Likologia A formal grammar for systems defined by constraint MAY 26 Systems do not usually fail suddenly. They fail when recovery can no longer keep up with drift. That is the simplest way into Likologia. Most of the time, when we talk about systems, we start with what they are made of. We name the parts. We describe the mechanism. We explain how the components interact. That works when the system is stable, because stable systems make component-level explanation look enough. But under pressure, that changes. The parts may stay the same while the behaviour shifts. A material under load can look fine until it yields. A person under sustained stress can appear functional until they shut down. A hospital can keep operating while backlog grows invisibly. An AI model can sound coherent while drifting away from the question it was meant to answer. In each case, the visible collapse looks sudden. Usually it is not. What appears suddenly is the boundary crossing. The drift was already happening. Likologia is my name for the grammar underneath that pattern. Not a theory of everything. Not a replacement for physics, medicine, psychology, engineering, computing, or politics. Not a claim that all systems are secretly the same thing. A grammar. A way of describing systems as systems before the language of a particular domain takes over. The canonical version defines Likologia as the study of systems independent of domain: not physics specifically, not cognition specifically, not computation specifically, not society specifically, but how systems exist, stabilise, fail, transition and recover under constraints. That last word matters. Constraint. A system is not only what it contains. It is what it is allowed to do. The first move The normal question is: what is this system made of? Likologia asks: what states can this system occupy, what transitions are allowed, and what constraints limit those transitions? That is the base grammar. A system has possible states. It can move between some of them. It cannot move freely. That is enough to begin. The formal draft reduces this to: System = (States, Transitions, Constraints) States are possible configurations. Transitions are allowed changes. Constraints are the limits on those changes. This sounds simple because it is meant to be simple. If something has distinguishable states, allowed transitions and constraints on those transitions, it can be treated as a system in this grammar. If it does not, then either it is not a system in this sense, or the model has not found the system yet. The point is not to erase the domain. A furnace is not a mind. A mind is not an economy. An economy is not an AI model. But each can stabilise. Each can drift. Each can collapse. Each can recover. The mechanisms differ. The behavioural grammar can still match. That is the opening. Systems move A system is not just a collection of parts. It is a moving position inside a space of possibilities. At one moment, the system is here. Later, it is somewhere else. The path between those positions is its trajectory. That word matters because collapse is not only an event. It is often the end of a trajectory that was already moving toward a boundary. In the formal version, this appears as a simple evolution rule: x(t + 1) = f(x(t), C, P) where x is the current system state, C is the active constraint set, and P is accumulated pressure or load. That is not there to make the piece look mathematical. It says something very concrete: The n