Learn English – Single word to replace “allowed to be missing”

logicsciencesingle-word-requeststerminology

I want to express my knowledge about the presence of absence of something. My knowledge is divided into three different cases:

  • I know that the thing doesn't exist.
  • I don't know whether the thing exists.
  • I know that the thing exists.

Sadly, neither of those is the negation of another one. However, I can define four cases, where each case is the negation of another case:

  1. Something is allowed to exist. (allowed)
  2. Something is allowed to be missing. (???)
  3. Something is guaranteed to exist. (guaranteed)
  4. Something is guaranteed to be missing. (prohibited)

I want to describe each of these cases by a single word, which is supposed to clearly distinguish it from the other three cases. As you can see, I already found three of the words. However, in the second case I am unable to find one.

Let me expand on what I mean by the negation. Consider the following table:

phrase single word doesn't exist don't know exists
allowed to exist allowed no yes yes
allowed to be missing ??? yes yes no
guaranteed to exist guaranteed no no yes
guaranteed to be missing prohibited yes no no

Note, that the first and the fourth case are supposed to be negations of each other, just like the second and the third case. Thus, if I say that something is not allowed to exist (allowed), then it is guaranteed to be missing (prohibited). Also, if I say that something is not allowed to be missing (???), then it is guaranteed to exist (guaranteed).

Thus, my question is: Which single word is able to replace the phrase "allowed to be missing"?

This question can be rephrased to: Which single word is the exact negation of "guaranteed to exist"?

The context is theoretical computer science. Here are two example sentences, which are negations of each other:

  • The connection from x to y is allowed and the connection from y to z is guaranteed.
  • The connection from x to y is prohibited or the connection from y to z is allowed to be missing.

I think the most helpful wording is the one suggested in this answer, using terms from modal logic:

  • The connection from x to y is possible and the connection from y to z is necessary.
  • The connection from x to y is not possible or the connection from y to z is not necessary.

Thanks for all the answers =)

Best Answer

The usual mathematical terms for these things (from the study of modal logic) are 'necessary' (for your 'guaranteed') and 'possible' (for your 'allowed'). All you need is negation to get all four possiblities.

  • necessary - it must exist
  • possible - it may exist
  • not necessary - it may not exist
  • not possible - it cannot exist

Depending on your (choice of) logic those two in the middle may be the same.

For a logic of probabilities, where 0 <= p <= 1:

  • necessary: p=1
  • possible: p > 0
  • not necessary: p < 1
  • not possible: p = 0

For example, you can see that 'not possible' is the same is the complement of 'possible'.

This mathematical use of these words follows our informal meaning.

So to your specific questions:

  • Which single word is able to replace the phrase "allowed to be missing?

    With respect to probability, this means that it could be any probability. So any combination that covers all possibilities, 'necessary or not necessary'

  • Which single word is the exact negation of "guaranteed to exist"?

    By negation, there are two possibilities that informal English allows. 1) the set complement, 2) the other point extreme of the spectrum.

    • For the set complement it is 'not necessary'.
    • for the other extreme it is 'not possible'.
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