Cancellative superposition decides the theory of divisible torsion-free abelian groups

In divisible torsion-free abelian groups, the efficiency of the cancellative superposition calculus can be greatly increased by combining it with a variable elimination algorithm that transforms every clause into an equivalent clause without unshielded variables. We show that the resulting calculus is a decision procedure for the theory of divisible torsion-free abelian groups

Automated deduction with built-in theories: completeness results and constraint solving techniques

Postprint (published version

How generic language extensions enable ''open-world'' design in Java

By \emph{open--world design} we mean that collaborating classes are so loosely coupled that changes in one class do not propagate to the other classes, and single classes can be isolated and integrated in other contexts. Of course, this is what maintainability and reusability is all about. In the paper, we will demonstrate that in Java even an open--world design of mere attribute access can only be achieved if static safety is sacrificed, and that this conflict is unresolvable \emph{even if the attribute type is fixed}. With generic language extensions such as GJ, which is a generic extension of Java, it is possible to combine static type safety and open--world design. As a consequence, genericity should be viewed as a first--class design feature, because generic language features are preferably applied in many situations in which object--orientedness seems appropriate. We chose Java as the base of the discussion because Java is commonly known and several advanced features of Java aim at a loose coupling of classes. In particular, the paper is intended to make a strong point in favor of generic extensions of Java

Symmetries in logic programs

We investigate the structures and above all, the applications of a class of symmetric groups induced by logic programs. After establishing the relationships between minimal models of logic programs and their simplified forms, and models of their completions, we show that in general when deriving negative information, we can apply the CWA, the GCWA, and the completion procedure directly from some simplified forms of the original logic programs. The least models and the results of SLD-resolution stay invariant for definite logic programs and their simplified forms. The results of SLDNF-resolution, the standard or perfect models stay invariant for hierarchical, stratified logic programs and some of their simplified forms, respectively. We introduce a new proposal to derive negative information termed OCWA, as well as the new concepts of quasi-definite, quasi-hierarchical and quasi-stratified logic programs. We also propose semantics for them

Cancellative superposition decides the theory of divisible torsion-free abelian groups

In divisible torsion-free abelian groups, the efficiency of the cancellative superposition calculus can be greatly increased by combining it with a variable elimination algorithm that transforms every clause into an equivalent clause without unshielded variables. We show that the resulting calculus is a decision procedure for the theory of divisible torsion-free abelian groups. (orig.)Available from TIB Hannover: RR 1912(1999-2-003) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman

Cancellative Superposition Decides the Theory of Divisible Torsion-Free Abelian Groups

In divisible torsion-free abelian groups, the efficiency of the cancellative superposition calculus can be greatly increased by combining it with a variable elimination algorithm that transforms every clause into an equivalent clause without unshielded variables. We show that the resulting calculus is not only refutationally complete (even in the presence of arbitrary free function symbols), but that it is also a decision procedure for the theory of divisible torsion-free abelian groups