2023/08/10 by David Roberts · 2 citations
Computer Science · #Advanced Algebra and Logic #Logic, Reasoning, and Knowledge #Logic, programming, and type systems
paper · pdf · doi:10.32408/compositionality-5-8
This article re-examines Lawvere's abstract, category-theoretic proof of the fixed-point theorem whose contrapositive is a `universal' diagonal argument. The main result is that the necessary axioms for both the fixed-point theorem and the diagonal argument can be stripped back further, to a semantic analogue of a weak substructural logic lacking weakening or exchange.