This is kind of a meta-question about another question I had. I am wondering about how to call words that express what I would call a converse relation in Mathematics.

First, a simple example: I know that “A is a consequence of B”. I could also write that “B is a cause of A” which means mostly the same. My question is therefore: what is the word cause to the word consequence? They are closely related, the Merriam-Webster thesaurus lists them in “Antonyms & Near Antonyms”, but they are not really antonyms, are they?

Now suppose that “Vaccination is mandatory to enter malls.”. I want to rewrite this sentence in terms of “Entering malls is … to vaccination”. But I don’t even know how to phrase that request. I don’t think I am looking for an antonym of mandatory.

I am looking for a way to describe the relationship between cause and consequence in the first example, or mandatory and [blank] in the second example. Is there a word for this?

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    Ï don't know what the word you seek is, if it exists. Your second example could be put "Entering malls requires (proof of) vaccination." Commented Jan 20, 2023 at 8:53
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    Loosely they're called opposites as in "give is the opposite of take" but that doesn't seem precise enough for this context, to differentiate a reverse relationship from another form of antonym ("take" vs "not give").
    – Stuart F
    Commented Jan 20, 2023 at 9:03
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    You shouldn't mix relations as issued from cartesian products with logical relations; the question "vaccination/entry into a mall" has nothing to do with sets. In basic logic, given the relation "A--->B" you call "B--->A" the converse. en.wikipedia.org/wiki/Converse_(logic)
    – LPH
    Commented Jan 20, 2023 at 11:23
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    Entering malls is contingent, conditional, dependent on... But the title of this question seems to be asking for the word antonym or equivalent, not a specific example. We need that to be clarified before posting or voting on answers Commented Jan 20, 2023 at 11:54
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    I'm afraid that the two examples you give are not equivalent in the way you wish. The first example seems to be a 'reciprocal' relationship. Logically, A causes B ENTAILS B is a consequence of A. But "A is 'mandatory' for B means not "If A then B" but "ONLY if A, B" in other words "if not-A then not-B". The two are in this case not 'reciprocal' because not gaining admission does not entail that you have not been vaccinated. There might be other conditions (you might be carrying a knife or an illegal offensive placard).
    – Tuffy
    Commented Jan 20, 2023 at 16:59

4 Answers 4


Inverse and converse are not just math terms.

In linguistics/semantics a pair of terms that name or describe a single relationship from opposite perspectives, such as parent versus child are called converse antonyms.

So searching for antonyms wil usually give you the term you are looking for somewhere in the list of results - you will just need to look at the definitions and usages of the various antonyms to find the one you are actually looking for.

Unfortunately if you use "converse" in a search term on Google or Bing, you are likely to be overwhelmed by information about trainers/sports shoes or whatever the local term is ...

BTW contingent upon is probably the most appropriate for the specific example you used.

Depending on the exact sentence you use, other options would be subject to and dependent on

  • Your answer could be improved with additional supporting information. Please edit to add further details, such as citations or documentation, so that others can confirm that your answer is correct. You can find more information on how to write good answers in the help center.
    – Community Bot
    Commented Jan 20, 2023 at 12:11
  • 1
    Hmmm. Not really sure what would constitute a useful citation for this one ... the only thing I can think of to cite would be the dictionary definitions of "converse antonym" "relational antonym" etc. as there isn't really a better or rather "more accurate" term than antonym that can be used as a search term.
    – Gwyn
    Commented Jan 20, 2023 at 14:14
  • It may be helpful to the future visitors to this page if you incorporate into the answer that converse antonyms are also called relational antonyms. It may also be a good idea to say that, even though they are a species of antonyms, they are not usually the first thing that comes to one's mind upon hearing the word antonym by itself; if one wants to ask for a converse/relational antonym of a given word, one therefore need to make it explicit that this is the kind of antonym one is looking for.
    – jsw29
    Commented Jan 21, 2023 at 21:31
  • Related: What is the difference between antonyms and negations?.
    – jsw29
    Commented Jan 21, 2023 at 21:39
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    Thanks, converse antonym looks like what I was looking for. I was initially confused because one online source defines it as “closely related words that can’t exist without each other. For example, “near” and “far” are converse antonyms because an object can’t be near without measuring it with something far away.” which is not really what I was looking for. However another source defines it as “a pair of words that establishes a relationship from opposite perspectives” which is more like it. Commented Jan 30, 2023 at 14:26

If V is mandatory for M then M is conditional on V.

(OALD) conditional adjective /kənˈdɪʃənl/ ​conditional (on/upon something) depending on something
• conditional approval/acceptance
• Payment is conditional upon delivery of the goods (= if the goods are not delivered, the money will not be paid)

  • Entering malls is conditional on vaccination.

