Bibliography · Foundations and Logic

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

  • Book I — Categorical Foundations Part 18
    Chapter 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
  • Book I — Categorical Foundations Part 18
    Chapter 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
  • Book I — Categorical Foundations Part 18
    Chapter The Enrichment Frontier
    Girard : fragments of linear logic from sub-logical operations
  • Book I — Categorical Foundations Part 18
    Chapter 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
  • Book I — Categorical Foundations Part 18
    Chapter 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

Bibliographic Details

BibTeX KeyEng2023
AuthorsBoris Eng
Year
TypePhD Thesis