Asymptotic Conditional Probability in Modal Logic: A Probabilistic Reconstruction of Nonmonotonic Logic
Proceedings of the Nineteenth International Joint Conference on Artificial Intelligence. Pages 1378-1382.
Abstract
We analyze the asymptotic conditional validity of modal formulas, i.e., the probability that a formula ψ is valid in the finite Kripke structures in which a given modal formula φ is valid, when the size of these Kripke structures grows to infinity. We characterize the formulas ψ that are almost surely valid (i.e., with probability 1) in case φ is a flat, S5consistent formula, and show that these formulas ψ are exactly those which follow from φ according to the nonmonotonic modal logic S5G. Our results provide – for the first time – a probabilistic semantics to a well-known nonmonotonic modal logic, establishing a new bridge between nonmonotonic and probabilistic reasoning, and give a computational account of the asymptotic conditional validity problem in Kripke structures.
@inproceedings{ijcai2005p185,
title = {Asymptotic Conditional Probability in Modal Logic: A Probabilistic Reconstruction of Nonmonotonic Logic},
author = {Rosati, Riccardo and Gottlob, Georg},
booktitle = {Proceedings of the Nineteenth International Joint Conference on
Artificial Intelligence, {IJCAI-05}},
publisher = {International Joint Conferences on Artificial Intelligence},
pages = {1378--1382},
year = {2005},
url = {https://ijcai.org/proceedings/2005/185},
}
TY - CPAPER TI - Asymptotic Conditional Probability in Modal Logic: A Probabilistic Reconstruction of Nonmonotonic Logic AU - Rosati, Riccardo AU - Gottlob, Georg T2 - Proceedings of the Nineteenth International Joint Conference on Artificial Intelligence, IJCAI-05 PB - International Joint Conferences on Artificial Intelligence PY - 2005 SP - 1378 EP - 1382 UR - https://ijcai.org/proceedings/2005/185 ER -Copied
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