Formalizing Contextual Truth Flips: Upside-Down Logic and ItsVariants

Abstract

In real settings, conclusions can flip: a claim once treated as true becomes false, or a prohibited
action later becomes required. We call this phenomenon Upside-Down Logic. Upside-Down Logic provides a
formal operator that, given a contextual trigger, reverses the accepted outcome (True→False / False→True)
while keeping the underlying information rather than discarding it. We define several concrete variants — defea-
sible, belief-based, paraconsistent, dynamic epistemic, and abductive — and show how each realizes controlled
reversal through priority flips, entrenchment inversion, model update, or explanation reordering. These log-
ics model realistic situations such as building access in emergencies, medication policy after contraindications,
travel advisories, market disclosures, and security assessment.