From the standpoint of supporting human-centered discovery of knowledge, the present-day model of mining association rules suuers from the following serious shortcomings: (i) lack of user exploration and control, (ii) lack of focus, and (iii) rigid notion of relationships. In eeect, this model functions as a black-box, admitting little user interaction in between. We propose, in this paper, an architecture that opens up the black-box, and supports constraint-based, human-centered exploratory mining of associations. The foundation of this architecture is a rich set of constraint constructs, including domain, class, and SQL-style aggregate constraints, which enable users to clearly specify what associations are to be mined. We propose constrained association queries as a means of specifying the constraints to be satissed by the antecedent and consequent of a mined association. In this paper, we mainly focus on the technical challenges in guaranteeing a level of performance that is commensurate with the selectivities of the constraints in an association query. To this end, we introduce and analyze two properties of constraints that are critical to pruning: anti-monotonicity and succinctness. We then develop characterizations of various constraints into four categories, according to these properties. Finally, we describe a mining algorithm called CAP, which achieves a maximized degree of pruning for all categories of constraints. Experimental results indicate that CAP can run much faster, in some cases as much as 80 times, than several basic algorithms. This demonstrates how important the succinctness and anti-monotonicity properties are, in delivering the performance guarantee.