We present a novel framework for defining memory models in terms of two properties: thread-local Instruction Reordering axioms and Store Atomicity, which describes inter-thread communication via memory. Most memory models have the store atomicity property, and it is this property that is enforced by cache coherence protocols. A memory model with Store Atomicity is serializable; there is a unique global interleaving of all operations which respects the reordering rules. Our framework uses partially ordered execution graphs; one graph represents many instruction interleavings with identical behaviors. The major contribution of this framework is a procedure for enumerating program behaviors in any memory model with Store Atomicity. Using this framework, we show that address aliasing speculation introduces new program behaviors; we argue that these new behaviors should be permitted by the memory model specification. We also show how to extend our model to capture the behavior of non-atomic memory models such as SPARC R TSO.