Semantic query optimization uses semantic knowledge in databases (represented in the form of integrity constraints) to rewrite queries and logic programs for the purpose of more efficient query evaluation. Much work has been done to develop various techniques for optimization. Most of it, however, is only applicable to top-down query evaluation strategies. Moreover, little attention has been paid to the cost of the optimization itself. In this paper, we address the issue of semantic query optimization for bottom-up query evaluation strategies with an emphasis on overall efficiency. We restrict our attention to a single optimization technique, join elimination. We discuss various factors that influence the cost of semantic optimization, and present two abstract algorithms for different optimization approaches. The first one pre-processes a query statically before it is evaluated; the second approach combines query evaluation with semantic optimization using heuristics to achieve the largest possible savings. (Also cross-referenced as UMIACS-TR-95-109)