Saturday 20 June 2020

Reliable Models

The governed world is hard to model. It's not a formal system: nothing is constant; nothing is precise; no event is truly atomic; every assertion is contingent; every causal link is vulnerable; everything is connected to everything else. This is the right-hand-side problem: no formal model can be perfectly faithful to the reality. This matters because the designed system behaviour relies on model fidelity: deviation brings system failure. But in practice all is not lost. A single unified model is unattainable; but specific models can be adequately faithful, at some time, for some period, in some context, for some purpose. The question, then, is how to take best advantage of these local, transient and conditional episodes of adequate fidelity?

The question answers itself. The desired system behaviour is an assemblage of concurrent constituent behaviours, providing different functions in different circumstances and contexts, and imposing different demands on the governed world. This complex assemblage responds to the same variability of context, need and purpose that invalidates any single unified model. The answer to the question is clear: the model must be structured to match the behaviour structure.

This correspondence of model and behaviour structures motivates the idea of a triplet. For each simple behaviour, a triplet brings together (1) a machine program; (2) a governed world model of the specific properties on which the program depends; and (3) the governed world behaviour resulting from the interaction of (1) and (2). Concurrent constituent behaviours rely on the concurrent validity of their respective models. If two behaviours cannot overlap in time, their models need not be consistent. Each constituent model and its corresponding behaviour are designed together. Reliability of a constituent model is judged relative to the context and demands of its corresponding constituent behaviour.

This co-design of model and behaviour structure realises modelling-in-the-large. By developing each constituent model along with its associated machine program, it also focuses and simplifies the task of modelling-in-the-small. Each constituent model is small because it is limited to just those domains and causal links that participate in the corresponding behaviour. It is simple because its behaviour satisfies the criteria of triplet simplicity. For example, a governed world domain may play only one participant role in the behaviour; modelled causal properties are not themselves mutable; the operational principle of the behaviour must be simply structured. The simplicity and small size of the model also enable and guide a deeper and more careful—and carefully documented—investigation of the residual risks to reliability.

Later, when constituent behaviours are to be combined in a bottom-up assembly of system behaviour, their respective models are ready to hand, their vulnerabilities to interference already examined. The combination task is easier. Only those models are to be reconciled and combined whose associated behaviours can be concurrently enacted; difficulty in reconciling two models may rule out concurrent enactment. For example, cruise control and self-parking cannot be enacted concurrently: their functional combination makes no behavioural sense, and—not coincidentally—their governed world models are irreconcilable.

Links to other posts:
 ↑ The Right-Hand Side: Why the model-reality relationship is problematic
 ↑ System Behaviour Complexity: The component structure of system behaviour
 ← Triplets: Triplets (Machine+World=Behaviour) are system behaviour elements

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