Defeasibility in CLP(\(\mathcal{Q}\)) through generalized slack variables

  • Christian Holzbaur
  • Francisco Menezes
  • Pedro Barahona
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1118)


This paper presents a defeasible constraint solver for the domain of linear equations, disequations and inequalities over the body of rational/real numbers. As extra requirements resulting from the incorporation of the solver into an Incremental Hierarchical Constraint Solver (IHCS) scenario we identified: a)the ability to refer to individual constraints by a label, b) the ability to report the (minimal) cause for the unsatisfiability of a set of constraints, and c) the ability to undo the effects of a formerly activated constraint.

We develop the new functionalities after starting the presentation with a general architecture for defeasible constraint solving, through a solved form algorithm that utilizes a generalized, incremental variant of the Simplex algorithm, where the domain of a variable can be restricted to an arbitrary interval. We demonstrate how generalized slacks form the basis for the computation of explanations regarding the cause of unsatisfiability and/or entailment in terms of the constraints told, and the possible deactivation of constraints as demanded by the hierarchy handler.


Constraint Logic Programming Linear Programming Defeasible Constraint Solving 


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Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Christian Holzbaur
    • 1
  • Francisco Menezes
    • 2
  • Pedro Barahona
    • 2
  1. 1.Austrian Research Institute for Artificial Intelligence, and Department of Medical Cybernetics and Artificial IntelligenceUniversity of ViennaViennaAustria
  2. 2.Departamento de Informática Faculdade de Ciências e TécnologiaUniversidade Nova de LisboaMonte da CaparicaPortugal

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