
328 Soft Computing and Its Applications
(ii) If we use arbitrary lattices, then we are using mathematical model that may
have no relation whatsoever to commonsense reasoning.
The problem of describing of formalization of “commonsense equivalence” that
is free from these three drawbacks was, in effect, formulated in the following terms.
It is an open question how to choose a notion of logical equivalence that simulta-
neously:
(i) Remains philosophically justifiable,
(ii) Allows useful inferences in practice, and
(iii) Removes the opportunity to prove results similar to Theorem 3.1 (that is, in-
consistency).
We address these problems as follows: ...