Probabilistic Algorithmic Knowledge

TL;DR

This paper extends the algorithmic knowledge framework to include randomized algorithms, analyzing how probabilistic answers provide evidence for facts and their implications for decision-making.

Contribution

It introduces a formal model for randomized knowledge algorithms and characterizes the evidence they provide when answers are probabilistic.

Findings

Randomized algorithms can be formalized within the knowledge framework.

Answers from such algorithms serve as evidence for the truth of facts.

The paper discusses how evidence from randomized answers influences decision processes.

Abstract

The framework of algorithmic knowledge assumes that agents use deterministic knowledge algorithms to compute the facts they explicitly know. We extend the framework to allow for randomized knowledge algorithms. We then characterize the information provided by a randomized knowledge algorithm when its answers have some probability of being incorrect. We formalize this information in terms of evidence; a randomized knowledge algorithm returning ``Yes'' to a query about a fact \phi provides evidence for \phi being true. Finally, we discuss the extent to which this evidence can be used as a basis for decisions.