Most open government data is encoded and published in structured tables found in reports, on the Web, and in spreadsheets or databases. Current approaches to generating Semantic Web representations from such data requires human input to create schemas and often results in graphs that do not follow best practices for linked data. Evidence for a table’s meaning can be found in its column headers, cell values, implicit relations between columns, caption and surrounding text but also requires general and domain-specific background knowledge. We describe techniques grounded in graphical models and probabilistic reasoning to infer meaning (semantics) associated with a table using background knowledge from the Linked Open Data cloud. We represent a table’s meaning by mapping columns to classes in an appropriate ontology, linking cell values to literal constants, implied measurements, or entities in the linked data cloud (existing or new) and discovering or and identifying relations between columns.