Probabilities on Sentences in an Expressive Logic

  title={Probabilities on Sentences in an Expressive Logic},
  author={Marcus Hutter and John W. Lloyd and Kee Siong Ng and William T. B. Uther},
  journal={J. Appl. Log.},
Abstract Automated reasoning about uncertain knowledge has many applications. [...] Key Method We also give explicit constructions and several general characterizations of probabilities that satisfy some or all of the criteria and various (counter)examples. We also derive necessary and sufficient conditions for extending beliefs about finitely many sentences to suitable probabilities over all sentences, and in particular least dogmatic or least biased ones. We conclude with a brief outlook on how the developed…Expand
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