Grammar of time travel

In many science fictions which feature time travel, the problem of
grammar for time travellers are often recognized. (Well, it's often
ignored too.) I wonder whether someone included grammar of time travel
to their languages?

Rough sketch of mine:

In normal timeline, time is totally ordered, and therefore,
trichotomous. So for any time a and b, exactly one of a<b, a=b, a>b is
true, which corresponds to past, present, and future.

With multiple timelines, time could be partially ordered, then one of
four things happen when comparing two times: less than, equal to,
greater than, not comparable. So let's give an "alternate" tense for
the last case.

When the time forms a lattice, say, in a closed universe, it would be
bounded, and has Big Bang and Big Crunch as least and greatest
element. When closed timelike curve is not involved, there can be a
partial order where any two times can meet and join.

Given two timelines, ax<a<bx<b<by<d<dy and a<cx<c<cy<d<dy, two
speakers in b and c may communicate via some exotic time-crossing
communication device.

ax and a, or anything before meet of b and c, are "our past".
bx, between meet and speaker's present, is "my past".
cx, betwwen meet and listener's present, is "your past".
b is "my present", c is "your present".
In the same way, by is "my future", cy is "your future".
d and dy, or anything after join of b and c, are "our future".

This creates 8 distinct tenses, and obviously differentitation of
shared timeline and non-shared timeline would be useful. In a simpler
system, your past/present/future could be compressed to alternate
tense discussed above. This leaves, shared-past, past, present,
future, shared-future, alternate.

Above system could be implemented by modifying tense markers with
pronominal markers, maybe omission defaults to "my", or defaults to
subject of current sentence. Or, when timeline marking is very
essential, omission of one could default to shared times.

--
Seo Sanghyeon

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