Models and Inferences: Logical, Epistemological, and Cognitive Issues
Sestri Levante, June 25-27
Crupi V., Nelson J., Meder B., Cevolani G., and Tentori K.
Shannon and beyond: Generalized entropies and rational information search
Abstract. We present a biparametric family of measures known as Sharma-Mittal entropies. This is a very comprehensive framework in contemporary information theory. It includes a number of important special cases arising across different fields such as generalized statistical thermodynamics, the study of biological and ecological diversity, and analyses of political and demographic concentration/fragmentation. Mathematically, relevant parameter settings in the Sharma-Mittal formalism generate classical Boltzmann/Shannon entropy as well as Rényi and Tsallis entropies, and more besides. We discuss applications for human reasoning, where entropy represents epistemic uncertainty and uncertainty reduction, in turn, is a major kind of epistemic utility. We argue that the Sharma-Mittal parameters can be given meaningful theoretical interpretations in this domain. We also explain how a variety of models ensue concerning the expected informational value of experiments, thus of information search options. Finally, we explicate formal and conceptual connections with related branches of the literature, including probabilistic theories of confirmation and scoring rules.
The talk is included in a symposium on Measure sensitivity and robust model-based argumentation in the study of reasoning and cognition. The symposium in turn arises from the activities of two ongoing research projects addressing related issues: priority program New Frameworks of Rationality, SPP 1516 (Deutsche Forschungsgemeinshaft, grant CR 409/1-2), and FIRB project Structures and Dynamics of Knowledge and Cognition (Italian Ministry of Scientific Research, Turin unit, D11J12000470001).