In most languages, the linear concept of time has led to similar concepts of past/present/future.
Now, suppose that we have a human or human-like society in which time travel is fairly common, and it is possible for an individual to travel forward or back in time on occasion, including making contact with their past or future selves, friends and family. This is achieved by magic, not technology, and while many individuals can time-travel themselves or send a non-time-traveller to another time, the majority (about 95%) cannot temporally displace themselves or others.
The one restriction on this time travel is that a time traveller cannot change what they know has happened in the past of a point in time in which they have been present. This includes influencing other time travellers to change things on their behalf, even if they don't tell the other time traveller why they want them to do certain things at a certain point in space-time.
E.g. an individual travels to the future, and learns about the death of their future self. Learning about this means that this time traveller cannot affect the outcome that his (now past) self learns about his future self's death at that point in the future. However, the possibility exists that either that now-past self was lied to by a witness, or if the time traveller was a witness to his future self's death, that the time traveller was deceived or mistaken. It is also possible that the event of the future-self's death was sufficiently unambiguous that it could not be other than what it appeared to be.
So, given that members of this society can travel in time relatively often, how would this affect the society's language?
There is no paradox, as causing a paradox is ultimately impossible, but the time travellers may suspect this to be the case, but don't know that with any certainty, and act as if paradox is a possibility. What exists and is remembered by time travellers and non-time travellers alike is the final state of any time travel loops.
For example, A time traveller cannot kill their own ancestor or the ancestor of anyone they know of (however indirectly) at a point in spacetime that would invalidate the existence of themselves or a known person. However, that is not to say that they couldn't, for example, kill the individual that they believe was their own grandfather before the conception of their parent, but it would ultimately turn out that they were mistaken as to the relationship, or they mistook the person they killed for their ancestor, or they only thought they had killed their ancestor.
As another example, a time traveller cannot pass information (via whatever means) to another time traveller, even if the two time travellers are unknown to each other in a social sense, that could cause that second time traveller to invalidate the first's memory of events or the existence of anything he knows: it is the transfer of information that defines knowledge.
An infinite loop is not a possibility (though it is possible for a loop to be repeated a great many times) as outcomes along a timeline are not predetermined. Each act of travelling back in time results in a new sequence of events. A common trope in time travel is that non-time travellers will always act in the same way to the same stimulus; this is false. It may be likely that they will do so, but quantum uncertainty means that each act of retrograde time travel will result in the subsequent events unfolding differently in some way, whether subtle or glaringly obvious. Sooner or later, this (or other time travel) will result in the loop diverging sufficiently that it ends. The time traveller would not remember all of these loops either, only the last one, so no Groundhog Day or Edge of Tomorrow loops with a time traveller retaining information from his future self, at least without meeting his future self and passing on that information.
For example, a time traveller in a loop meets an old friend (who is not a time traveller) in several iterations of the loop, in the same situation. However, the old friend will not always greet the time traveller in exactly the same way. In the first loop, he says "Hi", in the second "Hi", 3rd: "Hello", 4th: "Hi", 5th: he just nods, and so on.
Anyway, this question is about the linguistics of this scenario, not the physics save where it affects the linguistics. Time travellers believe that paradox may be possible, even though it is not, and the linguistics must reflect this.