The term "subject to" can be used as well.

(SOED) adj 6 Foll. by to: dependent or conditional upon, resting on the assumption of.

  • Admittance into the mall is subject to vaccination.

There is no notion of opposition connecting "mandatory" and "conditionnal upon" or "subject to".


I am adding some comments in the hope to dispell certain misconceptions that I could read in the comments to the OP.

On the contrary to a supposition that has been put forward, the two examples given are equivalent: they are both the everyday language rendering of the formula "E ---> V"; we are not considering "V ---> E". "E ---> V" is read formally either as "V is a necessary condition for E" or "E is a sufficient condition for V"; in this formal reading of the relation ("is a sufficient condition", "is a necessary condition") we have two equivalent readings; there is an inversion of the symbols but there is a change in the words too, so the same relation is being discussed. We now want to do that in less rigid language (as well as more informative).

We already have "mandatory" as "is a necessary condition" and what's left is finding the equivalent of "is a necessary condition" in language that applies to the context "Vaccination/Entry" but contains as well the idea of necessity. ("Mandatory" contains the idea of necessity. "Conditional on", for example, contains the idea of sufficiency. )

  • Can you expand on your last sentence? That seems to be the core of the question.
    – MJD
    Commented Jan 20, 2023 at 15:42
  • We say conditional on, not to.
    – Lambie
    Commented Jan 20, 2023 at 21:32
  • @Lambie Thanks, I can change that.
    – LPH
    Commented Jan 20, 2023 at 21:53
  • @MJD ex. The presence of clouds is necessary to the production of rain The production of rain is conditional on the presence of clouds. "Necessary to" is no more the contrary of "conditional on" than "mandatory" is the contrary of "conditional on". Nevertheless, the two propositions are of the same sort (implications, ---->). On the basic logic is superimposed a variety of meanings, and it is on that level that the notion of contrariness becomes relevant.
    – LPH
    Commented Jan 20, 2023 at 21:55
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    The OP is not really asking how to fill in the blank in 'Entering malls is ____ vaccination' but is using that as a part of an example that illustrates the question. The question asked is a meta-question relative to the question that is answered here. It is: what is the word for the relationship between mandatory and the word that fills in the blank?
    – jsw29
    Commented Jan 21, 2023 at 20:29

For the very specific instances of cause vs consequence, and mandatory vs [blank], yes, these are simply converses of each other.

For 'cause' and 'consequent', these two are reverse implications of each other. This is more of a description of the situation than the one label for it.

And the corresponding word to 'mandatory' is (roughly) 'allowed'. If vaccination is mandatory to enter a mall, then:

Entering malls is allowed with vaccination.

And the relation between these two words is that they are modal complements or duals of each other.

But there is a lot more here. Sure, one could mathematize all this and the mathematicians have words for all these situations, but there are words in natural non-technical English that cover a lot of the variation in describing some pairs of words.

Tchrist gave a list of many opposites for the word 'man'. It all depends on the semantic feature that you care about.

There are many kinds of names of these relations between two words A and B that are like opposites:

Note that some of these have precise mathematical definitions which fit only vaguely their non-technical uses

For example, the inverse (or converse) of 'mandatory' is 'optional' or 'allowed'.

But the opposite of mandatory is forbidden - there's a lot of room in between for those things that could be allowed.

And the complement of mandatory is 'not mandatory' (no single word for it) - this includes things that are allowed and things that are absolutely forbidden.


You can also express your idea by saying:

Entering malls presupposes vaccination.

Presuppose means

require as a precondition of possibility or coherence (OxfordL)

Macmillan explains

if one thing presupposes another, it cannot exist or happen unless the other thing is also true

  • Their spending plans presuppose continued economic growth.
  • 1
    Without explaining why, someone downvoted what seems a reasonable answer. I have compensated.
    – Anton
    Commented Jan 20, 2023 at 15:39
  • 1
    This doesn't answer the question. OP is looking for a name for this type of word relationship, not synonyms for their example.
    – MJD
    Commented Jan 20, 2023 at 15:40
  • @Anton Got used to it... I am guessing that the downvoter was not happy with me sticking to the OPs sentence. But The OP may find an even more concise way of saying things helpful. Also, the verb "presuppose" does exactly describe this relationship.
    – fev
    Commented Jan 20, 2023 at 15:41
  • @fev Agreed. A tightly formal approach has the disadvantage that it hinders further thought and helps not at all. On the other hand, partial answers are helpful.
    – Anton
    Commented Jan 20, 2023 at 16:47

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