Practical tools for reasoning about linear constraints

Tien Huynh*, Leo Joskowicz, Catherine Lassez, Jean Louis Lassez

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

9 Scopus citations


We address the problem of building intelligent systems to reason about linear arithmetic constraints. We develop, along the lines of Logic Programming, a unifying framework based on the concept of Parametric Queries and a quasi-dual generalization of the classical Linear Programming optimization problem. Variable (quantifier) elimination is the key underlying operation which provides an oracle to answer all queries and plays a role similar to Resolution in Logic Programming. We discuss three methods for variable elimination, compare their feasibility, and establish their applicability. We then address practical issues of solvability and canonical representation, as well as dynamical updates and feedback. In particular, we show how the quasi-dual formulation can be used to achieve the discriminating characteristics of the classical Fourier algorithm regarding solvability, detection of implicit equalities and, in case of unsolvability, the detection of minimal unsolvable subsets. We illustrate the relevance of our approach with examples from the domain of spatial reasoning and demonstrate its viability with empirical results from two practical applications: computation of canonical forms and convex hull construction.

Original languageAmerican English
Pages (from-to)357-380
Number of pages24
JournalFundamenta Mathematicae
Issue number3-4
StatePublished - Nov 1991
Externally publishedYes


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