Qualitative Intensional Logic

Qualitative Intensional Logic (QIL, pronounced “quill”) is a semantics for standard-sensitive talk. QIL evaluates claims inside profiles or bundles—classical, two-valued perspectives—and then lifts those verdicts to the world. A sentence is world-true if some active bundle says it is true, and world-false if some bundle says false, and both if there are multiple, active bundles that disagree. This records disagreement at the world without triviality. Vagueness is handled by fixed thresholds (strict and lowered), and “somewhat” is just the lowered standard with an inheritance switch. Typed identity captures “the same as a B-thing” for contextually relevant types. Modality uses anchored accessibility with simple rigidity options. I prove soundness for a shared-witness consequence relation, non-explosion, collapse to classical under unanimity, box-substitution for typed identity, and a small-model bound. QIL offers a compact, policy-transparent way to model standard-sensitive discourse while keeping classical reasoning inside each perspective.