It is possible through rough sets, specifically you can use explicit temporality or just a collection of information systems  over a directed set.

A predicate for "the "need" to know, and the tragedy of not being able to "know" anything predictively useful for long" is not a big thing.

But all this assumes that objects are defined by their properties.... 

Can you please provide more detailed references for your problem?

Thanks!

We should distinguish between subsymbolic and symbolic learning.

Subsymbolic learning (neural networks) is by definition

error-tolerant and not so prone to changes. A neural network

still works more or less if some parameters get lost/decay.

Symbolic learning has the property that there are no half

symbols. There is no half symbol for a rabbit. So how could

forgetting occur here? Long term memory must be organized

in tuples of symbols. Each tuple has up to 7+-2 symbols

(or fewer, some say 4). Why the Miller number? Because a

memory that's recalled must fit into working memory. You

can't retrieve a poem at once. These memory packets build

up the vertices of a graph. At the edges are associations.

For example (dogs are mammals) is associatively connected

with (burglars deterred-by dogs) since both tuples contain

the symbol dogs. When forgetting takes place in such a

memory, what could happen?

If one symbol decays (completely), the remaining tuple might

still bear meaning. (dogs are mammals) could lose one

symbol "are", leaving (dogs mammals). Such an entry in a

knowledge base could still allow the conclusion, with some

uncertainty, that dogs are mammals. Memory should decay in

a way that always rules allow some useful deduction.

Such a process is rather a compression with loss, and

maybe it involves conscious decisions. A conscious

decision to forget could be to repeat shortened tuples

(sentences) and not to repeat bloated ones.

Maybe of interest:

http://medicalxpress.com/news/2016-03-scientists-neural-mechanisms-mouse-brains.html

http://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.1004128

http://www.sciencealert.com/the-deepmind-ai-can-now-learn-how-to-use-its-own-memory

https://arxiv.org/abs/1510.03931

Regards,

Joachim