Table 1.
Cellular response properties.
Figure 1.
Neurons as functionally complete logic gates.
The circuit diagrams show that neurons with excitatory and inhibitory inputs and neurons that have continuously high outputs form a functionally complete set, meaning any logic circuit can be constructed with them. The label on each neuron represents its response. The maximum and minimum possible responses 1 and 0 can stand for the logical values true and false, making the network outputs logical functions of the inputs. The diagrams show logic gates for (A) X AND NOT Y, (B) X AND Y, and (C, D) NOT X. Arrows indicate excitatory input; blocks indicate inhibitory input. Spontaneously active neurons are square. To illustrate example inputs and outputs, active neurons are colored. Inactive inhibitory cells are shaded.
Table 2.
Recursive AND NOT Conjunction definitions and responses.
Figure 2.
Recursive AND NOT Conjunctions.
An n-RANC is a general logic circuit that produces conjunctions of n propositions. A complete n-RANC produces all conjunctions corresponding to the 2n possible combinations of truth values of n propositions. Examples of complete n-RANCs are shown here for n = 1-4. A single n-RANC produces one of the possible conjunctions. In C, the single 3-RANC that produces output number 3, , is indicated by thick lines. In D, the output number 14,
, represents the truth value of the conjunction “X2, X3, and X4 are high, and X1 is not high.” The other 15 conjunctions are false, and the corresponding RANC outputs are 0.
Figure 3.
Fuzzy logic of a complete 4-RANC.
The figure in A shows the approximate computations of a complete 4-RANC when one of the inputs has an intermediate value between 0 and 1. The graph in B illustrates the RANC interval measure property: The output intensities (approximately 0.7 and 0.3) are measures of the subintervals ([0, 0.7], and [0.7, 1]) of [0, 1] formed by the input intensities. The combination of output cells that respond uniquely identifies the ordering of the input intensities (0 = X3<X4<X1 = X2 = 1). The response
represents the fuzzy truth value of the conjunction “X1 and X2 are high and X3 and X4 are not high.”
Figure 4.
Relative Absorption Model responses to a greenish-yellow photostimulus.
A greenish-yellow photostimulus moderately represses the L cone response and strongly represses the M cone so that M<L<S. The RAM's responses to a somewhat desaturated greenish-yellow photostimulus, shown in A, are correlates of the perception of the photostimulus. The graph in B shows that the approximate RAM responses illustrate the RANC interval measure property. The response represents the fuzzy truth value of the conjunction “S and L are high and M is not high.” Since this state of cone responses is the condition for the perception of green,
also represents the fuzzy truth value of the proposition “The photostimulus is green.” That is,
is the correlate of the perceived strength of the green component of the photostimulus.