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.