Objective Bayesian probabilistic logic

  • Authors:
  • Jon Williamson

  • Affiliations:
  • Philosophy, SECL, University of Kent, Canterbury, CT2 7NF, UK

  • Venue:
  • Journal of Algorithms
  • Year:
  • 2008

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Abstract

This paper develops connections between objective Bayesian epistemology-which holds that the strengths of an agent's beliefs should be representable by probabilities, should be calibrated with evidence of empirical probability, and should otherwise be equivocal-and probabilistic logic. After introducing objective Bayesian epistemology over propositional languages, the formalism is extended to handle predicate languages. A rather general probabilistic logic is formulated and then given a natural semantics in terms of objective Bayesian epistemology. The machinery of objective Bayesian nets and objective credal nets is introduced and this machinery is applied to provide a calculus for probabilistic logic that meshes with the objective Bayesian semantics.