Foundations of Inference
Copyright policy )Foundations of Inference
We present a simple and clear foundation for finite inference that unites and significantly extends the approaches of Kolmogorov and Cox. Our approach is based on quantifying lattices of logical statements in a way that satisfies general lattice symmetries. With other applications such as measure theory in mind, our derivations assume minimal symmetries, relying on neither negation nor continuity nor differentiability. Each relevant symmetry corresponds to an axiom of quantification, and these axioms are used to derive a unique set of quantifying rules that form the familiar probability calculus. We also derive a unique quantification of divergence, entropy and information.
- University at Albany, SUNY United States
- State University of New York at Potsdam United States
- ALBANY STATE UNIVERSITY
FOS: Computer and information sciences, Artificial Intelligence and Robotics, Measures of information, entropy, Computer Science - Artificial Intelligence, probability, FOS: Physical sciences, Mathematics - Statistics Theory, measure, Statistics Theory (math.ST), Bayesian, information, QA1-939, FOS: Mathematics, Statistical Theory, lattice, inference, Probability (math.PR), Mathematics - Logic, Probability and inductive logic, Algorithmic information theory (Kolmogorov complexity, etc.), Artificial Intelligence (cs.AI), Physics - Data Analysis, Statistics and Probability, entropy, Logic (math.LO), divergence, Mathematics, Mathematics - Probability, Data Analysis, Statistics and Probability (physics.data-an), Logical aspects of lattices and related structures
FOS: Computer and information sciences, Artificial Intelligence and Robotics, Measures of information, entropy, Computer Science - Artificial Intelligence, probability, FOS: Physical sciences, Mathematics - Statistics Theory, measure, Statistics Theory (math.ST), Bayesian, information, QA1-939, FOS: Mathematics, Statistical Theory, lattice, inference, Probability (math.PR), Mathematics - Logic, Probability and inductive logic, Algorithmic information theory (Kolmogorov complexity, etc.), Artificial Intelligence (cs.AI), Physics - Data Analysis, Statistics and Probability, entropy, Logic (math.LO), divergence, Mathematics, Mathematics - Probability, Data Analysis, Statistics and Probability (physics.data-an), Logical aspects of lattices and related structures
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