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:
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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;
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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.
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References
Aumann, R.: Interactive epistemology: Knowledge. Int. J. Game Theory 28, 263–300 (1999)
Aumann, R.: Interactive epistemology: Probability. Int. J. Game Theory 28, 301–314 (1999)
Doberkat, E.E.: Stochastic Coalgebraic Logic. EATCS Mongraphs in Theoretical Computer Sciences. Springer, Heidelberg (2010)
Fagin, R., Halpern, J.: Reasoning about knowledge and probability. J. ACM 41, 340–367 (1994)
Fagin, R., Megiddo, N., Halpern, J.: A logic for reasoning about probabilities. Inf. and Comp. 87, 78–128 (1990)
Goldblatt, R.: Deduction systems for coalgebras over measurable spaces. J. Logic Comp. 20(5), 1069–1100 (2010)
Heifetz, A., Mongin, P.: Probability logic for type spaces. Games Econom. Behav. 35, 31–53 (2001)
Heifetz, A., Samet, D.: Topology-free typology of beliefs. J. Econom. Theory 82, 241–324 (1998)
Heifetz, A., Samet, D.: Coherent beliefs are not always types. J. Math. Econom. 32, 475–488 (1999)
Meier, M.: An infinitary probability logic for type spaces. Israel J. of Math. (to appear)
Moss, L., Viglizzo, I.: Final coalgebras for functors on measurable spaces. Inf. and Comp. 204, 610–636 (2006)
Zhou, C.: A complete deductive system for probability logic. J. Logic Comp. 19(6), 1427–1454 (2009)
Zhou, C.: Probability logics for finitely additive beliefs. J. Logic, Language and Information 19(3), 247–282 (2010)
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Zhou, C. (2011). Intuitive Probability Logic. In: Ogihara, M., Tarui, J. (eds) Theory and Applications of Models of Computation. TAMC 2011. Lecture Notes in Computer Science, vol 6648. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20877-5_25
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DOI: https://doi.org/10.1007/978-3-642-20877-5_25
Publisher Name: Springer, Berlin, Heidelberg
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