G.V. Kondratiev

Intention of people working in applied areas to weaken the Classical Logic in order to deal with uncertain assumptions brings an unresolvable contradiction in semantics. There is no weak truth value on a Boolean algebra gradually varying in the unit interval. Weakening of the very concept of truth value to a measure on a Boolean or Heyting algebra deforms meaning of logical connectives, but could be acceptable under the following restriction: there are truth values under and above the measure with respect to pointwise ordering of functions on Heyting algebra, such that the sup-norm distance between them is sufficiently small. This point brings Fuzzy Logic to a more honest, but harder position, because such evaluation of the measures being widely used in the applications is a nontrivial task. The intended area of application of this more rigorous notion of measure is the fuzzy knowledge bases.