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

2026-04-02

AI Summary

Existing logical systems struggle to uniformly handle context dependency, inconsistent information, and temporal reasoning. This work proposes the Qiana logical framework, which for the first time enables joint quantification over both contexts and formulas within first-order logic. It incorporates a paraconsistent mechanism to tolerate contradictions within individual contexts while maintaining compatibility with mainstream first-order theorem provers through finite axiomatization. The framework naturally accommodates temporal logics, event calculi, and modal logics, thereby establishing a unified formal foundation that balances expressive power with practical applicability.

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.

Problem

• context quantification
• formula quantification
• paraconsistent logic
• temporality
• first-order logic

Innovation

• quantification over contexts
• first-order logic
• paraconsistent reasoning
• finite axiomatizability
• temporal representation