A logical framework for data-driven reasoning

TL;DR

This paper proposes a logical framework for data-driven reasoning that models how data can reject hypotheses to varying degrees, addressing a gap in formal methods for scientific inference.

Contribution

It introduces a family of consequence relations based on rejection degrees, extending rational consequence relations in non-monotonic logic.

Findings

Develops a formal logical framework for data rejection in scientific hypotheses

Defines multiple consequence relations based on rejection degrees

Extends non-monotonic logic with novel variations

Abstract

We introduce and investigate a family of consequence relations with the goal of capturing certain important patterns of data-driven inference. The inspiring idea for our framework is the fact that data may reject, possibly to some degree, and possibly by mistake, any given scientific hypothesis. There is no general agreement in science about how to do this, which motivates putting forward a logical formulation of the problem. We do so by investigating distinct definitions of "rejection degrees" each yielding a consequence relation. Our investigation leads to novel variations on the theme of rational consequence relations, prominent among non-monotonic logics.