The representation and manipulation of natural human understanding of temporal phenomena is a fundamental field of study in Computer Science, which aims both to emulate human thinking, and to use the methods of human intelligence to underpin engineering solutions. In particular, in the domain of Artificial Intelligence, temporal knowledge may be uncertain and incomplete due to the unavailability of complete and absolute temporal information. This paper introduces an inferential framework for deriving logical explanations from partial temporal information. Based on a graphical representation which allows expression of both absolute and relative temporal knowledge in incomplete forms, the system can deliver a verdict to the question if a given set of statements is temporally consistent or not, and provide understandable logical explanation of analysis by simplified contradiction and rule based reasoning.