This book presents a systematic treatment of deductive aspects and
structures of fuzzy logic understood as many valued logic sui generis.
Some important systems of real-valued propositional and predicate
calculus are defined and investigated. The aim is to show that fuzzy
logic as a logic of imprecise (vague) propositions does have
well-developed formal foundations and that most things usually named
`fuzzy inference' can be naturally understood as logical deduction.
There are two main groups of intended readers. First, logicians: they
can see that fuzzy logic is indeed a branch of logic and may find
several very interesting open problems. Second, equally important,
researchers involved in fuzzy logic applications and soft computing. As
a matter of fact, most of these are not professional logicians so that
it can easily happen that an application, clever and successful as it
may be, is presented in a way which is logically not entirely correct or
may appear simple-minded. (Standard presentations of the logical aspects
of fuzzy controllers are the most typical example.) This fact would not
be very important if only the bon ton of logicians were harmed; but it
is the opinion of the author (who is a mathematical logician) that a
better understanding of the strictly logical basis of fuzzy logic (in
the usual broad sense) is very useful for fuzzy logic appliers since if
they know better what they are doing, they may hope to do it better. In
addition, a better mutual understanding between (classical) logicians
and researchers in fuzzy logic, promises to lead to deeper cooperation
and new results.
