Probabilistic Algorithmic Knowledge

Details Probabilistic Algorithmic Knowledge Probabilistic Algorithmic Knowledge

2005-03-08

arxiv.org/abs/cs/0503018v3

LMCS 1 (3:1) 2005

Computer Science

Artificial Intelligence

26 pages. A preliminary version appeared in Proc. 9th Conference on Theoretical Aspects of Rationality and Knowledge (TARK'03)

Scientific paper

10.2168/LMCS-1(3:1)2005

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.

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