Routledge Dictionary of Language and Linguistics
In formal logic, the characteristic of a two-place relation R in a set S, which is true if every element x in S is in the relation R with itself (notation: R(x, x)). This is true, for example, for the relation of identity: every element is identical to itself.
A relation R is non-reflexive in the cases where R(x, x) is not true for every element. This is, for example, the case in the relation of punishment, for not every individual punishes him/herself. One must distinguish between a non-reflexive relation R and a so-called irreflexive relation R', in which it is the case that for all elements ¬R'(x,x). Compare the (irreflexive) relation of being married: No one gets married to oneself.
References
formal logic, set theory
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