Applications of Hyperstructure Theory pp 275-282 | Cite as

# Artificial Intelligence

## Abstract

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 of* **A** _{n} *and those of* **A** _{1} *, 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.

## Keywords

Identity Element Initial Segment Relation Algebra Generalize Interval Standard Construction## Preview

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