Time periods are frequently used to specify time in metadata and retrieval. However, it is not easy to describe and retrieve information about periods, because the temporal ranges represented by periods are often ambiguous. This is because these temporal ranges do not have fixed beginning and end points. To solve this problem, basic logics to describe and process uncertain time intervals were developed in this study. An uncertain time interval is represented as a set of time intervals that indicate states when the uncertain time interval is determined. Based on this concept, a logic to retrieve uncertain time intervals satisfying a given condition was established, and it was revealed that retrieval results belong to three states: reliable, impossible, and possible matches. Additionally, to describe data about uncertain periods, an ontology (the HuTime Ontology) was constructed based on the logic. This ontology is characterized by the fact that uncertain time intervals can be defined recursively. It is expected that more data about time periods will be created and released using the result of this study.