Intuitive probability logic

Authors:
Chunlai Zhou
Affiliations:
Department of Computer Science and Technology, School of Information, Renmin University of China, Beijing
Venue:
TAMC'11 Proceedings of the 8th annual conference on Theory and applications of models of computation
Year:
2011

Citing 7
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Abstract

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.