Uncovering the Specific Product Rule for the Lattice of Questions

TL;DR

This paper introduces a specific product rule for the lattice of questions, highlighting differences from the rule for statements due to their distinct ordering principles based on relevancy versus implication.

Contribution

It presents the first explicit formulation of a product rule tailored to the lattice of questions, distinguishing it from the existing rule for statements.

Findings

The product rule for questions differs from that for statements.

Questions are ordered by relevancy, unlike statements ordered by implication.

The specific product rule accounts for the lower context of questions.

Abstract

We give here the specific product rule for the lattice of questions. This product rule differs from the product rule for the lattice of statements, hence the qualifier `specific'. This is because the elements in the lattice of statements are ordered by way of implication, an upper context, whereas the elements in the lattice of questions are ordered by way of relevancy, a lower context.