This paper concerns the question of how to create abstractions that are useful for program analysis. It presents a method that refines an abstraction automatically for analysis problems in which the semantics of statements and the query of interest are expressed using logical formulas. Refinement is carried out by introducing new instrumentation relations (defined via logical formulas over core relations, which capture the basic properties of memory configurations). A tool that incorporates the algorithm has been implemented and applied to several algorithms that manipulate linked lists and binary-search trees. In all but a few cases, the tool is able to demonstrate (i) the partial correctness of the algorithms, and (ii) that the algorithms possess additional properties -- e.g., stability or antistability.

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