An Introduction to the Semantic Information G Theory and Applications

Does semantic communication require a semantic information theory parallel to Shannon's information theory, or can Shannon's work be generalized for semantic communication? This paper advocates for the latter and introduces the semantic information G theory (with "G" denoting generalization). The core approach involves replacing the distortion constraint with the semantic constraint, achieved by utilizing a set of truth functions as a semantic channel. These truth functions enable the expression of semantic distortion, semantic information measures, and semantic information loss. Notably, the maximum semantic information criterion is shown to be equivalent to the maximum likelihood criterion and parallels the Regularized Least Squares criterion. The G theory is compatible with machine learning methodologies, offering enhanced capabilities for handling latent variables, often addressed through Variational Bayes. This paper systematically presents the generalization of Shannon's information theory into the G theory and its wide-ranging applications. The applications involve semantic communication, machine learning, constraint control, Bayesian confirmation, portfolio theory, and information value. Furthermore, insights from statistical physics are discussed: Shannon information is equated to free energy, semantic information to the free energy of local equilibrium systems, and information efficiency to the efficiency of free energy in performing work. The paper also proposes refining Friston's minimum free energy principle into the maximum information efficiency principle. Lastly, it discusses the limitations of the G theory in representing the semantics of complex data.