Artificial Intelligence

Weak representations of an interval algebra are the objects of interest in the Artificial Intelligence.Let us give some words about the Mathematicians who worked on this subject.Allen [3] defined the calculus of time intervals and Ladkin and Maddux [220] showed the interpretation of the calculus of time intervals, in terms of representations of a par ticular relation algebra, in the sense of Tarski [178]. They proved that there is, up to an isomorphism, a unique countable representation of this algebra.Ligozat [241] generalized the calculus of time intervals to a calculus of n-intervals and presented this generalization expressed in terms of relation algebras As.Defining canonical functors between the category of weak representations ofA_nand those ofA₁, Ligozat [241] extended the results obtained by Ladkin [219].Finally, it can be seen that the set of (p, q)-positions can be endowed with natural operations which give rise to a family of quasi—canonical hypergroupoids.