Convergent Deduction for Probabilistic Logic

TL;DR

This paper introduces a convergent proof system for Nilsson's probabilistic logic that computes narrowing probability intervals, allowing for partial conclusions and improving the inference process.

Contribution

It develops a convergent proof system for probabilistic logic that ensures the inference process produces increasingly precise probability intervals.

Findings

Proof system is sound within Nilsson's semantics.

Inference intervals converge to the smallest entailed probability.

Partial information can be obtained at any stage of the inference.

Abstract

This paper discusses the semantics and proof theory of Nilsson's probabilistic logic, outlining both the benefits of its well-defined model theory and the drawbacks of its proof theory. Within Nilsson's semantic framework, we derive a set of inference rules which are provably sound. The resulting proof system, in contrast to Nilsson's approach, has the important feature of convergence - that is, the inference process proceeds by computing increasingly narrow probability intervals which converge from above and below on the smallest entailed probability interval. Thus the procedure can be stopped at any time to yield partial information concerning the smallest entailed interval.