One of the strengths of data mining is to replace assumptions about the data model with information directly measured from real data. This paper analyzes this relationship between the mining process and the data for pattern discovery methods. We formalize this notion by identifying patterns, called linked patterns, which are necessary for the evaluation of a measure or a constraint. We then formulate three axioms that a well-behaving pattern mining method should satisfy. We also define the evaluation complexity that quantifies the data fitness of a method. These axioms and evaluation complexity are illustrated with many examples.