A First-Order Logic of Probability and Only Knowing in Unbounded Domains

Abstract

Only knowing captures the intuitive notion that the beliefs of an agent are precisely those that follow from its knowledge base. It has previously been shown to be useful in characterizing knowledge-based reasoners, especially in a quantified setting. While this allows us to reason about incomplete knowledge in the sense of not knowing whether a formula is true or not, there are many applications where one would like to reason about the degree of belief in a formula. In this work, we propose a new general first-order account of probability and only knowing that admits knowledge bases with incomplete and probabilistic specifications. Beliefs and non-beliefs are then shown to emerge as a direct logical consequence of the sentences of the knowledge base at a corresponding level of specificity.

Cite

Text

Belle et al. "A First-Order Logic of Probability and Only Knowing in Unbounded Domains." AAAI Conference on Artificial Intelligence, 2016. doi:10.1609/AAAI.V30I1.10108

Markdown

[Belle et al. "A First-Order Logic of Probability and Only Knowing in Unbounded Domains." AAAI Conference on Artificial Intelligence, 2016.](https://mlanthology.org/aaai/2016/belle2016aaai-first/) doi:10.1609/AAAI.V30I1.10108

BibTeX

@inproceedings{belle2016aaai-first,
  title     = {{A First-Order Logic of Probability and Only Knowing in Unbounded Domains}},
  author    = {Belle, Vaishak and Lakemeyer, Gerhard and Levesque, Hector J.},
  booktitle = {AAAI Conference on Artificial Intelligence},
  year      = {2016},
  pages     = {893-899},
  doi       = {10.1609/AAAI.V30I1.10108},
  url       = {https://mlanthology.org/aaai/2016/belle2016aaai-first/}
}