Around the middle of the 20th century Rudolf Carnap and Yehoshua Bar-Hillel gave a seminal account of semantic information which falls under the probabilistic approach. Their idea was to measure the semantic information of a statement within a given language in terms of an a priori logical probability space. The general idea is based on the Inverse Relationship Principle, according to which the information value of a proposition is inversely proportional to the probability of that proposition.
Here is a brief overview of their work: Bar-Hillel and Carnap’s Account of Semantic Information
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