 Semantic theories explain how the truth or falsity of whole sentences depends on the meanings of their parts by stating rules governing the interpretation of subsentential expressions and their modes of combination. A semantic framework provides a standard formalism for stating such rules. The simplest (0-dimensional) semantic frameworks work by assigning extensions as the semantic values of particular expressions. Intuitively, the extension includes those things in the actual world to which the expression applies: e.g., the extension of the name ‘Barack Obama’ is the man Obama, the extension of the predicate ‘is cool’ is the set of all the actual cool things, and the extension of a two-place predicate ‘is cooler than’ is the set of pairs of actually existing things the first of which is cooler than the second. A whole sentence is assigned a truth-value (True or False) as its extension, which is computed on the basis of the extensions of the component expressions: e.g., the sentence, ‘Barack Obama is cool’, will have the semantic value True just in case Obama is a member of the set of actual cool things. A two-dimensional semantic framework is the result of enriching this simple extensional framework in two distinct ways.