Abstract
The declarative specification of business processes is based upon the elicitation of behavioural rules that constrain the legal executions of the process. The carry-out of the process is up to the actors, who can vary the execution dynamics as long as they do not violate the constraints imposed by the declarative model. The constraints specify the conditions that require, permit or forbid the execution of activities, possibly depending on the occurrence (or absence) of other ones. In this chapter, we review the main techniques for process mining using declarative process specifications, which we call declarative process mining. In particular, we focus on three fundamental tasks of (1) reasoning on declarative process specifications, which is in turn instrumental to their (2) discovery from event logs and their (3) monitoring against running process executions to promptly detect violations. We ground our review on Declare, one of the most widely studied declarative process specification languages. Thanks to the fact that Declare can be formalized using temporal logics over finite traces, we exploit the automata-theoretic characterization of such logics as the core, unified algorithmic basis to tackle reasoning, discovery, and monitoring. We conclude the chapter with a discussion on recent advancements in declarative process mining, considering in particular multi-perspective extensions of the original approach.