A Logic With Higher Order Conditional Probabilities
Publications de l'Institut Mathématique, _N_S_82 (2007) no. 96, p. 141
Cet article a éte moissonné depuis la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts
We investigate probability logic with the conditional probability operators.
This logic, denoted $LCP$, allows making statements such as:
$P_{\geq s}\alpha$, $CP_{\geq s}(\alpha\mid\beta)$, $CP_{\leq 0}(\alpha\mid\beta)$
with the intended meaning ``the probability of $\alpha$ is at least $s$",
``the conditional probability of $\alpha$ given $\beta$ is at least
$s$", ``the conditional probability of $\alpha$ given $\beta$ at most $0$".
A possible-world approach is proposed to give semantics to such formulas.
Every world of a given set of worlds is equipped with a probability space
and conditional probability is derived in the usual way:
$P(\alpha\mid\beta)=\frac{P(\alpha\wedge\beta)}{P(\beta)}$,
$P(\beta)>0$, by the (unconditional) probability measure that is
defined on an algebra of subsets of possible worlds.
Infinitary axiomatic system for our logic which is sound and complete with
respect to the mentioned class of models is given.
Decidability of the presented logic is proved.
@article{10_2298_PIM0796141O,
author = {Zoran Ognjanovi\'c and Neboj\v{s}a Ikodinovi\'c},
title = {A {Logic} {With} {Higher} {Order} {Conditional} {Probabilities}},
journal = {Publications de l'Institut Math\'ematique},
pages = {141 },
year = {2007},
volume = {_N_S_82},
number = {96},
doi = {10.2298/PIM0796141O},
zbl = {1203.68206},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.2298/PIM0796141O/}
}
TY - JOUR AU - Zoran Ognjanović AU - Nebojša Ikodinović TI - A Logic With Higher Order Conditional Probabilities JO - Publications de l'Institut Mathématique PY - 2007 SP - 141 VL - _N_S_82 IS - 96 UR - http://geodesic.mathdoc.fr/articles/10.2298/PIM0796141O/ DO - 10.2298/PIM0796141O LA - en ID - 10_2298_PIM0796141O ER -
%0 Journal Article %A Zoran Ognjanović %A Nebojša Ikodinović %T A Logic With Higher Order Conditional Probabilities %J Publications de l'Institut Mathématique %D 2007 %P 141 %V _N_S_82 %N 96 %U http://geodesic.mathdoc.fr/articles/10.2298/PIM0796141O/ %R 10.2298/PIM0796141O %G en %F 10_2298_PIM0796141O
Zoran Ognjanović; Nebojša Ikodinović. A Logic With Higher Order Conditional Probabilities. Publications de l'Institut Mathématique, _N_S_82 (2007) no. 96, p. 141 . doi: 10.2298/PIM0796141O
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