A module structure over maximal consistent sets

TL;DR

This paper constructs a module structure over maximal consistent sets of propositions, enabling linear algebraic operations on proofs and presenting an algorithmic method for managing such deductions.

Contribution

It introduces a novel module framework over maximal consistent sets of propositions and an algorithmic approach for proof manipulation.

Findings

Module structure enables linear algebra on proofs

Algorithmic method for proof deductions

Framework extends proof analysis capabilities

Abstract

It is shown the construction of a module structure [2] with universe over a set of a particular kind of mathematical proofs, the base ring of this module will be built on a maximal consistent extension of a set of propositions, this provides the possibility to do some linear algebra on proofs. It will also be presented an algorithmic proceeding in order to deal with these particular type of deductions.