Description

The aim of this course is to introduce quantitive temporal and modal
logics, to survey the most important techniques and results, and to
give an idea about their applications. The addressed logics are
obtained by extending standard (qualitative) modal logics with
numerical metric operators that allow to refer to the distance of
objects, in time, in space, and in metric similarity spaces. The
course starts with an introduction to quantitative temporal logics,
which have been investigated extensively over the last 15 years and
are now the standard tool for reasoning about real-time systems.
Besides the standard qualitative temporal operators such as
`eventually' or `until', they provide operators for making
statements such as `within 10 minutes.' We then discuss quantitive
spatial logics, which are a relatively new direction of research. To talk
about spatial distances, they provide operators such as `within distance
5' or `not closer than 3.75 miles'. Finally, we address metric
logics for reasoning about similarity spaces. Such similarity spaces play
an important role e.g. in bioinformatics and can be described by modal
logics that allow us to express the `distance in similarity' between
objects.

A number of revelant research papers for the course can be found at

http://www.csc.liv.ac.uk/~dmitry/projects/KRRaD/index_js.php?button=pub

Additional material (in particular, slides) will be distributed at the
beginning of the course.