In this thought-provoking article, the author delves into the complex concepts of substructurality and modality and explores how they intersect with negation in a fibrational framework. By examining negation and contradiction as type-theoretic and categorial objects, the author seeks to engage in an immanent critique of the prevailing univalent paradigm.
Throughout the piece, the author explores the epistemic and intra-mundane problematics that arise from these discussions. They navigate the intricacies of equivalence and identity, highlighting their limitations and potential downsides when confronted with negation.
It is crucial to note that the article does not conclude at this point but aims to further investigate the implications of these ideas. The author’s ultimate goal is to present a mode theory of an intuitionistic modal logic that incorporates a limitation on the Double Negation Elimination rule.
This limitation suggests a shift towards a more nuanced understanding of the interplay between intuitionistic logic and modal logic. By internalizing this restriction, the author hints at the potential for refining our comprehension of modal logic within an intuitionistic framework.
Overall, this article offers a deep and thought-provoking exploration of substructurality, modality, and negation. Through a rigorous analysis and expert insights, the author encourages readers to question prevailing paradigms and opens up avenues for further research and development in this field.