Information processing and communication are described by a tri-state system, in classical systems such as FPGAs, ICs, CPUs, and others, in multiple applications programmed by Verilog, an IEEE standard. This has replaced the Boolean algebra of a two-state system indicated by Shannon, also in gate construction with physical systems. The primary reason, in my opinion, is in dealing more effectively with noise.
Although, constructionally, a three-state system can always be embedded in a two-state system, efficiency and scalability suffers. This should be more evident in quantum computing, as explained in the preprint
https://www.researchgate.net/publication/347563918_Tri-state_Quantum_Information_Model
As new evidence accumulates, including in modern robots interacting with humans in complex computer-physical systems, this question asks first whether only the mathematical nature is evident as a description of reality, while a physical description is denied. Thus, ternary logic should replace the physical description of choices, with a possible and third truth value, which one already faces in physics, biology, psychology, and life, such as more than a coin toss to represent choices.
The physical description of "heads or tails", is denied in favor of opening up to a third possibility, and so on, to as many possibilities as needed. Are we no longer black or white, but accept a blended reality as well?
In reference to tri-state, ternary, or three-valued logic, and why it may solve cases that two-value logic, or Boolean algebra, struggles with, see
Pablo Cobreros, Paul Égré, David Ripley & Robert van Rooij (2014) Foreword: Three-valued logics and their applications, Journal of Applied Non-Classical Logics, 24:1-2, 1-11, DOI: 10.1080/11663081.2014.909631
at https://www.tandfonline.com/doi/citedby/10.1080/11663081.2014.909631
The question, "Who is the King of France?" has no True or False answer, not even "no one." There is no King of France presently, the correct answer is not the name of a person, or vacant.
Three-valued logics, besides contingency, reference failure, and vagueness, have been associated with at least three other phenomena of interest in which the notion of indeterminacy plays a central role – namely conditionals, computability, and the semantic paradoxes. Our work adds quantum, as in the Bohr hypothesis of all-states at-once, obscurity, ambivalence, lack of perceived form, and many others (e.g., the addition of a third value in ternary logic leads to a total of 3^3 = 27 distinct operators on a single input value, and operators with 2 inputs present ternary logic with 3^(3×3) = 19,683 possibilities), as given in
https://www.researchgate.net/publication/290284114_What_Is_Identification_That_We_Can_Identify_It_Part_I
https://www.researchgate.net/publication/290283924_What_Is_Identification_That_We_Can_Identify_It_Part_II
https://www.researchgate.net/publication/347563918/
Whether or not we can observe something directly, contemplating its possible existence and reference frames may allow us to understand how it might play a role in how the world works. Physics takes this commonly.
For it is impossible for science to pursue the truth, because we do not know where truth is and so we have to base ourselves on experiments and observations, which can be flawed in more than one way. This, of course, can lead to flawed conclusions, so even the most secure scientific statements can never be confused with truth nor its absence. It is not two-level logic.
In normal two-state computing today, one can achieve a higher throughput by simply replacing multiplication by "repeated addition". This unrolls the loop and uses fast addition instead of sluggish mutiplication. One can find many videos on YouTube on this "trick".
Similar effect happens with tri-state, so pre-computation of binary results in three logical truth values can offer a twenty thousand better discrimination. This is without any quantum consideration.
In the control and protective circuits of complex electrical systems it is frequently necessary to make intricate interconnections of relay contacts and switches. Examples of these circuits occur in automatic telephone exchanges, industrial motor control equipment and in almost any circuits designed to perform complex operations automatically. Two problems that occur in connection with such networks of switches will be treated here. The first, which will be called analysis, is to determine the operating characteristics of a given circuit. It is, of course, always possible to analyze any given circuit by setting up all possible sets of initial conditions (positions of switches and relays) and following through the chain of events so instigated. This method is, however, very tedious and open to frequent error.
The second problem is that of synthesis. Given certain characteristics, it is required to find a circuit incorporating these characteristics. The solution of this type of problem is not unique and it is therefore additionally desirable that the circuit requiring the least number of switch blades and relay contacts be found. Although a solution can usually be obtained by a "cut and try" nethod, first satisfying one requirement and then making additions until all are satisfied, the circuit so obtained will seldom be the simplest. This method also has the disadvantages of being long, and the resulting design often contains hidden "sneak circuits."
The method of solution of these problems which will be developed here may be described briefly as follows: Any circuit is represented by a set of equations, the terms of the equations representing the various relays and switches of the circuit. A calculus is developed for manipulating these equations by simple mathematical processes, most of which are similar to ordinary algebraic algorisms. This calculus is shown to be exactly analogous to the Calculus of Propositions [Boolean algebra] used in the symbolic study of logic. For the synthesis problem the desired characteristics are first written as a system of equations, and the equations are then manipulated into the form representing the simplest circuit. The circuit may then be immediately drawn from the equations. By this method it is always possible to find the simplest circuit containing only series and parallel connections.
