What do you call two words that describe reciprocal relations?

Question

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?

Answer 1

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

Answer 2

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".

Addition

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. )

Answer 3

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.

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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:

• opposite
• antonym
• negative
• complement
• reciprocal
• inverse
• converse
• counterpart

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.

Answer 4

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.