Dear All,
Is this analysis of "part addition z has added y to x" correct?
start of z:
x and y already exist
y is not part of x
end of z:
x and y still exist
y is part of x
together:
z is temporally (properly) within the "existence" condition states of x and y
y has a "part of x" condition state p:
* p is within the existence of x and y
* p includes or starts with the end of z: starts after the start but before or
with the end of z, ends after the end of z
* y is part of x during p: the presence of y is within the presence of x
y has a "not part of x" condition state n:
* n is within the existence of y (and x)
* n includes or ends with the start of z: starts before the start of z, ends
with or after the start but before the end of z
* y is not part of x during n: the presence of y is not within the presence of x
n is the predecessor of p: ends with the start of p (ends before or with the
start of p, does not end before the start of p ?)
Some questions:
Is it actually possible to infer that the presence of y is not within the
presence of x at the start of the part addition / during n?
If not, is there anything meaningful left to say about n?
Are "existence" and "is part of x" allowed uses of condition states at all?
Or use temporal entities instead and simply leave out the part "y has condition
state"?
Would "contains y" be better than "is part of x" because x is probably
physically changed by the part addition?
Would it make sense to say that a "y is part of x" condition state belongs to
both x and y? (Current quantification says no.)
Ruling out edge cases:
Here as well as in the P46 axiom about presences ("P46(x,y) ⇒ (∃t) [y is part
of x during the time-span t"]), there are some edge cases that could make the
right-hand side of the axiom trivially true.
For example, the P46 axiom needs to rule out that the time-span is empty. Is
there an empty time-span?
* If yes, we can introduce a constant ∅ with the property E52(∅) ∧ (∀t) [E52(t)
⇒ P86(∅,t)]. In the P46 axiom, add ¬(t=∅).
* If no, we need to add an axiom like this (so that we don’t have to do it in
the P46 axiom): (¬∃t) [E52(t) ∧ (∀s) [E52(s) ⇒ P86(t,s)]].
* If deliberately unspecified, we need to add something like this to the P46
axiom: (∃q) [E52(q) ∧ P86(q,t) ∧ ¬(q=t)]
Do empty time-spans exist?
Do non-empty time-spans with length 0 exist?
Do empty presences exist, i.e, where the existence of x has no temporal overlap
with the specified time-span t?
Are there condition states of x that are partially or completely before or
after the existence of x?
Do condition states (or temporal entities in general) always have a positive
duration?
Best,
Wolfgang
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