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:
  1. normal partitioning, joint refinement, Schauder partitions
  2. the inverse problem of detecting, given y, the most appropriate corresponding value of x, and
  3. the relationships between "defuzzification" and the minlink problem in computational geometry (robot vision).