Chu spaces as a semantic bridge between linear logic and mathematics

Authors:
Vaughan Pratt
Affiliations:
Department of Computer Science, Stanford University, Stanford, CA
Venue:
Theoretical Computer Science - Linear logic
Year:
2003

Citing 8
Cited 6

Introduction to higher order categorical logic

Introduction to higher order categorical logic
Modeling concurrency with partial orders

International Journal of Parallel Programming
Linear logic

Theoretical Computer Science
Games and full completeness for multiplicative linear logic

Journal of Symbolic Logic
The Second Calculus of Binary Relations

MFCS '93 Proceedings of the 18th International Symposium on Mathematical Foundations of Computer Science
A Dialectica-like Model of Linear Logic

Category Theory and Computer Science
The Stone Gamut: A Coordinatization of Mathematics

LICS '95 Proceedings of the 10th Annual IEEE Symposium on Logic in Computer Science
Full Completeness of the Multiplicative Linear Logic of Chu Spaces

LICS '99 Proceedings of the 14th Annual IEEE Symposium on Logic in Computer Science

Event-State Duality: The Enriched Case

CONCUR '02 Proceedings of the 13th International Conference on Concurrency Theory
A Monoidal Category of Bifinite Chu Spaces

Electronic Notes in Theoretical Computer Science (ENTCS)
Bifinite Chu spaces

CALCO'07 Proceedings of the 2nd international conference on Algebra and coalgebra in computer science
Generalizations of approximable concept lattice

CLA'06 Proceedings of the 4th international conference on Concept lattices and their applications
Linear process algebra

ICDCIT'11 Proceedings of the 7th international conference on Distributed computing and internet technology
Morphisms in context

ICCS'05 Proceedings of the 13th international conference on Conceptual Structures: common Semantics for Sharing Knowledge

Quantified Score

Hi-index	0.00

Visualization

Abstract

The motivating role of linear logic is as a "logic behind logic". We propose a sibling role for it as a logic of transformational mathematics via the self-dual category of Chu spaces, a generalization of topological spaces. These create a bridge between linear logic and mathematics by soundly and fully completely interpreting linear logic while fully and concretely embedding a comprehensive range of concrete categories of mathematics. Our main goal is to treat each end of this bridge in expository detail. In addition, we introduce the dialectic lambda-calculus, and show that dinaturality semantics is not fully complete for the Chu interpretation of linear logic.