In recent years, biological event extraction has emerged as a key natural language processing task, aiming to address the information overload problem in accessing the molecular biology literature. The BioNLP shared task competitions have contributed to this recent interest considerably. The first competition (BioNLP09) focused on extracting biological events from Medline abstracts from a narrow domain, while the theme of the latest competition (BioNLP-ST11) was generalization and a wider range of text types, event types, and subject domains were considered. We view event extraction as a building block in larger discourse interpretation and propose a two-phase, linguistically-grounded, rule-based methodology. In the first phase, a general, underspecified semantic interpretation is composed from syntactic dependency relations in a bottom-up manner. The notion of embedding underpins this phase and it is informed by a trigger dictionary and argument identification rules. Coreference resolution is also performed at this step, allowing extraction of inter-sentential relations. The second phase is concerned with constraining the resulting semantic interpretation by shared task specifications. We evaluated our general methodology on core biological event extraction and speculation/negation tasks in three main tracks of BioNLP-ST11 (GENIA, EPI, and ID).