To Logic, or not to Logic that is the question

Thankyou, the paper was very informative.

If I understand this properly we have a Non-Mu Trinary logic. Non-Mu because the intermediate position still activates the toggle, but in a much weaker form. An interesting question would be frequency of state, Does the toggle stay in the intermediate state more often than the two extremes? I am afraid I don't really understand the phase diagram and so can't see this determination in your work. What it sounds like here, is more a State Machine than a logic, but the output can seem logical. If it is a state machine, then other regulatory mechanisms might show a larger number of states, and only the head to head or equivalent GRF's would show the trinary characteristics. If the GRF for head to head regulatory mechanisms stays in the intermediate state more, it could be simulated with a self-centering double throw toggle. If not the simulation would need to be with a spring loaded toggle where it stays in an extreme lysis? and if centered does a low and if pushed to extreme a high output value.

Perhaps it is more a Cultural Assumption, partly why I feel this is a point worth pursuing is that I often am told that people want quick convergence on an output solution, while this is an economic factor, I think it is also an expectation factor associated with logic, and so there is this cultural assumption in Western cultures that crisp output is better. Since the Assumption seems culturally linked to logic, I think that Satisfycing Systems do not as a rule, meet the cultural assumption of crispness for mathematical logic, and either the cultural assumptions need to be changed, or the Satisfycing system needs to be moved to a different classification that is more amenable to slower convergence, or lack of crispness.

I can't get the full text from here, but essentially, the abstract seems to point out that there are a class of systems, that do not respond to the Optimal control structures implied by logic. It then goes on to suggest Satisfycing as an alternative control mechanism for these cases. In natural systems, many of the control systems predated the discovery of logic, so it can be practical, to suggest that natural control systems are more likely to have some other mechanism, but that we are projecting our assumptions about mathematical logic onto these systems. Just because they do the same job, does not in fact mean that they work the same way, or that they can be all characterized as a "Form" of logic.

I think mischaracterization of a satisfycing system as logic, might be extremely dangerous. If you assumed that it made the same crisp decisions that a mathematical logic would. Often Logic, and Mathematical Logic seem to want to reach an ideal state of crispness, that many natural systems never could or should. Can we overcome this danger if we never admit it exists?

The reason I asked, was that I have found a number of systems that make decisions but do not act exactly like a mathematical logic, and I think that we have a tendency to expect things we label as logic to act in the same way that mathematical logics might. An example is a satisfycing system, which at first glance looks like a redundant logic, and can be created by relaxing certain parameters of logic by allowing a partial match. It is certainly a mathematical decision making system, but is it a logic? I ask whether we know the decision making system of Quantitative Gene Regulation well enough to claim full mathematical logic value, or can it be implemented as something less rigorous like a satisfycing system and still work?