In literature, different deductive systems are developed for probability logics. But, for formulas, they provide essentially equivalent definitions of consistency. In this paper, we present a guided maximally consistent extension theorem which says that any probability assignment to formulas in a finite local language satisfying some constraints specified by probability formulas is consistent in probability logics, and hence connects this intuitive reasoning with formal reasoning about probabilities. Moreover, we employ this theorem to show two interesting results:

  • The satisfiability of a probability formula is equivalent to the solvability of the corresponding system of linear inequalities through a natural translation based on atoms, not on Hintikka sets;

  • the Countably Additivity Rule in Goldblatt [6] is necessary for his deductive construction of final coalgebras for functors on Meas, the category of measurable spaces.


Probability Logic Belief Types Modal Logic Probability Measure 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Chunlai Zhou
    • 1
  1. 1.Department of Computer Science and Technology, School of InformationRenmin University of ChinaBeijingChina

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