Difference between partial order and total order planning

Partial-order planning is an approach to automated planning that leaves decisions about the ordering of actions as open as possible. It contrasts with total-order planning, which produces an exact ordering of actions.

 Numbers have a total order because, given two numbers, one is always less than or equal to the other. It doesn't matter which two numbers we pick: they're either equal, or one is smaller. So a total order is just like ≤ for numbers.

A total order is a partial order, but apartial order isn't necessarily a total order. A totally ordered set requires that every element in the set is comparable: i.e. totality: it is alwaysthe case that for any two elements in a totally ordered set, a ≤ b or b ≤ a , or both, e.g., when .