We study complexity of methods using rigid variables, like the method of matings or the tableau method, on a decidable class of predicate calculus wi th equality. We show some intrinsic complications introduced by rigid variables. We also consider strategies for increasing multiplicity in rigid-variable methods, and formally show that the use of intelligent strategies can result in an essential...

In a previous paper, we have showed that Hybrid Modal Logic can be successfully used to model semistructured data and provides a simple and well suited formalism for capturing “well typed” references and of course a powerful language for expressing constraint. This paper builds on the previous one and provides a tableau proof technique for constraint satisfiability testing in the presence of sc...

We address the problem of combining decision procedures for sets with decision procedures for objects that are not (necessarily) sets. We present Nelson-Oppen-based and tableau-based combination methods, we prove their correctness, analyze their complexity, and we describe heuristics that aim for efficiency.

We combine techniques originally developed for refutational first-order theorem proving within the clause tree framework with techniques for minimal model computation developed within the hyper tableau framework. This combination generalizes well-known tableaux techniques like complement splitting and foldingup/down. We argue that this combination allows for efficiency improvements over previou...

In this paper we outline a Matrix Ansatz approach to some problems of combinatorial enumeration. The idea is that many interesting quantities can be expressed in terms of products of matrices, where the matrices obey certain relations. We illustrate this approach with applications to moments of orthogonal polynomials, permutations, signed permutations, and tableaux. To Dennis Stanton with admir...

In this work we suggest the use of a set-theoretical interpretation of semantic tableaux for teaching propositional logic. If the student has previous notions of basic set theory, this approach to semantical tableaux can clarify her the way semantic trees operate, linking the syntactical and semantical sides of the process. Also, it may be useful for the introduction of more advanced topics in ...

We present the first tableau method with an ExpTime (optimal) complexity for checking satisfiability of a knowledge base in the description logic SHOQ, which extends ALC with transitive roles, hierarchies of roles, nominals and quantified number restrictions. The complexity is measured using binary representation for numbers. Our procedure is based on global caching and integer linear feasibili...

Résumé. Nous avons conçu un outil de classification de données original que nous détaillons dans le présent article. Cet outil comporte un module de création de résumés et un module d’affichage. Le module de création de résumés prend en charge les données mixtes (qualitatives et quantitatives) ainsi que les grands volumes de données en utilisant une méthode de classification incrémentale et agg...

We give a solution to a problem posed by Corteel and Nadeau concerning permutation tableaux of length n and the number of occurrences of the dashed pattern 32–1 in permutations on [n]. We introduce the inversion number of a permutation tableau. For a permutation tableau T and the permutation π obtained from T by the bijection of Corteel and Nadeau, we show that the inversion number of T equals ...

In previous work we showed that two apparently unrelated formulas for the Hall-Littlewood polynomials of type A are, in fact, closely related. The first is the tableau formula obtained by specializing q = 0 in the HaglundHaiman-Loehr formula for Macdonald polynomials. The second is the type A instance of Schwer’s formula (rephrased and rederived by Ram) for HallLittlewood polynomials of arbitra...