A temporal knowledge graph (TKG) stores the events derived from the data involving time. Predicting events is extremely challenging due to the time-sensitive property of events. Besides, the previous TKG completion (TKGC) approaches cannot represent both the timeliness and the causality properties of events, simultaneously. To address these challenges, we propose a Logic and Commonsense-Guided Embedding model (LCGE) to jointly learn the time-sensitive representation involving timeliness and causality of events, together with the time-independent representation of events from the perspective of commonsense. Specifically, we design a temporal rule learning algorithm to construct a rule-guided predicate embedding regularization strategy for learning the causality among events. Furthermore, we could accurately evaluate the plausibility of events via auxiliary commonsense knowledge. The experimental results of TKGC task illustrate the significant performance improvements of our model compared with the existing approaches. More interestingly, our model is able to provide the explainability of the predicted results in the view of causal inference. The appendix, source code and datasets of this paper are available at https://github.com/ngl567/LCGE.