# Tactical Diagrammatic Reasoning

## TL;DR

This paper enhances an interactive diagrammatic proof assistant for Euler diagrams by integrating tactics, increasing automation, improving user interaction, and enabling higher-level explanations of proofs.

## Contribution

It introduces tactics into Speedith, a diagrammatic proof system, to automate proof construction and facilitate explanations, addressing a gap in diagrammatic reasoning tools.

## Key findings

- Tactics improve proof automation in Euler diagram reasoning.
- Enhanced tactics support better explanation and readability.
- Metrics used guide the design for human-friendly proofs.

## Abstract

Although automated reasoning with diagrams has been possible for some years, tools for diagrammatic reasoning are generally much less sophisticated than their sentential cousins. The tasks of exploring levels of automation and abstraction in the construction of proofs and of providing explanations of solutions expressed in the proofs remain to be addressed. In this paper we take an interactive proof assistant for Euler diagrams, Speedith, and add tactics to its reasoning engine, providing a level of automation in the construction of proofs. By adding tactics to Speedith's repertoire of inferences, we ease the interaction between the user and the system and capture a higher level explanation of the essence of the proof. We analysed the design options for tactics by using metrics which relate to human readability, such as the number of inferences and the amount of clutter present in diagrams. Thus, in contrast to the normal case with sentential tactics, our tactics are designed to not only prove the theorem, but also to support explanation.