P = I - A > 0

This is an interesting way to think about problems and solutions.  A ticket to a movie costs $11 (call this I for what we would ideally like to accomplish).  You have only $6 (call this A for what we can currently accomplish).  You need $5 more to get into the movie (call this P for your needs or the problem). 

Thus, a problem P = I - A > 0.  That is, a problem exists whenever P - the difference between our ideals, I, and our current abilities, A - is greater than zero.  To "solve" a problem P means to make P = 0, that is, I = A.  We can do this in two different ways - - (1) we raise our actual abilities (means) up to our ideals (ends), or (2) we lower our ideals (aspirations or ends) down to our abilities (means).  If all stakeholders agree that the first or the second way is acceptable, then the problem is solved.

Notice that strictly speaking only well-structured problems have solutions such that P = 0 (engineering is not about well-structured problems).  Ill-structured and wicked problems do not have solutions is this sense of the term (see previous blog on wicked problems - - The Wicked).  They are "coped with" and "managed," but never fully solved.

Consider the three alternatives:

1. Resolve - - means to contain it within acceptable limits.  We no longer insist that P = 0, but instead that P be bounded within acceptable limits.  Unemployment is the classic example - - the goal of problem resolution is acceptable limits by the stakeholders.
2. Dissolve - - means to lower or redefine a problems particular importance.  When we dissolve a problem, we say that other problems within the system in which the problem exists deserve our attention more.  The problem P still exists with acceptable limits, but we shift our attention to other problems.  To "dissolve" a problem also means to redesign the system within which the problem is located.
3. Absolve - - means to accept the fact that the problem P may never fully vanish.  It may even grow worse over time.  For example, it means accepting that problems such as terrorism are not "wars that can be won" but "social diseases or pathologies" that can only be managed as best we can over time.  This is a functional form of absolving because it leaves room for future resolutions or dissolutions.

See - - Swans, Swine, and Swindlers: Coping with the Growing Threat of Mega-Crises and Mega-Messes by Can Alpaslan and Ian Mitroff.