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There are many theories explicating specific features of the naive or intuitive notion of information.
The academic sites of these theories range over philosophy, mathematics (type theory, measure theory / probability theory / statistics), computer science, physics, communication sciences, psychology / sociology, economics, semiotics, cybernetics, etc.
Statistical information theory: Claude Shannon, Warren Weaver, Ronald Fisher
Semantic information theory: Yehoshua Bar-Hillel, Rudolf Carnap
Algorithmic information theory: Ray Solomonoff, Andrey Kolmogorov, Gregory Chaitin
Constructive-type-theoretical information theory:
Fred Dretske
Keith Devlin
Jon Barwise
Jeremy Seligman
Jaakko Hintikka
Giuseppe Primiero, information and knowledge - a constructive type-theoretical approach, Springer, 2008
Mark Burgin, Theory of information, 2010