Feature
Interaction Algebras + Review of a Paper
CORRECTIONS IN RED
Part 1: FIAs
It
was stated in class that mathematics does not always allow you to have
arbitrary mixing and matching of axioms. In particular, there
are only a few universes in which Feature Interaction Algebras have a
consistent set of axioms.
In class, we showed that the axioms:
Lead
to × and + coinciding. In this assignment, you are to
determine why axioms:
are
problemmatic too. Here is the complete axiom set on which you are to work:
The first posted set of axioms was infact incorrect. + Identity was listed as (A+0=0), which clearly is a problem.
I
will accept submissions with this axiom. However, the correct +
identity axiom is listed below. A (small) challenge
awaits you to demonstrate this (updated) set of axioms is still wrong.
I
will get you started. Here is a fact about this universe, which
is not true of the universes that are consistent -- namely universes that have
the axiom A+A=0.
A
≤ A + B for all A and
B
(A)
The
reason, incidentally, is that the + identity, commutatitivy,
associativity and idempotence axioms lead to an upper semilattice or
join-semilattice, from which (A) can be derived or made.
- Anyways, start with (A)
and prove that all 2-way interactions, such as A#B, are always 0.
Which, incidentally, leads to all interaction terms are 0.
- Show that (A) is not consistent with universes that have axiom A+A=0.
Part II: Review of a Paper
The following paper has been submitted for publication at a high-end software engineering conference. Provide me with your review of it.
Submission
via Canvas
Submit
via Canvas a PDF file that contains your answers to Parts I and II along with any
necessary
explanations. Non-PDF submissions will be returned.
Also, your PDF document must contain your name and email
address as text in the document, otherwise points will be deducted.
