# Intuitionistic Existential Graphs from a non traditional point of view

## TL;DR

This paper introduces a new version of intuitionistic existential graphs, combining recursive rules and geometric representations to improve deduction management and better connect topology with propositional logic.

## Contribution

It develops an enhanced intuitionistic existential graph system with recursive rules and geometric symbols, improving deduction handling and logical-topological representation.

## Key findings

- Equivalent to the intuitionistic propositional calculus
- Incorporates second-degree deductive rules for better deduction management
- Uses geometric symbols to relate topology with propositional logic

## Abstract

In this article we develop a new version of the intuitionist existential graphs presented by Arnol Oostra [4]. The deductive rules presented in this article have the same meaning as those described in the work of Yuri Poveda [5], because the deductions according to the parity of the cuts are eliminated and are replaced by a finite set of recursive rules. This way, $ Alfa_I $ the existential graphs system for intuitional propositional logic follows the course of the deductive rules of the system $ Alfa_0 $ described by Poveda [5], and is equivalent to the intuitionistic propositional calculus. In this representation the $ Alfa_0 $ system is improved, there are a series of deductive rules of second degree incorporated that previously had not been considered and that allow a better management of deductions and finally from the ideas proposed by Van Dalen [6], a mixture is incorporated in the deduction techniques, the natural deductions of the Gentzen system are combined with new system rules $ Alfa_0 $ and $ Alfa_I $. The symbols proposed for the $Alfa_I$ representation relate open, closed and quasi-open sets of the usual topology of the plot with the intuitional propositional logic, usefull for approaching new problems in the representation of this logic from a more geometrical perspective.