Vast amounts of information is encoded in tables found in documents, on the Web, and in spreadsheets or databases. Integrating or searching over this information benefits from understanding its intended meaning and making it explicit in a semantic representation language like RDF. Most current approaches to generating Semantic Web representations from tables 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. Approaches that work well for one domain, may not necessarily work well for others. We describe a domain independent framework for interpreting the intended meaning of tables and representing it as Linked Data. At the core of the framework are techniques grounded in graphical models and probabilistic reasoning to infer meaning associated with a table. Using background knowledge from resources in the Linked Open Data cloud, we jointly infer the semantics of column headers, table cell values (e.g., strings and numbers) and relations between columns and represent the inferred meaning as graph of RDF triples. A table’s meaning is thus captured 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.