The proper representation of invariances (which include allowed set of values of the free parameters) is conditional on the reason for an invariance. The relationship to this reason is itself an invariance that needs to be made conditional on the foundations of its semantics.
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Most of our models are perceptual. Proofs in perceptual models are conducted by creating global coherence between all perceived features via propagating the state of the free parameters along their relationship functions to each other until a stable configuration is reached.
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Reasoning is not just an alternative to perception. It is a tool that combines a toolbox of algorithms that are being used to repair perceptual models that don't achieve full coherence.
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Yes. You are supposed to identify the operators, prove the desirability of their properties, and then prove that the substrate actually implements that operator.
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