A la différence de la fouille d’articles fréquents, la recherche de sous-séquences fréquentes tient compte de l’apparition multiple et de l’ordre des articles. L’algorithme proposé parcourt la base de données une seule fois. Durant cette passe, il construit un vecteur VS contenant toutes les combinaisons de séquences présentes dans la base. A ce vecteur est associé un tableau de bit TB codant t...

Equality handling has been traditionally one of the weaknesses of tableau-based theorem provers in general, from which those based on the Connection Tableau Calculus are not an exception. The Intermediate Lemma Extension is based on a simple extension to Logic Programming in which positive subgoals are skipped and all clauses treated as Horn clauses, allowing to derive clauses consisting of onl...

In this paper we present tableau proof systems for various justification logics. We show that the tableau systems are sound and complete with respect to Mkrtychev models. In order to prove the completeness of the tableaux, we give a syntactic proof of cut elimination. We also show the subformula property for our tableaux.

The paper presents Leviathan, an LTL satisfiability checking tool based on a novel one-pass, treelike tableau system, which is way simpler than existing solutions. Despite the simplicity of the algorithm, the tool has performance comparable in speed and memory consumption with other tools on a number of standard benchmark sets, and, in various cases, it outperforms the other tableau-based tools.

We present tableau calculi for some logics of nonmonotonic reasoning, as defined by Kraus, Lehmann and Magidor. We give a tableau proof procedure for all KLM logics, namely preferential, loop-cumulative, cumulative and rational logics. Our calculi are obtained by introducing suitable modalities to interpret conditional assertions. We provide a decision procedure for the logics considered, and w...

This paper is concerned with various schemes for enhancing the performance of modal tableau procedures. It discusses techniques and strategies for dealing with the nondeterminism in tableau calculi, as well as simplification and backjumping. Benchmark results obtained with randomly generated modal formulae show the effect of combinations of different schemes.

Authors of the Handbook of Description Logic present tableaux algorithms by means of a collection of so-called completion rules intended to generate a completion of ABox with respect to a corresponding TBox of a knowledge base S. An approach we present here is slightly modified. We use a set S of DL formulas of a knowledge base Σ containing DL formulas of ABox and transcriptions of definitions ...

This paper introduces MetTeL2, a tableau prover generator producing Java code from the specifications of a logical syntax and a tableau calculus. It is intended to provide an easy to use system for nontechnical users and allow technical users to extend the implementation of generated provers.

We explain the basics of description logics and tableau provers for reasoning with them. The implementation of tableau provers is a complicated matter and demanding from a software engineering point of view. We present and discuss their implementation in COMMON LISP and motivate and introduce some novel software abstractions for description logic system construction, which are embodied in the M...

The Tableaux Work Bench (TWB) is a meta tableau system designed for logicians with limited programming or automatic reasoning knowledge to experiment with new tableau calculi and new decision procedures. It has a simple interface, a history mechanism for controlling loops or pruning the search space, and modal simplification.