You can't make a computer perform tasks with data that it known to be erroneous, it's just a logical impossibility. As such, the design of the system - on paper, before a single line of code was written - clearly defined that in a case where it is unable to do its job, the best hope lies with the pilots. So issue a "stop" command to the relevant module (beyond which nothing other than a full reset can bring it back up again), notify the pilots of the failure and leave the flying to them.
Sure you can create models to handle any situation, but the risks are naturally increasing with each missing parameter. It's no fuzzy logic, although that would be a good concept to start with
I read many inputs on random newspaper forums, asking why cannot GPS-data be used calculate speed if pitots freeze... Beyond the obvious of not understanding the difference between air speed and ground speed, I came to think about something:
Would it be out of question to create an automation graceful degradation, which:
a) would use a pattern of ground speed vs IAS to judge faulty airspeed readings. Give an advisory to pilots before actually making the call to consider it faulty (less voting of three pitot readings).
b) in case of actually loosing reliable IAS and forced switching to alternate law or what ever mode, would use GPS for displaying pilots an educated guess of airspeed, and would use GPS for calculating altitude and a safe attitude and power setting, which would keep the plane in the air in those conditions. The pilot would then have the option of flying the plane manually or rely on an rude "autopilot" using only pre-calculated values to keep the plane in a safe as possible envelope with data available.
c) use GPS to judge whether the plane is stalling or IAS too far out to be considered reliable (re: no stall warning below 60kts).