On Approximate Truth
Abstract
We propose a definition for the relation: structure U approximates structure S. A first order sentence is then defined to be approximately true in a structure just in case it is true (standardly) in an approximating structure. The deductive and inductive logic of approximate truth in this sense is discussed. Regarding deduction, we consider a modal language where ▪θ is true in a structure S just in case θ is approximately true in S, and show that the set of theorems of this language is not recursively enumerable. Regarding induction, we define a paradigm of probably approximately correct truth detection, and show that successful induction is possible in this paradigm with respect to a wide class of sentences.
Cite
Text
Osherson et al. "On Approximate Truth." Annual Conference on Computational Learning Theory, 1989. doi:10.1016/B978-0-08-094829-4.50009-XMarkdown
[Osherson et al. "On Approximate Truth." Annual Conference on Computational Learning Theory, 1989.](https://mlanthology.org/colt/1989/osherson1989colt-approximate/) doi:10.1016/B978-0-08-094829-4.50009-XBibTeX
@inproceedings{osherson1989colt-approximate,
title = {{On Approximate Truth}},
author = {Osherson, Daniel N. and Stob, Michael and Weinstein, Scott},
booktitle = {Annual Conference on Computational Learning Theory},
year = {1989},
pages = {88-101},
doi = {10.1016/B978-0-08-094829-4.50009-X},
url = {https://mlanthology.org/colt/1989/osherson1989colt-approximate/}
}