We present work on understanding natural language in a situated domain in an incremental, word-by-word fashion. We explore a set of models specified as Markov Logic Networks and show that a model that has access to information about the visual context during an utterance, its discourse context, the words of the utterance, as well as the linguistic structure of the utterance performs best and is robust to noisy speech input. We explore the incremental properties of the models and offer some analysis. We conclude that MLN<small>S</small> provide a promising framework for specifying such models in a general, possibly domain-independent way.