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April 22, 20260 citationsOpen Access

Propositional Homotopy Type Theory as a Topological Framework for Deductive Systems

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

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Authors

YYYijie Yang

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Overview

This work introduces a topological framework that integrates propositional logic and homotopy theory, suggesting new deductive methods.

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
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Yijie Yang (2026) studied this question.

synapsesocial.com/papers/69e866ad6e0dea528ddeb0edhttps://doi.org/10.5281/zenodo.19664407
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