A Logic-based Tractable Approximation of Probability

TL;DR

This paper introduces a logical framework enabling resource-bounded agents to approximate probabilistic reasoning efficiently by using depth-bounded belief functions, making uncertain reasoning more tractable.

Contribution

It presents conditions for approximating propositional probabilities with hierarchical belief functions and demonstrates tractability under certain restrictions.

Findings

Hierarchies of depth-bounded belief functions can approximate propositional probabilities.

Under specific restrictions, probabilistic approximations become computationally tractable.

The framework supports resource-bounded reasoning in uncertain environments.

Abstract

We provide a logical framework in which a resource-bounded agent can be seen to perform approximations of probabilistic reasoning. Our main results read as follows. First we identify the conditions under which propositional probability functions can be approximated by a hierarchy of depth-bounded Belief functions. Second we show that under rather palatable restrictions, our approximations of probability lead to uncertain reasoning which, under the usual assumptions in the field, qualifies as tractable.