Title:
Qualitative Calculi as a generalisation of Tarski's Relation Algebras
(joint work with Robin Hirsch and Marcel Jackson)
Abstract:
Qualitative Calculi arose in certain areas of Artificial Intelligence,
as a means of modelling the natural (human, sloppy) reasoning, mostly
about time and space. Accordingly, the two most famous Qualitative
Calculi are: Allen's Interval Algebra (for reasoning about time
intervals), and Region Connection Calculus (for reasoning about space).
From the very beggining it was realised that Qualitative Calculi bear a
connection to Tarski's Relation Algebras, but the mathematical
foundations of this observation were not explored. We will explore them
in some detail, touching upon some universal algebra, some model theory
and some computational complexity.