## Approximate Constraint Logic Programming

By *Stefan Ratschan* .

Advised by Gerti Kappel

This work has been finished in June 1998.

This thesis describes results that can be used to improve constraint logic programming (CLP) by increasing its expressivity and efficiency. This is done by introducing

- approximate answers and
- approximate quantifiers

into constraint logic programming and providing a computer implementation of a CLP system using these inprovements. For reaching this goal, work has been done in the following main areas, corresponding to the three parts of the term „constraint logic programming“:

Logic: An extension of the first-order predicate language, defining the notions of „approximate solution set“ and „approximate quantifier“ has been introduced.

Programming (Language Design and Implementation): The syntax and semantics of a new constraint logic programming language allowing first-order constraints with approximate quantifiers and approximate answers has been defined and implemented.

Constraint (Solving): A new algorithm for approximately solving first-order constraints with approximate quantifiers has been devised. The algorithm has been implemented over the domain of the real numbers.