Continuous First-Order Constraint Satisfaction with Equality and Disequality Constraints

  • Stefan Ratschan
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2470)


In an earlier paper we have shown, how one can successfully use constraint satisfaction techniques for proving and solving formulae in the first-order predicate language over the real numbers (i.e., real first-order constraints). This approach was restricted to inputs that contain inequality symbols such as ≤, but no equality symbols (=) or disequality symbols (≠). In this paper we lay the basis for extending this approach to inputs that contain (dis)equalities. This considerably widens the practical applicability of numerical constraint satisfaction methods.


Constraint Satisfaction Equality Symbol Order Constraint Interval Constraint Atomic Constraint 


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  1. [1]
    F. Benhamou and F. Goualard. Universally quantified interval constraints. In Proc. of the Sixth Intl. Conf. on Principles and Practice of Constraint Programming (CP’2000), number 1894 in LNCS, Singapore, 2000. Springer Verlag.Google Scholar
  2. [2]
    G. E. Collins. Quantifier elimination for the elementary theory of real closed fields by cylindrical algebraic decomposition. In B. F. Caviness and J. R. Johnson, editors, Second GI Conf. Automata Theory and Formal Languages, volume 33 of LNCS, pages 134–183. Springer Verlag, Wien, 1975.Google Scholar
  3. [3]
    A. Neumaier. Interval Methods for Systems of Equations. Cambridge Univ. Press, Cambridge, 1990.MATHGoogle Scholar
  4. [4]
    S. Ratschan. Applications of real first-order constraint solving — bibliography., 2001.
  5. [5]
    S. Ratschan. Continuous first-order constraint satisfaction. In Artificial Intelligence, Automated Reasoning, and Symbolic Computation, number 2385 in LNCS. Springer, 2002.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Stefan Ratschan
    • 1
  1. 1.Institut d’Informatica i AplicacionsUniversitat de GironaSpain

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