Following this notation, we can formalize rigid existential dependence as follows: "□(Ex → Ey)", which can be read as "x rigidly depends for its existence on y", or alternatively "x rigidly necessitates y".
So object x is strongly rigidly dependent on object y if x depends for its existence on y and y is not a proper part of x.
Timings were not rigidly fixed and depended on the availability of electricity, the weather, and the household engagements of women.
This effect appears to depend on the Gd chelate being rigidly fixed to the exterior surface of the liposome, such that the nanocomplex rotates as a rigid body thus reducing the rotational tumbling rate of these large nanocomplexes [51].
What the matrix reveals is that the expression 'I' rigidly designates different individuals, depending on the context in which it is used.
"It all depends on how rigidly you want to read the law," he replied, according to an audio recording from the Distressed Real Estate Summit on May 13 at a downtown hotel.
We have mentioned one example of rigid existential dependence, namely, sets ontologically depending on their members (more precisely, a set depends rigidly on the very members it has, i.e., any change in a set's members will change the set itself).
One is hierarchical, rigidly organized, likes spit and polish, and depends on a lot of grunts to do most of the work.
An immediate implication of (ID-EX) in conjunction with (EDR) is that if x depends for its identity upon y, then x is rigidly existentially dependent upon y (although not necessarily vice versa, of course).
Although epithelial characteristics are often rigidly defined, epithelia are actually dynamic structures with variable integrity and tightness depending on physiological requirements throughout the body or during ontogeny [17].
