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.
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