Constraints (2013) 18:144–165 DOI 10.1007/s10601-013-9141-7 Formulating the template ILP consistency problem as a constraint satisfaction problem Roman Barták · Radomír ˇ Cernoch · Ondˇ rej Kuželka · Filip Železný Published online: 12 February 2013 © Springer Science+Business Media New York 2013 Abstract Inductive Logic Programming (ILP) deals with the problem of finding a hypothesis covering positive examples and excluding negative examples, where both hypotheses and examples are expressed in first-order logic. In this paper we employ constraint satisfaction techniques to model and solve a problem known as template ILP consistency, which assumes that the structure of a hypothesis is known and the task is to find unification of the contained variables. In particular, we present a con- straint model with index variables accompanied by a Boolean model to strengthen inference and hence improve efficiency. The efficiency of models is demonstrated experimentally. Keywords Constraint modeling · Inductive logic programming · Meta-reasoning 1 Introduction Inductive logic programming (ILP) is a subfield of machine learning which uses first- order logic as a uniform representation for examples, background knowledge and R. Barták (B ) Faculty of Mathematics and Physics, Charles University in Prague, Praha 1, Czech Republic e-mail: bartak@ktiml.mff.cuni.cz R. ˇ Cernoch · O. Kuželka · F. Železný Faculty of Electrical Engineering, Czech Technical University in Prague, Praha 1, Czech Republic R. ˇ Cernoch e-mail: cernorad@fel.cvut.cz O. Kuželka e-mail: kuzelon2@fel.cvut.cz F. Železný e-mail: zelezny@fel.cvut.cz