Journal ArticleDOI
Transcendental syntax I: deterministic case
Reads0
Chats0
TLDR
In this paper, the Kantian distinction between analytic (untyped, meaningless, locative) answers and synthetic answers was studied in a proof-theory setting, where the upper part of the proof-net is locative, whereas the lower part is spiritual.Abstract:
We study logic in the light of the Kantian distinction between analytic (untyped, meaningless, locative) answers and synthetic (typed, meaningful, spiritual) questions. Which is specially relevant to proof-theory: in a proof-net, the upper part is locative, whereas the lower part is spiritual: a posteriori (explicit) as far as correctness is concerned, a priori (implicit) for questions dealing with consequence, typically cut-elimination. The divides locative/spiritual and explicit/implicit give rise to four blocks which are enough to explain the whole logical activity.read more
Citations
More filters
Journal ArticleDOI
Interaction Graphs: Graphings
Thomas Seiller,Thomas Seiller +1 more
TL;DR: This paper considers a generalization of graphs named graphings, which is in some way a geometric realization of a graph, which leads to a number of new models of multiplicative-additive linear logic which generalize Girard's geometry of interaction models and opens several new lines of research.
Book ChapterDOI
Transcendental Syntax iv: Logic Without Systems
TL;DR: A derealistic, system-free approach to arithmetic, with an example: arithmetic.
Journal ArticleDOI
Multiplicative linear logic from a resolution-based tile system
Boris Eng,Thomas Seiller +1 more
TL;DR: The stellar resolution is presented, a"flexible"tile system based on Robinson's first-order resolution and ideas of a new alternative to proof-net theory sketched by Girard in his transcendental syntax programme are formalised and extended.
Posted Content
Stellar Resolution: Multiplicatives - for the linear logician, through examples
TL;DR: This paper obtains a new model of linear logic with computational objects as its foundation: proofs, cut-elimination, formulas/types, correctness and provability are reconstructed very naturally.
Journal ArticleDOI
The Explosion Calculus
TL;DR: A calculus for classical propositional sequents is introduced that consists of a restricted version of the cut rule and local variants of the logical rules that explode a given sequent into its elementary structural sequents, which do not contain any logical constants.
References
More filters
Journal ArticleDOI
Linear logic
TL;DR: This column presents an intuitive overview of linear logic, some recent theoretical results, and summarizes several applications oflinear logic to computer science.
Journal ArticleDOI
The structure of multiplicatives
Vincent Danos,Laurent Regnier +1 more
TL;DR: Investigating Girard's new propositionnal calculus, which aims at a large scale study of computation, there is a stumble quickly on that question: What is a multiplicative connective?
Book ChapterDOI
Geometry of Interaction 1: Interpretation of System F
TL;DR: The chapter describes the development of a semantics of computation free from the twin drawbacks of reductionism and subjectivism and that a representative class of algorithms can be modelized by means of standard mathematics.
Book
Advances in Linear Logic
TL;DR: Linear logic: its syntax and semantics J. Girard, a category arising in linear logic, complexity theory and set theory, and noncommutative proof nets V. Girards.