A Propositional CONEstrip Algorithm

We present a variant of the CONEstrip algorithm for checking whether the origin lies in a finitely generated convex cone that can be open, closed, or neither. This variant is designed to deal efficiently with problems where the rays defining the cone are specified as linear combinations of propositional sentences. The variant differs from the original algorithm in that we apply row generation techniques. The generator problem is WPMaxSAT, an optimization variant of SAT; both can be solved with specialized solvers or integer linear programming techniques. We additionally show how optimization problems over the cone can be solved by using our propositional CONEstrip algorithm as a preprocessor. The algorithm is designed to support consistency and inference computations within the theory of sets of desirable gambles. We also make a link to similar computations in probabilistic logic, conditional probability assessments, and imprecise probability theory

The Role of Ignorance about Keynes’s Inexact, Approximation Approach to Measurement in the A Treatise on Probability in the Keynes-Tinbergen Exchanges of 1938-1940 in the Economic Journal

J.Tinbergen and J. M. Keynes held diametrically opposed positions on measurement. Tinbergen’s physics background led him to deploy an exact approach to measurement based on the specification of probability distributions, like the normal and log normal, with exact and precisely probabilities that were linear, additive and definite. All probabilities for Tinbergen were assumed to be well defined, precise, exact, determinate, definite, additive, linear, independent single number answers, whether the field was physics or economics. Keynes’s approach was an inexact one. Probabilities for Keynes were, with a few exceptions, partially defined, imprecise, inexact, indefinite, indeterminate ,non additive, non linear, and dependent. Probability estimates for Keynes required two numbers to specify the probability within a lower and upper bound (limit), and not one single number like Tinbergen’s approach. Keynes called this approach Approximation. Keynesian probabilities are interval valued.The problem, from Keynes’s perspective, was that Tinbergen was trying to apply to economic data techniques which were only sound when applied in physics ,where laboratory controlled environments with detailed experimental design could generate data and replicate/duplicate the experiments. Keynes had always argued that economics was not a physical or life science like physics, engineering, biology or chemistry and that it could never be like physics

Probabilistic Satisfiability With Imprecise Probabilities

AbstractTreatment of imprecise probabilities within the probabilistic satisfiability approach to uncertainty in knowledge-based systems is surveyed and discussed. Both probability intervals and qualitative probabilities are considered. Analytical and numerical methods to test coherence and bound the probability of a conclusion are reviewed. They use polyhedral combinatorics and advanced methods of linear programming