If you don't have any idea, then I think this post will
give 2 cents. Otherwise, if you know the basics, it won't add
nothing more:
Our usual algebra, and the deduction schemes therein, is
based, among others, on the axiom of 'no contradiction'. That
is,
p or -p (-p stands for 'no-p')
is a tautology in the Logic of Propositions, which implies
we are working with a bi-valued logic. Any sentence is a proposition
iif it can be asigned a truth value which will be either 'true' or 'false'.
A natural generalization of this scheme was proposed long ago
by Lukasiewicz. He set up a discrete n-valued logic were any
proposition could be assigned the truth value
Pk = (k-1)/(n-1) k=1,...,n
This, of course, will change our usual connectivities, that is, the
logic operators: AND, OR, IF-THEN, IIF-THEN, NOT. For instance,
p AND q = min(p,q)
p -> q = min(1,1+q-p)
p <-> q = 1 - abs(p-q)
A step further in this process of generalizing our classical Logic,
is making the truth value a continuos parameter.Then you get a
continous-valued-logic. Roughly, this is what is called ''Fuzzy Logic'.
It will make it possible to deal with reasoning schemes like:
Usually, antic furniture is difficult to find
What is difficult to find is expensive
----------------------------------------------
Usually, antic furniture is expensive
This involves, fuzzy quantifiers like 'usually' and also
fuzzy predicates like: 'antic', 'difficult' and 'expensive'.
How can we sistematically decide about the correctness of this
reasonig ? For there is no agreement upon what these expressions mean:
wveryone will understand something slightly different. Well,
Fuzzy Logic provides us with a way.
Unfortunately, I don't remember the details, so I can't tell you,
at this moment, much more.