 The most natural starting point for any overview of semantic conceptions of information is Carnap and Bar-Hillel’s “An Outline of a Theory of Semantic Information” (1952). Bar Hillel and Carnap’s theory of semantic information is a quantitative theory that emerged from more general theories of information (see  section 4.2 on Shannon in the entry on  information).  Their theory was designed with the goal of giving us a usable framework for calculating the amount of semantic information encoded by a sentence in a particular language. In their case the language in question is monadic predicate logic. The philosophical details are grounded on an idea that has come to be known as the inverse range principle (IRP). Loosely, IRP states that the amount of information carried or encoded by a sentence is inversely proportional to something else, where this something else is something to which one can attach a precise numerical value. Once this has been done, one can use this numerical value to calculate the measure of semantic information as understood by the theory of semantic information.