Qiana: A First-Order Formalism to Quantify over Contexts and Formulas with Temporality

Abstract

We introduce Qiana, a logic framework for reasoning on formulas that are true only in specific contexts. In Qiana, it is possible to quantify over both formulas and contexts to express, e.g., that ``everyone knows everything Alice says''. Qiana also permits paraconsistent logics within contexts, so that contexts can contain contradictions. Furthermore, Qiana is based on first-order logic, and is finitely axiomatizable, so that Qiana theories are compatible with pre-existing first-order logic theorem provers. We show how Qiana can be used to represent temporality, event calculus, and modal logic. We also discuss different design alternatives of Qiana.