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Interval Temporal Logics: a Journey Dario Della Monica

Summary: Interval Temporal Logics: a Journey
Dario Della Monica
Valentin Goranko
Angelo Montanari
Guido Sciavicco §
We discuss a family of modal logics for reasoning about relational struc-
tures of intervals over (usually) linear orders, with modal operators asso-
ciated with the various binary relations between such intervals, known as
Allen's interval relations. The formulae of these logics are evaluated at
intervals rather than points and the main effect of that semantic feature is
substantially higher expressiveness and computational complexity of the in-
terval logics as compared to point-based ones. Without purporting to pro-
vide a comprehensive survey of the field, we take the reader to a journey
through the main developments in it over the past 10 years and outline some
landmark results on expressiveness and (un)decidability of the satisfiability
problem for the family of interval logics.
1 Introduction
Temporal reasoning is pervasive in many areas of computer science and artificial
intelligence, such as, for instance, formal specification and verification of sequen-


Source: Aceto, Luca - School of Computer Science, Reykjavík University


Collections: Mathematics; Computer Technologies and Information Sciences