In the last decades, the increasing amount of data available in all fields raises the necessity to discover new knowledge and explain the hidden information found. On one hand, the rapid increase of interest in, and use of, artificial intelligence (AI) in computer applications has raised a parallel concern about its ability (or lack thereof) to provide understandable, or explainable, results to users. In the biomedical informatics and computer science communities, there is considerable discussion about the `` un-explainable" nature of artificial intelligence, where often algorithms and systems leave users, and even developers, in the dark with respect to how results were obtained. Especially in the biomedical context, the necessity to explain an artificial intelligence system result is legitimate of the importance of patient safety. On the other hand, current database systems enable us to store huge quantities of data. Their analysis through data mining techniques provides the possibility to extract relevant knowledge and useful hidden information. Relationships and patterns within these data could provide new medical knowledge. The analysis of such healthcare/medical data collections could greatly help to observe the health conditions of the population and extract useful information that can be exploited in the assessment of healthcare/medical processes. Particularly, the prediction of medical events is essential for preventing disease, understanding disease mechanisms, and increasing patient quality of care. In this context, an important aspect is to verify whether the database content supports the capability of predicting future events. In this thesis, we start addressing the problem of explainability, discussing some of the most significant challenges need to be addressed with scientific and engineering rigor in a variety of biomedical domains. We analyze the ``temporal component" of explainability, focusing on detailing different perspectives such as: the use of temporal data, the temporal task, the temporal reasoning, and the dynamics of explainability in respect to the user perspective and to knowledge. Starting from this panorama, we focus our attention on two different temporal data mining techniques. The first one, based on trend abstractions, starting from the concept of Trend-Event Pattern and moving through the concept of prediction, we propose a new kind of predictive temporal patterns, namely Predictive Trend-Event Patterns (PTE-Ps). The framework aims to combine complex temporal features to extract a compact and non-redundant predictive set of patterns composed by such temporal features. The second one, based on functional dependencies, we propose a methodology for deriving a new kind of approximate temporal functional dependencies, called Approximate Predictive Functional Dependencies (APFDs), based on a three-window framework. We then discuss the concept of approximation, the data complexity of deriving an APFD, the introduction of two new error measures, and finally the quality of APFDs in terms of coverage and reliability. Exploiting these methodologies, we analyze intensive care unit data from the MIMIC dataset
