# What is reflexivity in temporal logic?

According to Stanford Encyclopedia of Philosophy, reflexivity can be defined by :

∀x(x ≺ x)

Where means "Precedes" : `For all x, x precedes x`

But what does it mean for an instant in time x to precede itself? I do not get this point?

The Question : What does reflexivity mean?

Reference

https://plato.stanford.edu/entries/logic-temporal/

• Does it mean recurrent time? Commented Jan 24, 2019 at 11:18

It is just a definition

If the definition is useful really depends on what you want to model. The author of the SEP article does not know what you want to do, so he includes a reasonable amount of hopefully useful definitions.

Usually, it doesn't make sense to be reflexive, the article itself says so.

There are some basic properties which can naturally be imposed on instant-based flows of time. It is usually required to be a strict partial ordering, that is, an irreflexive and transitive relation

From SEP, my emphasis.

But as an example, if you want to describe a repeating process, circular time is a natural way to do so. Since transitivitiy still holds, every point precedes itself. Or think of a process that might branch, and possibly has loops. Then points that "precede themselve" are exactly those which sit in a loop.

• Thank you so much, I thought there is another way to look at this definitions other than circular (recurrent) time or possible loops. Because another string of thinking may suggest that even if an instant x repeats in time, every instance of the same instant is not identical to another one, even if the same instant repeats itself, that's why I thought that maybe I misunderstood the point, after all it is all definitions, thanks Commented Jan 24, 2019 at 11:39