Declarative process mining is a family of techniques for the analysis of business processes that focuses on the use of high-level declarative modeling languages and formal methods for getting insight from event data. The most used declarative modelling language is Declare, that provides a set of logic-based constraints that process executions must satisfy. In particular, a Declare model is a conjunction of constraints, that have semantics rooted in LTLf, which limit process instances behavior by introducing dependencies between process activities. 

A knowledge graph is a type of database that represents information as interconnected nodes and edges, rather than as flat data. The nodes in a knowledge graph represent entities, such as people, places, or things, while the edges represent the relationships between those entities. Knowledge graphs in process mining can be used to represent multi-dimensional event logs and allow for easy visualisation and analysis of such type of event data. 

Linear Temporal Logic (LTL) is a mathematical formalism used to describe properties of systems that evolve over time. It is a type of temporal logic that extends propositional logic by adding temporal operators that can reason about time. These operators allow for the specification of temporal relationships between events and for the modeling of the behavior of systems over time. LTL is widely used in process mining as a mean to express temporal constraints over activities in process executions.

Answer Set Programming (ASP) is a declarative programming paradigm used to model and solve complex problems in fields such as Artificial Intelligence, Robotics, and Planning. The main idea behind ASP is to find one or more answers that satisfy a set of rules and constraints. The programmer writes the rules in a formal language, and an ASP solver computes the answer sets representing the possible solutions to the problem. ASP has proven to be an effective tool for solving problems that are difficult to solve with traditional programming techniques, making it a valuable tool for researchers and developers in the process mining field.