This book constitutes the proceedings of the International Joint Conference on Rules and Reasoning, RuleML+RR 2021, held in Leuven, Belgium, during September, 2021. This is the 5th conference of a new series, joining the efforts of two existing conference series, namely "RuleML" (International Web Rule Symposium) and "RR" (Web Reasoning and Rule Systems). The 17 full research papers presented together with 2 short technical communications papers and 2 abstracts of invited papers were carefully reviewed and selected from 39 submissions.

This book constitutes the proceedings of the International Joint Conference on Rules and Reasoning, RuleML+RR 2020, held in Oslo, Norway, during June-July 2020*. This is the 4th conference of a new series, joining the efforts of two existing conference series, namely "RuleML" (International Web Rule Symposium) and "RR" (Web Reasoning and Rule Systems). The 7 full research papers presented together with 6 short technical communications papers were carefully reviewed and selected from 30 submissions. *The conference was held virtually due to the COVID-19 pandemic.