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Let me essay a fuller but still short and simplified account.
All words are predicates (except magic zoi-like words).
Each predicate is inflected to show which of its argument places are saturated implicitly and which explicitly (by merger with another argument place (of another predicate)).
For the first word of the sentence, all explicitly saturated argument places (ESAPs) are added to a virtual list.
For the next word, for each of the word's ESAPs the word is inflected to
(a) show which ESAP on the virtual list it merges with, with the merged ESAP removed from the virtual list, or
(b) show which ESAP on the virtual list it merges with, with the merged ESAP left on the virtual list, or
(c) show the ESAP does not merge with any ESAP on the virtual list, and is added to the list
And so on, iteratively, for each next word. The sentence ends when the virtual list is empty
A further unergonomic feature of the system is that most of the info in a sentence is in the inflections, not in the predicates (i.e. stems), though I haven't yet been able to assess how extreme the imbalance between stem and inflection is.