities of queries according to the DISPONTE “distribution semantics of probabilistic logic programming.”

The two TRILL algorithms are compared on simulated knowledge bases (KBs) of increasing size to Pellet, an algorithm based on Reiter’s hitting set algorithm written in Java. Both TRILL algorithms proved to be superior. For probabilistic reasoning, the authors compared the TRILL algorithms to BUNDLE and PRONTO using four existing KBs. In this case, the TRILL algorithms were competitive, but not always better; however, their memory usage was substantially smaller.

The algorithms are clearly explained with substantial details on the implementations. Readers should be able to reproduce the implementations based on the information provided. The authors provide a web-based application (http://trill.lamping.unife.it) that “allows users to write a KB in the RDF/XML format” and query the KB. It is gratifying to see a Prolog implementation that is both efficient and lucid.