This special issue of Theory and Practice of Logic Programming consists of extended versions of five selected papers from the 3rd International Joint Conference on Rules and Reasoning (RuleML+RR 2019). RuleML+RR 2019 was held in conjunction with the 5th Global Conference on Artificial Intelligence, GCAI 2019, as part of the Bolzano Rules and Artificial INtelligence Summit in Bolzano, Italy, from 17 to 19 of September 2019.