Descriptive names for logic operations on a pair (x, y)

It reads as “The output is TRUE only when the reduction (x,y)\rightarrow z meets the description of the operations below”

0 inputs:

  • Constant: gives the same hard-coded result regardless of inputs

1 input:

  • Transfer: Hardwired to one of the inputs
  • Complement: NOT

2 inputs (symmetric):

  • Comparison: different (XOR), identical (NXOR or equivalence)
  • Arithmetic: AND, OR and its complements NAND, NOR

2 inputs (asymmetric):

  • Inhibition: ONLY 1 followed by 0 is an inhibition. It’s a WHITE-list: anything else is not an inhibition (starting with 0 doesn’t inhibit)
  • Implication: ANYTHING GOES as long as 1 is be followed by 1. It’s a BLACK-list: anything else qualifies as an implication (starting with 0 does not break the implication)

Implication is the complement of Inhibition, as the only case that breaks an implication is inhibition.

This ‘operator’ instead of truth-table view is more often used in electrical engineering than in computer science. There are many names for the same thing, but I put in some thought to find the intuitive words to make it easy to understand and remember

WARNING: Those there are tempting faint similarities between logic and set theory, there’s no direct tight duality between the two. Whitelist/Blacklist in inhibition/implication do not make sense with set-diff/subset as we are talking about a one-shot relationship here in logic, while set theory talks about the relationship between elements picked after it is quantified by “for all” vs “there is”. i.e. Truth table do not mix with sets

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