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A key property in the definition of logic programming languages is the completeness of goal-directed proofs. This concept originated in the study of logic programming languages for intuitionistic logic in the (single-conclusioned) sequent calculus LJ, but has subsequently been adapted to multiple-conclusioned systems such as those for linear logic. Given… (More)

Logic programs consist of formulas of mathematical logic and various proof-theoretic techniques can be used to design and analyse execution models for such programs. We brieey review the main problems, which are questions that are still elusive in the design of logic programming languages, from a proof-theoretic point of view. Existing approaches and… (More)

Many important results in proof theory for sequent calculus (cut-elimination, completeness and other properties of search strategies, etc) are proved using permutations of sequent rules. The focus of this paper is on the development of systematic and automated-oriented techniques for the analysis of permutability in some sequent calculi. A representation of… (More)

The aim of this paper is to present a new algorithm for proving mixed trigonometric-polynomial inequalities of the form n i=1 α i x pi cos qi x sin ri x > 0, by reducing to polynomial inequalities. Finally, we show the great applicability of this algorithm and as examples, we use it to analyze some new rational (Padé) approximations of the function cos 2 x,… (More)

In many application areas of automated reasoning it is not sufficient to show that a given assertion is true. A good reasoning system should include tools not only for the generation of proofs, but also for the analysis of and manipulations with unsuccessful proof attempts. This paper focuses on the development of automated techniques for the transformation… (More)

Logic programs consist of formulas of mathematical logic and various proof-theoretic techniques can be used to design and analyse execution models for such programs. We brieey review the main problems, which are questions that are still elusive in the design of logic programming languages, from a proof-theoretic point of view. Existing strategies which lead… (More)