3 Protocols
A protocol is a relation \(R\) over a set \(T\) of roles: what each role does relative to the others. This is a working definition and is not yet formalized.
A protocol system is a protocol together with participants acting in relation to it. Walch, The Fundamentals of Protocol Systems (2023), p. 5: “A protocol system is made up of a protocol, at least two people, and those people taking actions in relation to the protocol.” This is a working definition and is not yet formalized.
Let \(T\) be a set of roles and \(P\) a set of participants. A protocol system has three layers.
(L0) Definition: a relation \(R \subseteq T \times T\).
(L1) Occupancy: an assignment \(a \colon P \to T\) of participants to roles.
(L2) Enactment: actions by participants, over time, in relation to \(R\).
A protocol is (L0). A protocol system is all three. With arrows from dependent to depended-on,
(L2) has no arrow. It is time, which the kernel holds a place for and cannot fill (Theorem 2.2).
Three definitions of protocol, read by layer. Walch (2023): “rules created by humans that shape the behavior of groups of people” (p. 4) at (L0), “at least two people” at (L1), and “taking actions in relation to” the protocol at (L2) (p. 5). Rao, Beiko, Ryan, Stark, Van Epps, and Aue, The Unreasonable Sufficiency of Protocols (2023), p. 3: a “codified set of behaviors” at (L0) that, “when adopted by a sufficient number of participants” (L1), “reliably leads to good-enough outcomes for all” (L2). Tay, A Phenomenology of Protocols (2023), p. 3: “rules or procedures” at (L0), with participants and protocols that “co-constitute reality” (p. 10) at (L2). Every source puts the protocol at (L0). Only Walch names the protocol system as a separate thing.
Does a protocol exist before anyone adopts it? Rao et al. (p. 7): a protocol that falls short “arguably … wouldn’t exist at all”. Yet they describe IPv6 as ratified in 2017 with adoption still slow (p. 16). Position: yes. \(R\) needs roles, not occupants, so what fails to get established is the protocol system, at (L1) and (L2).
Klir places systemhood in \(R\). Walch (p. 3): “Protocol systems are always two things at once—individuals and a group.” Position: both hold, at different layers. Organization lives at (L0). The two-sidedness lives at (L1): the same participants, seen through \(a\), are individuals in roles, and seen through \(R\), are a group.
Some rules create the activity they govern: there is no checkmate before the rules of chess. If a role is made by its rules, then \(T\) depends on \(R\) and the arrow reverses. Position: a role has a label, which tells the position apart, and a function, what its holder does. The label belongs to \(T\) (Walch, p. 6: a role “has a name that distinguishes it from other roles within the system”). The function is \(R\). Rules make labels into roles. A piece carved as a bishop and assigned no moves is \((T, \varnothing )\). “Moves diagonally” cannot be stated without saying what moves.
Define a protocol as a relation over roles and a protocol system as an assignment of participants to those roles, and prove that every protocol system is a kernel.