Dynamic implicit strict partially ordered sets

Sets may be ordered, unordered, or partially ordered. Amongst partially ordered sets (posets), if the relation between the ordered elements is one of ≥ then this is a standard poset, but if the relation between the ordered elements is one of >; then this is called a strict poset. It is the author´s contention that many strict posets exist implicitly: for example, most examples of preference ordering are actually only partial orders, since one may easily rank one´s most-favorite and least-favorite of anything, but of all that is in-between, there has probably not been formed a complete total ordering. Furthermore, even if there was a complete total ordering, the solicitation of the preference order information often results in only a partial order being known: for example, it is easier to ask “which of these two do you like better” than it is to ask “please rank all of these from most favorite to least favorite” for large sets. Additionally, preferences change over time, and as a result, finding and identifying which piece of ordering information is now invalid is a challenge for a variety of reasons. This paper seeks to identify some initial possibilities for remedying and meeting that challenge.