The logic of if-then-else, with applications
Daniele Mundici (University of Florence, Italy)
Using infinite-valued Lukasiewicz logic we provide a
rigorous and natural set up for the problem of describing
by means of if-then-else "rules" a
function x->y defined by possibly overlapping
"cases" . These cases form a nonboolean partition of
the domain of the independent variable.
We shall focus attention on the following main issues:
- normal partitioning, joint refinement, Schauder partitions
- the inverse problem of detecting, given y,
the most appropriate corresponding value of x, and
- the relationships between "defuzzification"
and the minlink problem in computational geometry (robot vision).