This book presents an innovative new approach to interval analysis. Modal Interval Analysis
(MIA) is an attempt to go beyond the limitations of classic intervals in terms of their
structural algebraic and logical features. The starting point of MIA is quite simple: It
consists in defining a modal interval that attaches a quantifier to a classical interval and in
introducing the basic relation of inclusion between modal intervals through the inclusion of
the sets of predicates they accept. This modal approach introduces interval extensions of the
real continuous functions identifies equivalences between logical formulas and interval
inclusions and provides the semantic theorems that justify these equivalences along with
guidelines for arriving at these inclusions. Applications of these equivalences in different
areas illustrate the obtained results. The book also presents a new interval object: marks
which aspire to be a new form of numerical treatment of errors in measurements and
computations.