These were the first words by Shannon (see file attached) to start his Master Thesis. They are true for idealized switches, or relays. However, for real cases one needs three states. This deeply modifies quantum computing, deprecating qubits as we show (op. cit.)
Trust is what gives meaning to information (Ed Gerck, op. cit.) and allows information to be evaluated. That needs more than just information.
For example, the same letters for GIFT can mean “present” or “poison”, depending on one’s trust on the speaker’s language (English or German). Shannon arguments do not even address this discrepancy, which does not relate to information “in the wire”.
See (PDF) Tri-state Quantum Information Model. Available from: https://www.researchgate.net/publication/347563918_Tri-state_Quantum_Information_Model
The Texas energy crisis, and the Capitol voting revolt, are trying to show us more than failure. That the systems that make our lives run are fallible is not new. But we should think about what we'll do when they fail. A third truth value gives us a different logic, to deal with indeterminacy. Not just true or false, but also obscure and ambiguous, as well as other forms of indeterminacy, affect the results. Not all answers are yes and no.
Voting fraud includes fraud against voting. Things are not so black/white, and we are seeing it all around us. What will be the next example?
Yep, this is already part of more fault-tolerant languages in the shape of the "null" value (true times null equals null, false times null equals null).
I've argued in the past that nulls ought to be supported at the hardware level. Currently, standard signed integer ranges tend to be asymmetrical -- the range of eight-bit values going from zero to 127, and minus zero to minus 127, with the "minus zero" treated as an additional integer value of "minus 128". Asymmetrical ranges mean that if we take clipped measurement data (such as recorded audio), and invert it, the -128 values become +128, which is an unsupported value leading to an overflow and a crash.
With hindsight it would have been far more sensible to have used the extra value to signify "null". You'd no longer risk crashing an app just by inverting a datastream's polarity, you wouldn't need so many manual overflow checks, and if your software accidentally did somethign silly like dividing by zero, the result would be a legitimate "null" ("disregard me, I'm not reliable data") rather than a program halt.
The absence of a null in badly-designed computer systems was also partly responsible for the "y2k" problem. Without the option of adding "unknown" as a date value, programmers used specific real two-digit year codes as "private code" for "unknown", or "null", and when those real dates came around ... problems.
Some languages will use "certainty registers", so that 2 times null is null, but two plus null is two higher than zero plus null - this might be expressed as a "two", and an additional error code flag. The use of multi-purpose error-state registers allows calculations to continue even with unreliable input data, and can be especially useful in the contexts of avionics and spacecraft design, where you may need to be able to continue calculating even if critical sensors fail or go offline.
In the case of our two-sensor problem, where one sensor gives outputs of zero and then two, and the other is offline, and where both values need to be added, then with consecutive inputs from the "good" sensor of zero and two (plus a state error flag), we can at least see that the new combined reading has just increased by two, rather than discard the entire calculation. For calculations based on multiple sensors, certainty or uncertainty (or probability) values can be calculated in the background in parallel to the actual data, so that uncertainty over the values reported by a sensor are automatically reflected in the certainty of the final calculated answer. If the sensor only play a small part in the calculations or decision-making, the result is reported as confident ... if its dubious data is critical to the final decision or calculation, its assigned uncertainty makes a correspondingly larger contribution to the final reported uncertainty.
Normally these uncertainty registers are implemented at the language level. It would be nice if (for processors used in spacecraft and other critical applications like maybe self-driving cars) they could be implemented at the processor level, as hardware registers. Ideally, you want to be able to aim for having multi-processor systems, where wires can be cut, or modules can be switched in and out "live" and "hot-swapped" while the vehicle is in motion, and have the distributed decision-making system not care. As soon as a module's electrics are compromised, it flags itself as unreliable, and its contribution to the final decisions are downgraded accordingly. If it's completely unplugged, or is datastream stops, or shows checksum corruptions, then again, the status of its data values get downgraded w.r.t. their credibility.
If a seven-redundant-processor deep-space craft has multiple failures, and its seven modules are reduced to two, and these two report conflicting results, then ideally we ought to be able to choose one of them based on which set of data is more reliable. Or if multiple modules give conflicting results, then if module A has a rotten gyrocope but good optics, B has bad optics and a partially-working acceleration sensor, and C has a great gyro, but dodgy optics, then instead of discarding all three modules's data as unreliable, we can still feed their data into the algorithm, and with proper uncertainty values, still be able to carry out meaningful calculations. All three might normally provide conflicting final data that's flagged as utterly unreliable (leading to all three modules being disregarded), but with certainty registers, they they can still share their source sensor data and hopefully calculate the same output.
of course, a certainty register isn't a complete answer, since some people might want a second register to express how confident we are that the first register's certainty values are reliable. In some case, we might not need the certainty register to have the same resolution as the actual data, in which case we can steal a few bits from the certainty register and use them as general error flags and state flags, for differently-nuanced versions of "null" ("this certainty value seems legitimate, when manually sanity-checked, outside the usual calculations", "We're declaring all these generated certainty values as good, because the module had a full checkup recently" "this number represents a calculation where even the supposed certainty is unreliable")
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