Most SRS implementations assume that a full reconsolidation happens after review, regardless of whether the review passed or failed. That is, the probability of recall/success is always restored back to 100% even after a failed attempt.

However, it's possible that only a partial reconsolidation happens whenever the user fails, and that a full reconsolidation is perhaps only possible after a "successful" attempt via a refresher (e.g., via an Anki-style relearning step) or a follow-up review in the future.

What I mean by "partial reconsolidation" is that the probability of recall/success isn't restored to 100%, but rather somewhere below. In the event of zero reconsolidation (or complete lack of reconsolidation), the probability of recall/success is the same as before, as if the review didn't happen at all. And if so, we can assume that the date of 100% recall (or 100% probability of success) is still in the past (i.e., it's still the same as before, prior to today's review, as if today's review didn't happen). If a partial reconsolidation happens instead, the date of 100% recall is somewhere in the past as well but could be much later than before: much later than the prior review's date but earlier than today's review.

So when there's a partial or zero reconsolidation currently in place, and we used the algorithm to update the model, it would be as if there's some kind of inherent interval in addition to the current interval since last review. That is, to simulate a less than 100% recall even after the review happened today, it would be as if the 100% recall is in the past, at an interval equal to the inherent interval.

So in essence, suppose X days have passed since the user reviewed with a failed attempt, then there will be Y days of inherent interval, to accommodate for the partial/zero reconsolidation that might have taken place. When updating the model with the X interval, what the algorithm actually sees is that X+Y days have passed (instead of just X days) – and that is why I call the Y an inherent interval. The inherent interval is only cleared (or becomes completely zero), once a full reconsolidation happens. If instead, a zero reconsolidation happened in the last review, the inherent interval will be exactly the same as the interval inputted in that last review.

Partial reconsolidation can therefore be simulated by introducing some kind of inherent intervals and combining that with Ebisu's soft-binary fuzzy quiz feature. Also, we can view the act of "displaying the correct answer after a failed attempt" as some kind of passive review, with a weak influence on the probability of successful active recall: hence, passively seeing the correct answer contributes only a partial reconsolidation. A zero reconsolidation is even possible if the user simply glanced at the correct answer after a failed review, without internalizing the correct answer, or without a follow-up refresher.

Partial reconsolidation is also possible if an item partially influences the recall of another item, either through some kind of strengthening or interference, i.e., a model correlation. For interference, a successful recall attempt of a certain item could be a partial failed recall attempt on another item – and I think in most cases, only the fuzzy quiz feature is necessarily involved here, but if the item reminded of the other item's answer after a failed recall of the latter, then the inherent intervals might be needed to be involved also.

Now, I lack the mathematical background regarding the feasibility of this feature, and also, I don't know if this is a good feature at all. Nonetheless, I believe this is a handy feature with very niche applications, especially for the implementation of model correlations (as that is the primary motivator that made me think about all of these).