A common limitation of many retrieval models, including the recently proposed axiomatic approaches, is that retrieval scores are solely based on exact (i.e., syntactic) matching of terms in the queries and documents, without allowing distinct but semantically related terms to match each other and contribute to the retrieval score. In this paper, we show that semantic term matching can be naturally incorporated into the axiomatic retrieval model through defining the primitive weighting function based on a semantic similarity function of terms. We define several desirable retrieval constraints for semantic term matching and use such constraints to extend the axiomatic model to directly support semantic term matching based on the mutual information of terms computed on some document set. We show that such extension can be efficiently implemented as query expansion. Experiment results on several representative data sets show that, with mutual information computed over the documents in either the target collection for retrieval or an external collection such as the Web, our semantic expansion consistently and substantially improves retrieval accuracy over the baseline axiomatic retrieval model. As a pseudo feedback method, our method also outperforms a state-of-the-art language modeling feedback method.