An Exegesis of Transcendental Syntax
PhD Thesis
Formal Antecedent
Foundations and Logic
Citation
Boris Eng. (2023). An Exegesis of Transcendental Syntax.
Why this reference is included
Eng’s doctoral thesis An Exegesis of Transcendental Syntax (2023) is cited as a primary technical source. Cited across Book I (Categorical Foundations), Part 18, Chapter The Self-Hosting Landscape; Book I (Categorical Foundations), Part 18, Chapter The Enrichment Frontier — the central framing is “The multiplicative fragment of linear logic has been recovered from stellar resolution, and Eng’s thesis provides a rigorous formalization for this fragment”.
Cited in
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Book I — Categorical Foundations Part 18Chapter The Self-Hosting Landscape
The multiplicative fragment of linear logic has been recovered from stellar resolution, and Eng's thesis provides a rigorous formalization for this fragment
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Book I — Categorical Foundations Part 18Chapter The Self-Hosting Landscape
The stellar resolution calculus (formalized for fragments by Eng ) replaces the traditional sequent calculus with a calculus of interaction where the basic operation is not logical deduction but physical-style cut: two designs interact, and the interaction either converges or diverges
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Book I — Categorical Foundations Part 18Chapter The Enrichment Frontier
Girard : fragments of linear logic from sub-logical operations
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Book I — Categorical Foundations Part 18Chapter The Enrichment Frontier
Girard's transcendental syntax program envisions logic emerging from sub-logical operations — stellar resolution, constellations, designs that compute without presupposing logical connectives
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Book I — Categorical Foundations Part 18Chapter The Enrichment Frontier
citeAltenkirchKaposi2016; Bocquet–Kaposi–Sattler 2023 & Non-Boolean, constructive adaptation to four-valued Ω_τ & Earned topos E_τ (I.D59) , E_1 → E_2 & Joyal arithmetic universes ; Abel graded modal DTT & Linear DTT not yet complete; no internal cut-elimination & 5 diagonal discipline; three-grade semiring , E_2 → E_3 & Willard 2001 (weak); Girard TX (fragments) & No full system at CIC-level proof-theoretic strength & *-autonomous proof theory via 5 (I.T39) , Book III proposes to attempt something that has not been done before