A Logic of Uncertain Interpretation
Adam Bjorndahl
TL;DR
The paper tackles uncertainty about how statements are interpreted by treating meanings as variable across possible worlds and introducing a meaning-entailment connective to capture semantic implications beyond the material conditional. It then integrates this with a probabilistic framework to define a conservative notion of evidentially supported belief via Dempster-Shafer mass functions, grounded in variable-meaning interpretations. A running coin-flip example clarifies how different dispositions of an informant affect the interpretation and the associated beliefs. The work also reveals a novel approach to combining evidence by aligning mass functions with the same underlying world, opening avenues for new epistemological analyses.
Abstract
We introduce a logical framework for reasoning about "uncertain interpretations" and investigate two key applications: a new semantics for implication capturing a kind of "meaning entailment", and a conservative notion of "evidentially supported" belief that takes the form of a Dempster-Shafer belief function.