Symmetric Monoidal Categories with Attributes

TL;DR

This paper introduces a new categorical framework that integrates attribute information into symmetric monoidal categories, enhancing their applicability in planning and robotics.

Contribution

It defines the concept of symmetric monoidal categories with attributes, extending existing formalisms to include attribute information for objects.

Findings

Examples and semantics in robotics demonstrate the framework's applicability.

The formalism allows for attribute retrieval and interaction modeling.

Potential for improved planning in engineering systems.

Abstract

When designing plans in engineering, it is often necessary to consider attributes associated to objects, e.g. the location of a robot. Our aim in this paper is to incorporate attributes into existing categorical formalisms for planning, namely those based on symmetric monoidal categories and string diagrams. To accomplish this, we define a notion of a "symmetric monoidal category with attributes." This is a symmetric monoidal category in which objects are equipped with retrievable information and where the interactions between objects and information are governed by an "attribute structure." We discuss examples and semantics of such categories in the context of robotics to illustrate our definition.