This seems related in spirit to the fact that time is only partially ordered in physics as well. You could even use special relativity to make a model for concurrency ambiguity in parallel computing: each processor is a parallel worldline, detecting and sending signals at points in spacetime that are spacelike-separated from when the other processors are doing these things. The database follows some unknown worldline, continuously broadcasts its contents, and updates its contents when it receives instructions to do so. The set of possible ways that the processors and database end up interacting should match the parallel computation model. This makes me think that intuitions about time that were developed to be consistent with special relativity should be fine to also use for computation.
If you mark something like causally inescapable subsets of spacetime (not sure how this should be called), which are something like all unions of future lightcones, as open sets, then specialization preorder on spacetime points will agree with time. This topology on spacetime is non-Frechet (has nontrivial specialization preorder), while the relative topologies it gives on space-like subspaces (loci of states of the world “at a given time” in a loose sense) are Hausdorff, the standard way of giving a topology for such spaces. This seems like the most straightforward setting for treating physical time as logical time.
This seems related in spirit to the fact that time is only partially ordered in physics as well. You could even use special relativity to make a model for concurrency ambiguity in parallel computing: each processor is a parallel worldline, detecting and sending signals at points in spacetime that are spacelike-separated from when the other processors are doing these things. The database follows some unknown worldline, continuously broadcasts its contents, and updates its contents when it receives instructions to do so. The set of possible ways that the processors and database end up interacting should match the parallel computation model. This makes me think that intuitions about time that were developed to be consistent with special relativity should be fine to also use for computation.
If you mark something like causally inescapable subsets of spacetime (not sure how this should be called), which are something like all unions of future lightcones, as open sets, then specialization preorder on spacetime points will agree with time. This topology on spacetime is non-Frechet (has nontrivial specialization preorder), while the relative topologies it gives on space-like subspaces (loci of states of the world “at a given time” in a loose sense) are Hausdorff, the standard way of giving a topology for such spaces. This seems like the most straightforward setting for treating physical time as logical time.