First, a terminology lesson. Then explain why you cannot do this. Thirdly, an alternative solution that is not perfect, but can lead you to where you need to go.
Terminology
From the point of view of your question, you are not trying to "redefine" the class, you are trying to rewrite the class. Class rewriting is where you add Magento configuration nodes to report it
Create this class instead of this class
"override" is where you copy the class from the Magento core to the local code pool. In other words, copy
app/code/core/Mage/Rule/Model/Abstract.php
to
app/code/local/Mage/Rule/Model/Abstract.php
An override is where you tell Magento to "use this class file instead of another class file." Sounds like, but different from rewriting. Rewriting is considered best practice because it is less damaging and less likely to cause problems with updates and extension compatibility.
You cannot do it
You cannot rewrite an abstract class. The rewrite system works because Magento uses the factory template to create models, blocks and helpers
$class = Mage::getModel('catalog/product');
What is rewriting in pseudo-code
function getModel($model) { if("can I find a rewrite configuration for $model") {
Because an abstract class is never created, it can never be rewritten.
Decision
From what I can tell, there are only three classes that inherit this abstract class in a standard Magento installation.
catalogrule/rule Mage_CatalogRule_Model_Rule rule/rule Rule/Model/Rule.php salesrule/rule SalesRule/Model/Rule.php
You can add a rewrite for each of these classes separately, ideally putting your new logic in a common helper class. You will need to handle extensions or custom code in a similar way, but this is one possible way forward.
Another alternative is to use a traditional class override and copy
app/code/core/Mage/Rule/Model/Abstract.php
to
app/code/local/Mage/Rule/Model/Abstract.php
This will allow you to change one Abstract class, but you will need to merge any changes from the updated versions into this class - and you can cause system problems when (and not if) you forget to do it.
Good luck