A polystore system evaluates queries that span multiple disparate data models; this character introduces a unique query optimization challenge. Specialized database engines such as array and graph databases support partially overlapping sets of query processing operations. Among their common or similar semantics, different systems could have completely different performance profiles for the same query, making their relative usefulness vary from query to query. We hypothesize that a polystore system could exploit this context-dependent disparity of performance by making choices between executing a sub-query locally and migrating the inputs for remote executions. In this work, as part of the larger ISTC BigDAWG project, we examine the challenges of polystore query optimization through the lens of equivalent semantics among back-end databases.