Turns out that .txt is not among the file formats that Discourse supports (jpg, jpeg, png, gif, pdf, doc, docx). Bearing in mind that this was an abandoned draft-in-progress, here’s the content of logic-gates.txt:
Powers assumed that above the Configuration and Transition levels the brain manipulates symbols, just like a digital computer. The following quotations are from Powers (1979).
At the program level, the activities … involve manipulating symbols according to preprogrammed rules and applying contingency tests at appropriate places. (p. 204)
The reason I want category perceptions to be present, whether generated by a special level or not, is that the eighth level seems to operate in terms of symbols and not so interestingly in terms of direct lower-level perceptions. (p. 200)
Perhaps it is best merely to say that this level works the way a computer program works and not worry too much about how perception, comparison, reference signals, and error signals get into the act. I think that there are control systems at this level, but that they are constructed as a computer program is constructed, not as a servomechanism is wired. (p. 201)
Operations of this sort using symbols have long been known to depend on a few basic processes: logical operations and tests. Digital computers imitate the human ability to carry out such processes, just as servomechanisms imitate lower-level human control actions. As in the case of the servomechanism, building workable digital computers has informed us of the operations needed to carry out the processes human beings perform naturally–perhaps not the only way such processes could be carried out, but certainly one way… (p. 202)
I disagree
The heart of programming logic, as he put it, is branching or conditional choice where, after the choice is made, either A is controlled or B is controlled.
At this level, we have what are called contingencies. If one relationship is contingent on another–if a grapefruit will fit into a jar only if its diameter is smaller than that of the jar’s mouth–we can establish the contingent relationship if the other it depends on is also present. (p. 200)
However, the operations of programming logic are not limited to inference. My purpose here is to look more closely at the logical operations and tests that are employed in digital computation, and inquire into “how perception, comparison, reference signals, and error signals get into the act.” If the brain employs the tools of Boolean logic, how might those tools be implemented in neural structures.
There is a more essential issue that I will state here and then defer to a later discussion for which this present essay lays a foundation. If category perceptions function as abstract symbols, the path from a specific controlled variable to a category is straightforward. But once the proposed program-level functions have manipulated those symbols and deduced an abstract conclusion, how do the category perceptions (the symbols) in the conclusion become instantiated as the relevant particular perceptions which are members of those categories? A given program routine may have countless specific applications over time.
A number of logic gates
have been specified to implement functions of Boolian logic
in digital computers. A boolean function returns one of (usually) two values, true/false, and a logic gate returns one of two bit values, 1/0. This Boolean value functions in a program as a control variable– Control flow - Wikipedia a computer science term that must not be confused with the ‘control variable’ which is held constant in an experiment, much less with the controlled variable in a control system. A control variable in digital computation determines the path of program control through the program code.
Control flow - Wikipedia
(Declarative programming ‘languages’
Declarative programming - Wikipedia
handle logic functions without distinct control variables, but this need not concern us here.)
The 16 possible logic gates that take two values as inputs are listed below. Except for the first two, I give three specifications for each:
- The symbolic logic gate definition.
- A perceptual input function, or a synaptic function in a chain of transmission.
- A reference value for controlling input.
For (1), logical True = 1 and logical False = 0. For (2) and (3), I interpret logical True as presence of the specified perception and logical False as its absence.
Null and Identity
Null always returns 0 and Identity always returns 1 regardless of input.
Some systems, for stability, require some pin to be always ‘up’ or always ‘down’. This strikes me as an engineering kludge, but I could be wrong. I see no function for these in control theory. Maybe someone else can.
Transfer
- Pass the value of the input variable.
- A synapse in a chain of transmission for a perceptual signal.
- Input of perception X sets r>0 for control of X.
NOT
- Pass the negated value of the input variable.
- Sense of excitatory signal is changed to inhibitory.
- Input X sets r=0 for control of X.
AND
- Value = 1 only if both input values = 1
- Synapse two excitatory signals to one excitatory signal.
- Input function requires both X and Y in order to generate Z; or Input function requires both X and Y in order to set r>0 for control of Z
NAND
- Value = 0 only if both input values = 1
- Synapse two excitatory signals to one inhibitory signal.
- Input function generates Z unless both X and Y are input (turning Z off); or Input function requires both X and Y in order to set r=0 for control of Z
OR
- Value = 0 only if both input values = 0
- Input function must receive both A and B to generate Z
- Input X or Y sets r>0 for control of Z
NOR
- Value = 1 only if both input values = 0
- Input function generates Z only when both A and B are absent (unlikely input function)
- While controlling Z with r>0, input X or Y sets r=0
Implication
- (If X, then Y) is logically equivalent to (not-X AND Y)
- Input X to input function, it generates Y
- Input X sets r>0 for control of Y
Inhibition (Similar to transfer)
- X and not Y
- Input X, the input function synapses -Y with Y
- Input X sets r=0 for control of Y
EX-OR
- X or Y but not both
- OR combined with inhibition (flip-flop)
- Input X sets r>0 for control of Y and input Y sets r>0 for control of X; or input X and Y sets r=0 for control of Z
EX-NOR
- Value = 1 if X = Y
- NOR (X, Y) combined with inhibition (flip-flop)
- X - Y = 0 sets r>0 for control of Z
Now let’s look a bit more closely at the two senses of disjunction, inclusive (OR and NOR) and exclusive (EX-OR and EX-NOR)
Inclusive or (OR and NOR)
Given any one or more of the set of inputs, the input function generates a perceptual signal. This is Bill’s (1979) proposal for a Category level, a particular form of Relationship input function.
In Bill’s conception, they are simply synapsed together, and the strength of the category relationship perception increases proportionally to the number of distinct perceptions actually input, and their strengths. “Strength of a perception” apparently corresponds to the rate of firing. Strength of a reference signal (rate of firing) specifies the amount of the referenced perception that is to be produced.
But we do not control the category, we control a member of the category. The OR-set is an important function of associative memory that sends reference signals to systems that control aspects of the perception of that category member (those aspects that we might call the criteria for category membership).
Exclusive or (EX-OR and EX-NOR) – either-or
Given two signals, one is admitted to an input function and the other is not. Martin adapted the flip-flop function of digital computer design
He and Rupert developed this notion
as a mechanism for categorial distinctions when the ORed input sets for two categories intersect, and a given input perception (or plurality of perceptions) is in that intersection.
However, it is of more general utility in trial-and-error processes of planning and trouble-shooting. While controlling an outcome in imagination, more than one potential sequence culminating in that outcome may be controlled. The one favored by the flip-flop is pursued unless and until control of it fails, and then another becomes the favored path.
The trial-and-error processes of planning and trouble-shooting often become rather complex, with sequences of sequences, interruptions for sub-sequences, including sequences to arrange environmental feedback functions for control, and alternations between controlling in imagination and controlling through the environment. I began a very limited investigation of these kinds of cognitive processes in the paper that I gave in Manchester in 2019.
This is a continuation of the phenomenological methodology by which Bill Powers identified the levels of the perceptual hierarchy that he proposed.