Multi-sorted logic and logical geometry: some problems

TL;DR

This survey explores the relationship between many-sorted and one-sorted logical theories, highlighting their parallel development and the bridges that enable transferring concepts and results between them.

Contribution

It demonstrates the parallelism and interconnectedness of multi-sorted and single-sorted theories, providing insights into how results can be transferred between these frameworks.

Findings

Both approaches are parallel and interconnected.

Bridges exist for transferring results and concepts.

Enhanced flexibility in choosing logical frameworks.

Abstract

The paper has a form of a survey and consists of three parts. It is focused on the relationship between the many-sorted theory, which leads to logical geometry and one-sorted theory, which is based on the important model-theoretic concepts. Our aim is to show that both approaches go in parallel and there are bridges which allow to transfer results, notions and problems back and forth. Thus, an additional freedom in choosing an approach appear.