Can first order logic represent a past occurring adverbial dependent clause with a present main clause to form the perfect tense?

Is this the way to represent an adverbial dependent clause with first order logic?

I have existed since before Bill was born.


Since BORN(BILL) can be represented with BORN(e1,BILL) can first order logic represent E, R and U as described in this example for present perfect?

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  • 2
    This is not propositional logic, which is the simplest formal logic, not even predicate logic, it’s a higher-order formalism. Aside from this, your formula is one way of expressing the sentence, but I’d consider using the Davidsonian notation, which is more elegant (and more straightforward).
    – Atamiri
    Jun 1 '20 at 0:11
  • 1
    @Atamiri It's my first attempt. I am very interested in seeing your examples.
    – user27672
    Jun 1 '20 at 1:22
  • 1
    I was attempting to use something from @jlawler - www-personal.umich.edu/~jlawler/logicguide.pdf
    – user27672
    Jun 1 '20 at 1:57
  • 1
    Davidsonian semantics is first-order, it uses “individuals” to denote predication, so “born(Bill)” becomes “born(e1, Bill)” and you can then say “past(e2, e1)” instead of “past(born(Bill))” (which isn’t first-order). It has a number of technical advantages but there’s no semantic difference.
    – Atamiri
    Jun 1 '20 at 8:57
  • 1
    That's only important for logicians. Formal logics are just stick-figure representations of certain aspects of natural language; it's clear that humans use all kinds of informal (and formally incorrect or incoherent) logics. And don't forget tense is a complication that logics don't often undertake. For one thing, tenses have a habit of presupposing, which predicate calculus can't handle -- just the assertions, ma'am. Lacking a real theory of time, tense is usually handled ad hoc.
    – jlawler
    Jun 1 '20 at 20:18

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