𝜇⁢𝜆⁢ϵ⁢𝛿-Calculus: Self Optimizing Language that Seems to Exhibit Paradoxical Transfinite Cognitive Capabilities (arxiv.org) AI

The arXiv preprint proposes a “μλϵδ-calculus” based on contracting directed multigraph rewriting, claiming it extends and optimizes the lambda calculus in a way that always terminates and can produce self-similar “fractal” graphs resembling the original program. It argues for using a Wittgenstein-style paraconsistent logic to enable paradoxical self-referencing without logical explosion, and suggests two related extensions (ϵ-expressions for macro-like expansion and δ-functionals for minimal input/output modeling), with step-by-step interpreter/compiler/optimizer construction and proof-of-concept code.