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What is the precise meaning of "non-reciprocal?" Two definitions of "reciprocal" taken from the Merriam-Webster dictionary are:

  • shared, felt, or shown by both sides
  • serving to reciprocate : consisting of or functioning as a return in kind

The definition provided in the dictionary of non-reciprocal is essentially just 'not reciprocal.' This raises some questions relating to existential qualifiers and colloquial usage. Consider the following statements:

  1. Alice likes Bob while Bob likes Alice
  2. Alice likes Bob while Bob dislikes Alice
  3. Alice likes Bob while Bob is ambivalent towards Alice

Clearly, statement 1 describes a reciprocal relationship between Alice and Bob. If we are given the information that statement 1 is not true, we cannot infer whether statements 2 or 3 are true. In a strict logical sense, if the relationship between Alice and Bob is non-reciprocal, it is not possible to distinguish whether statements 2 or 3 are true, but I have heard people use non-reciprocal to refer sometimes to statement 2 or sometimes to statement 3.

Are there any clear guidelines or more specific definitions for usage of the word 'non-reciprocal'?

Thank you.

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    In a directed graph where an edge from A to B means A loves B, not having an edge from A to B does not mean that A hates B (although she could hate him). So I don't see how you can conclude anything about general reciprocal relationships from directed graphs. Jul 20, 2023 at 2:32
  • It seems as if you should focus on the meaning of "reciprocal". Preceding it with "non-" simply negates whatever that is, without being more specific. Jul 20, 2023 at 3:17
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    Are you asking about its meaning in graph theory or in the context of interpersonal relationships? Mathematical terminology rarely corresponds to everyday English.
    – alphabet
    Jul 20, 2023 at 3:26
  • (I think "reciprocated" is more common than "reciprocal" in such contexts, no?)
    – alphabet
    Jul 20, 2023 at 3:27
  • @PeterShor I am particularly interested in usage in the context of statistical physics. The reference to graphs is somewhat irrelevant to my interest; it was not a good choice to include it. In a recent paper titled “Non-reciprocal phase transitions” by Fruchart, et al., ‘non-reciprocal’ seems to refer to something like case 2 in my post. alphabet asks whether I am interested in everyday or mathematical contexts. I cannot find a precise definition of ‘non-reciprocal’ in physics, so I am curious how it might be used in more formal contexts that may not involve precise mathematical definitions.
    – Emmy B
    Jul 20, 2023 at 5:22

1 Answer 1

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Not much can be inferred from the statement that Alice’s liking for Bob is not reciprocated. Besides your two options, Bob may be simply unaware of Alice.

Reciprocity, as your definitions note, is used in cultural relations and international relations. There’s extensive literature in both areas. Countries often establish reciprocal relationships in areas of trade, law, and diplomacy. But the absence of, say, reciprocity in landing rights at airports doesn’t tell us what the non-reciprocal relationship actually is.

Reciprocity is a defined term in a variety of mathematical formulations, as listed in Wikipedia’s effort to disambiguate the term. There’s no reason to expect that any one of these would correspond to the use of the term in standard English.

https://en.m.wikipedia.org/wiki/Reciprocity

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