| Incomplete information is defined for the statistical theory devoted to complex systems having interactions which cannot be written explicitly or equations of motion which cannot be resolved to give exact knowledge about the systems. In this case, a part of the information necessary for complete description of the systems is never accessible to the theory. In other words, the physics theory contains only incomplete information. For detailed discussion, see the introduction to incomplete information theory or the references (1), (2) and (3) If the unaccessible information is not negligible with respect to the accessible information, the theory can no more answer all the questions that can be asked about itself or about the systems it describes. This kind of theory is incomplete. As a matter of fact, according to G�del, any axiomatic system is incomplete in the sense that there are always statements that can not be proved within the system containing a finite amount of information related to the axiomes. There are always statements of which the proof needs more information than contained in the axioms, i.e., in the theory itself.. |