I am trying to understand what an abstract BPMN process means. Honestly, I think this is a much overused of not abused term. It could mean an abstraction of the process definition, or it could mean a parent process which is detailed out in a child process, or an externally visible process interface or may be a combination of these. e.g. an abstract process might be EMployee onboarding process which inturn may be actually be subdivided into multiple smaller processes.
A public process is one that is visible to external world. It may call internal processes and services but is shared with the external world. e.g. the process of buying an item on ebay is very much an example of public process.
So does public process have to be non -executable? If I see the example of buying items on ebay - it is executed by a system - thus it is executable. In my opinion public vs private is orthogonal to executable vs non executable.
Going back to abstract processes - well since different backgrounds lead to different interpretations of abstract process, I would rather break this monolith into two specific terms Public/Private and Executable / Non executable. Now executable does not mean ready to execute. Every tool vendor will have a set of vaidations to run besides the standard XSD validations. Today's business user is not in an ivory tower to make that decision without consulting with process analysts / IT experts. Before the process goes into production, it will go thru its lifecycle of dev - test - stage - production and may move from a ready to execute to a non ready state multiple times during this lifecycle.
Let me know what you the people in real world see these types of processes as and feel free to correct me!