A negation is an invalidation, but not reciprocally - since an invalidation signifies a (partial or total) degree of negation, so invalidation may not necessarily be a complete negation.
Therefore, in one space a statement may be valid, in another space it may be invalid, and invalidation can be done in various ways.
An invalidation of <A> is noted by i(A), while a validation of <A> is noted by v(A):
A pseudo-norm is a particular case of an S-denied norm since we may have vectorial spaces over some given scalar fields where there are some vectors and scalars that satisfy the third axiom [validation], but others that do not satisfy [invalidation]; or for all vectors and scalars we may have either [parallel]x + y[parallel] = 5 * [parallel]x[parallel]* [parallel]y[parallel] or [parallel]x + y[parallel] = 6 * [parallel]x[parallel] * [parallel]y[parallel], so invalidation (since we get [parallel]x + y[parallel] > [parallel]x[parallel] * [parallel]y[parallel]) in two different ways.
Keywords: : Mobile computing, cache invalidation, wireless, data broadcast, invalidation report, disconnection, failure.
In order to assist mobile clients in maintaining the consistency of their caches, a number of cache invalidation techniques have been proposed [1-14].
To overcome the limitations of existing cache invalidation strategies, this paper presents a synchronous stateful caching strategy where cache consistency is maintained by periodically broadcasting update reports (URs) and request reports (RRs).
Section 2 gives a brief review on some representative approaches on cache invalidation.
A number of broadcast based cache invalidation strategies have been proposed for mobile environments.
Hu and Lee  have proposed a family of invalidation algorithms.
As a result, valid items could be falsely invalidated; that is, false invalidations set in.
In order to reduce false invalidations, a hierarchically structured, more detailed report has been proposed [Jing 97].
Clearly, this "half-update" scheme may not yield minimal false invalidations.
Specifically, we will investigate the division of the n overlapping subintervals in the report such that the false invalidations can be minimized.
It is observed that the false invalidations are due to the inaccuracy of the report as the exact time of updates has been replaced by fewer rough timestamps (to save bandwidth).