In linear logic, a constructive approach is used in arriving at conclusions. That is, a conclusion is arrived as a result of our knowledge embodied in premises of a deduction. For example, we might want to use linear logic to arrive at a solution of Zeno's tortoise (see attached image) and Achilles paradox:

http://platonicrealms.com/encyclopedia/zenos-paradox-of-the-tortoise-and-achilles

A good introduction to linear logic is given by Gerard in

http://girard.perso.math.cnrs.fr/Synsem.pdf

See, also:

Article Linear Logic