Propositional Homotopy Type Theory: A Topological Framework for Formal Deductive Systems

Key Points

• The aim is to develop a new topological foundation for formal deductive systems using homotopy theory.
• Constructed a framework based on simplicial complexes
• Encoded deductive steps using homotopy classes of paths
• Integrated algebraic topology with propositional reasoning
• Established a new connection between deductive systems and homotopy theory
• Demonstrated the viability of using simplicial complexes in formal logic
• Indicated potential advancements in homotopy type theory research