Abstract
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.
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Holzbaur, C., Menezes, F., Barahona, P. (1996). Defeasibility in CLP(\(\mathcal{Q}\)) through generalized slack variables. In: Freuder, E.C. (eds) Principles and Practice of Constraint Programming — CP96. CP 1996. Lecture Notes in Computer Science, vol 1118. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61551-2_76
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DOI: https://doi.org/10.1007/3-540-61551-2_76
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