By Jean-Pierre Jouannaud, Ralf Treinen (auth.), Gerhard Goos, Juris Hartmanis, Jan van Leeuwen, Hubert Comon, Claude Marché, Ralf Treinen (eds.)

Constraints offer a declarative approach of representing countless units of knowledge. they're like minded for combining various logical or programming paradigms as has been identified for constraint good judgment programming because the Eighties and extra lately for useful programming. using constraints in automatic deduction is newer and has proved to be very winning, relocating the keep an eye on from the meta-level to the limitations, that are now first class objects.

This monograph-like booklet provides six completely reviewed and revised lectures given by way of best researchers on the summer time university geared up by means of the ESPRIT CCL operating crew in Gif-sur-Yvette, France, in September 1999. The publication bargains coherently written chapters on constraints and constraint fixing, constraint fixing on phrases, combining constraint fixing, constraints and theorem proving, useful and constraint good judgment programming, and construction business applications.

**Read or Download Constraints in Computational Logics: Theory and Applications International Summer School, CCL ’99 Gif-sur-Yvette, France, September 5–8, 1999 Revised Lectures PDF**

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**Additional resources for Constraints in Computational Logics: Theory and Applications International Summer School, CCL ’99 Gif-sur-Yvette, France, September 5–8, 1999 Revised Lectures**

**Example text**

Tree automata. Techniques and Applications, April 1999. grappa. fr/tata/. [CDJK99] Hubert Comon, Mehmet Dincbas, Jean-Pierre Jouannaud, and Claude Kirchner. A methodological view of constraint solving. Constraints, 4(4):337–361, December 1999. [CJ99a] Hubert Comon and Yan Jurski. Counter automata, fixpoints and additive theories. December 1999. [CJ99b] Hubert Comon and Yan Jurski. Timed automata and the theory of real numbers. In Jos C. M. Baeten and Sjouke Mauw, editors, Concurrency Theory, volume 1664 of Lecture Notes in Computer Science, pages 242– 257, Eindhoven, The Netherlands, August 1999.

Jouannaud and R. Treinen where v is a feature variable. Note that feature variables may occur in c only in the equational part, hence the condition is very easy to decide. The crucial point here is that I(c, x[v]y) is not defined if c contains no definition for v. In this case we say that the constraint x[v]y is suspended since it is “waiting” for its feature variable to get defined by some other agent. Nonlinear Equations. Our last example is non-linear equations between integers. Constraints are conjunctions of one of the three forms x = n, x = y + z and x = y ∗ z where n is an integer constant and x, y, z are variables.

Treinen Satisfiability of CFT Constraints. Since existential quantifiers are not relevant when testing satisfiability of constraints we can simply ignore them for the moment, hence for the purpose of checking satisfiability of constraints we assume that a constraint is just a conjunction of atomic constraints. A CFT constraint c is said to be a solved form if it contains no equation and 1. 2. 3. 4. if if if if x[f ]y ∈ c and x[f ]z ∈ c then y = z A(x) ∈ c and B(x) ∈ c then A = B xF ∈ c and x[f ]y ∈ c then f ∈ F xF ∈ c and xG ∈ c then F = G A variable x is called constrained by a solved form c if c contains an atomic constraint of one of the forms A(x), xF or x[f ]y.