I’ve been working for a while now on an ontology for representing events (which includes process, of course). One of the requirements of a system that is to monitor, govern, implement, or reason about processes is that it consider “situations”, which are things that happen or occur, including events and states. (See, for example, the perdurants of the DOLCE ontology, BFO‘s occurents, or OpenCyc’s situations.) This requires the representation of time-variant information at various points or during various intervals of time (more than just the Allen relations or OWL Time). If you’re interested in such things, I’d recommend Parsons‘ “Events in the Semantics of English” or Pustejovsky‘s “Syntax of Event Structure“, both of which look at the subject from a linguistic rather than inferential perspective. When you pursue this to the point that you implement the axioms that an artificial intelligence needs to provide assistance in defining or governing a business process (or answering questions about molecular biological processes) you land up in some pretty abstract stuff, including the Stanford Encyclopedia of Philosophy. I found the title of this post entertaining within the page on temporal logic.
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I love the title of the post. It’s a great tongue twister. Interesting food for thought. One area of temporal logic that I’ve been pondering on the last few years is temporal versioning and temporal distance. I’m interested to hear how you address the expression of intervals of time.