Artificial Intelligence

  • Piergiulio Corsini
  • Violeta Leoreanu
Part of the Advances in Mathematics book series (ADMA, volume 5)


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.


Identity Element Initial Segment Relation Algebra Generalize Interval Standard Construction 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer Science+Business Media Dordrecht 2003

Authors and Affiliations

  • Piergiulio Corsini
    • 1
  • Violeta Leoreanu
    • 2
  1. 1.Department of Mathematics and Computer SciencesUniversity of UdineUdineItaly
  2. 2.Faculty of Mathematics“AI.I Cuza” UniversityIaşiRomania

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