The problem is that most people know how to handle only total order relations, for which only 6 operations with Boolean results can be defined (equal and not-equal, less and greater-or-equal, greater and less-or-equal).

While it is possible to handle partial orders using ternary logic, it is easier to handle them with operations with Boolean results, so this is what all programming languages either provide or they should provide.

The difference is that for partial orders you no longer have only 6 operations with Boolean results (3 plus their negations), but you have 14 operations (7 + their negations).

One operation pair is ordered / unordered (ordered means either equal or less or greater).

The other 6 pairs correspond to the 6 well known relational operators from the total order, which now no longer are each other's negation, together with their 6 negations, which now include the possibility that the 2 operands are unordered.

For example, corresponding to the negation pair less and greater-or-equal from the total order, for a partial order there are 2 negation pairs, less and not-less (i.e. greater, equal or unordered) and greater-or-equal and neither-greater-nor-equal (i.e. less-or-unordered).

In the education of the programmers there should be more stress on the possible relational operators for partial order relations, because they appear in many situations, both for FP computations and for databases, and handling partial orders is only slightly more complex than handling total orders, but many people are not accustomed to this.