The Digital Press

This paper develops new logic algorithms for AI agents to reason about complex structured objects beyond simple sets. It adapts categorical logic and Horn logic rules for richer symbolic reasoning in diverse semantic categories.

Why it matters: Enables AI to reason symbolically about more complex and structured data beyond traditional set-based logic.

The big picture: Uses categorical logic and sequent calculus to improve forward reasoning and unification in multi-sorted, non-classical logic settings.

Stunning stat: Introduces adapted first-order unification supporting contexts and fragments of first-order logic in cartesian categories.

The stakes: Without these advances, AI reasoning remains limited to classical logic, restricting applications in semantic categories lacking full logical connectives.