A Completeness Theorem for "Total Boolean Functions"

TL;DR

This paper proves that the boolean centroidal calculus is complete for representing all total boolean functions within an algebraic model of linear logic, establishing a foundational correspondence.

Contribution

It provides a completeness theorem linking the boolean centroidal calculus to total boolean functions in a linear logic model.

Findings

The boolean centroidal calculus is complete for total boolean functions.

The paper confirms the algebraic notion of totality aligns with the calculus.

It advances the understanding of total boolean functions in linear logic models.

Abstract

Christine Tasson introduced an algebraic notion of totality for a denotational model of linear logic in the category of vector spaces. The notion of total boolean function is, in a way, quite intuitive. This note provides a positive answer to the question of completeness of the "boolean centroidal calculus" w.r.t. total boolean functions.