Symmetric Monoidal Categories with Attributes
This work addresses the need to handle attributes in planning formalisms for engineering domains like robotics, but it appears incremental as it builds on existing categorical frameworks.
The paper tackles the problem of incorporating attributes, such as robot location, into categorical formalisms for planning by defining symmetric monoidal categories with attributes, which equip objects with retrievable information governed by an attribute structure, and illustrates this with robotics examples.
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.