This paper develops a homotopy-theoretic framework for the interpretation of logical structure in higher topos. We propose that classical logical structure arises as a 0-truncation of higher homotopical data, and can be understood as a decategorified shadow of higher topos theory. The main construction is based on: higher topoi as a homotopy-theoretic foundation the truncation functor tau less or equal zero the interpretation of logical structure as tau less or equal zero of T We show that logical structure can be systematically recovered from homotopy-theoretic data without assuming logic as a primitive notion. Philosophical interpretations concerning the nature of logic and structure are included as a separate appendix and are not part of the formal results.
Yugo Hidaka (Wed,) studied this question.