I think it might be more useful to use the term "goal" instead of "task", since task implies a series of steps -- a sequence of operations that change the state of the world, whereas a "problem" is a state of the world.

IOW, task = goal state - problem state. (Except it's not really subtraction, because there are potentially an infinite number of task sequences that will get you to the goal state from the current state... which is another reason why I think that maybe "goal" is a better word here.)

Goldratt's "Theory of Constraints" (used heavily in manufacturing and other types of businesses) includes a set of "thinking processes" -- semi-formal planning tools based on boolean logic, that have an excellent breakdown of these notions into a very-reduced form. A couple of good books on them include "Thinking For A Change", by Lisa Scheinkopf, and "Goldratt's Theory Of Constraints", by H. William Dettmer.

There are also a fair number of TOC tutorials online, but I can't remember the last time I saw one that actually explained the logical basis of the tools, or things like the Categories of Legitimate Reservation (which are used to validate the logic of your problem analysis and plans).