TRILL answers queries to SHOIQ knowledge bases using a tableau algorithm. Prolog non-determinism is used for easily handling non-deterministic expansion rules that produce more than one tableau.

You can try it online at


Source Code

The downloadable version is a preliminary version of the reasoner, much work still lies ahead! 
For running TRILL is necessary to use the YAP compiler. 
TRILL is completely written in Prolog. For downloading it, click here, select "" and then click on Save or Download.
The file "" is the probabilistic version of TRILL with which is possible to compute the probability of a query. contains TRILLP, the version of TRILL which computes a general Boolean pinpointing formula using the techniques proposed by Baader and Penaloza [1].
In the same folder, a short manual is downloadable.
TRILL is compatible with SWI Prolog. The version for SWI-Prolog can be installed by the goal 
After this call, TRILL can be loaded with the command 
TRILL is able to translate OWL/RDF files into Prolog and manage knowledge bases defined using OWL-Functional Syntax like syntax.
An example of use is:

?- use_module(library(trill)).

?- load_kb('<your_owl_file>').

?- instanceOf('<your_class>','<your_individual>',Explanations).

If you are using YAP, you need to propare a prolog file containing the OWL knowledge base translated into prolog predicates. In order to do this translation we suggest to exploit Thea2 library (compilable only with SWI Prolog) by running file.
NOTE: TRILL needs the latest version of SWI-Prolog!

To run probabilistic queries, after the translation, all the probabilistic axioms must be asserted following the syntax presented in the manual.


For downloading the datasets for testing TRILL, click here, select "" and then click on Save or Download.

Report an issue

[1] Franz Baader and Rafael Penaloza. "Axiom Pinpointing in General Tableaux". Journal of Logic and Computation, 20(1):5–34, 2010.

  • Riccardo Zese, Elena Bellodi, Fabrizio Riguzzi, and Evelina Lamma. Tableau reasoners for probabilistic ontologies exploiting logic programming techniques. In Proceedings of the Doctoral Consortium (DC) co-located with the 14th Conference of the Italian Association for Artificial Intelligence (AI*IA 2015), volume 1485 of CEUR Workshop Proceedings, pages 1-6, Aachen, Germany, 2015. © by the authors, Sun SITE Central Europe. [ bib | .pdf ]
  • Riccardo Zese, Elena Bellodi, Evelina Lamma, and Fabrizio Riguzzi. Logic programming techniques for reasoning with probabilistic ontologies. In International Workshop on Ontologies and Logic Programming for Query Answering, © by the authors, 2015. [ bib | .pdf | http ]
  • Zese, R., Bellodi, E., Lamma, E., Riguzzi, F., Aguiari, F.: Semantics and inference for probabilistic description logics. In Uncertainty Reasoning for the Semantic Web III - ISWC International Workshops, URSW 2011-2013, Revised Selected Papers, volume 8816 of Lecture Notes in Computer Science, pages 79-99. Springer, 2013
  • Zese, R.: Reasoning with Probabilistic Logics. ArXiv e-prints 1405.0915v3. An extended abstract / full version of a paper accepted at the Doctoral Consortium of the 30th International Conference on Logic Programming (ICLP 2014), July 19-22, Vienna, Austria.
  • Zese, R., Bellodi, E., Lamma, E., and Riguzzi, F.: A description logics tableau reasoner in prolog. In: CILC 2013, CEUR Workshop Proceedings,vol. 1068., 33–47.