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OFAI-TR-96-21 ( 53kB g-zipped PostScript file)

Defasibility in CLP(Q) through Generalized Slack Variables

Christian Holzbaur, Francisco Menezes, Pedro Barahona

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.

Keywords: Constraint Logic Programming, Linear Programming, Defeasible Constraint Solving

Citation: Holzbaur C., Menezes F., Barahona P.: Defasibility in CLP(Q) through Generalized Slack Variables, Proc. of the Second International Conference on Principles and Practice of Consstraint Programming (CP96), Cambridge, Massachusetts, USA, August 19-22, 1996.