The Ontology

Two grapplers are one physical system. The ontology says what that system consists of before anything in it is named: bodies and their stable properties, a state that changes, what each person commands and what nobody does, the paths an exchange takes, what each person can see, can do and chooses, and the rules that decide what any of it is worth. An armbar can be available, executable, recognised and chosen, and those are four different facts. This is the account of where each of them lives.

Ask what a grappling exchange is made of and most answers arrive as a list of positions and techniques. The ontology answers one level down, with an inventory of kinds of thing, sorted into three levels. At the physical level: two embodied participants and the things around them; the stable properties of bodies and room; the state that changes as the exchange runs; what each person can command; what each body does on its own; what gravity and the mat contribute; the rule by which the whole system moves to its next state; the paths it takes; and the policies that steer it. At the constitutive and contest level: what makes an interaction grappling at all, and what a particular ruleset makes legal, valuable, terminal or resettable. At the agent level: what each person can observe, what they know, what they can reliably execute, and what they decide. From those the ontology derives the adversarial relations the rest of the theory is built on, reachability, enforceability and defensive viability among them.

Positions, techniques and invariants are on none of the three levels. They are derived descriptions over the state, the policies, the transitions and the equivalences beneath them, which is why a theory built on this ontology can disagree with another theory about what advantage is while agreeing entirely about what exists. The inventory, in the ontology’s own closing words:

how particular rules alter legality, value, termination and reset

how policy selection differs from capability and information

how termination events and causal attribution differ from terminality

Every item is a kind of thing, or a kind of relation, that the ontology keeps distinct from the others. The rest of this page walks through them from the physics up, and hands the relations at the end of the list to the theory of control.Positions, techniques and invariants are not treated as primitive physical objects. They are derived descriptions over deeper state, policy, transition and equivalence structure.Two bodies, one system