I've spent some time talking about starting with an axiomatic system and expanding it to include actions. Now, I want to take another step forward. Can we take subsets of axioms and actions, encapsulate them into subunits, and create an agent based system? This would be similar to object oriented axioms/actions. Granted, this sounds a lot like what we already have in agent-based systems, but a different low-level basis for those agents.
What would an axiomatic agent-based system give us?
A bit of redundency. Axioms and actions would be copied in multiple agents, unless we set up a remote access system that each agent links to. Pros and cons for each. Theorems derived from an agent's sxiom/action set would be duplicated by other agents. Unless each agent represents a single theorem.
A LOT of axioms. To be able to handle the number of agents within a realistic agent-based system, it would take a large number of axioms to make them even remotely distinct. This is troublesome, as an axiom is supposed to be self-evident, or not provable by any other axiom.
I'm starting to wonder about an axiom-action system. I need to read up on them some more, but I feel that I may be looking at things the wrong way.