Chu spaces as a semantic bridge between linear logic and mathematics
| Autor: | Vaughan R. Pratt |
|---|---|
| Rok vydání: | 2003 |
| Předmět: |
Predicate logic
Chu spaces General Computer Science Universal mathematics Substructural logic Computational logic Multimodal logic Linear logic Higher-order logic Theoretical Computer Science Algebra TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES Philosophy of logic Computer Science::Logic in Computer Science Many-valued logic Dynamic logic (modal logic) Computer Science(all) Mathematics |
| Zdroj: | Theoretical Computer Science. 294:439-471 |
| ISSN: | 0304-3975 |
| DOI: | 10.1016/s0304-3975(01)00169-4 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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