This volume presents a number of systems of logic which can be
considered as alternatives to classical logic. The notion of what counts
as an alternative is a somewhat problematic one. There are extreme views
on the matter of what is the 'correct' logical system and whether one
logical system (e. g. classical logic) can represent (or contain) all
the others. The choice of the systems presented in this volume was
guided by the following criteria for including a logic as an
alternative: (i) the departure from classical logic in accepting or
rejecting certain theorems of classical logic following intuitions
arising from significant application areas and/or from human reasoning;
(ii) the alternative logic is well-established and well-understood
mathematically and is widely applied in other disciplines such as
mathematics, physics, computer science, philosophy, psychology, or
linguistics. A number of other alternatives had to be omitted for the
present volume (e. g. recent attempts to formulate so-called
'non-monotonic' reason- ing systems). Perhaps these can be included in
future extensions of the Handbook of Philosophical Logic. Chapter 1
deals with partial logics, that is, systems where sentences do not
always have to be either true or false, and where terms do not always
have to denote. These systems are thus, in general, geared towards
reasoning in partially specified models. Logics of this type have arisen
mainly from philo- sophical and linguistic considerations; various
applications in theoretical computer science have also been envisaged.
