We present an extension of classical tableau-based model checking procedures to the case of innnite-state systems, using deductive methods in an incremental construction of the behavior graph. Logical formulas are used to represent innnite sets of states in an abstraction of this graph, which is repeatedly reened in the search for a counterexample computation, ruling out large portions of the g...

In this paper we study a relatively new combinatorial object called staircase tableaux. Staircase tableaux were introduced by Corteel and Williams in the connection with Asymmetric Exclusion Process and has since found interesting connections with Askey–Wilson polynomials. We develop a probabilistic approach that allows us to analyze several parameters of a randomly chosen staircase tableau of ...

The paper proposes a way to analyze logical reasoning in a deductive version of the Mastermind game implemented within the Math Garden educational system. Our main goal is to derive predictions about the cognitive difficulty of game-plays, e.g., the number of steps needed for solving the logical tasks or the working memory load. Our model is based on the analytic tableaux method, known from pro...

Résumé. Dans le domaine de l’apprentissage supervisé, les méthodes de groupage des modalités d’un attribut symbolique permettent de construire un nouvel attribut synthétique conservant au maximum la valeur informationnelle de l’attribut initial et diminuant le nombre de modalités. Nous proposons ici une généralisation de l’algorithme de discrétisation Khiops pour le problème du groupage des mod...

The aim of this paper is to make restriction strategies based on orderings of the Herbrand universe available for semantic tableau-like calculi as well. A marriage of tableaux and ordering restriction strategies seems to be most promising in applications where generation of counter examples is required. In this paper, starting out from semantic trees, we develop a formal tool called refutation ...

An axiomatic formulation of a logic called LPS4 appears in [3]. Here that logic is proved sound and complete with respect to the weak semantics of [7]. Also a tableau system for LPS4 is introduced, and also proved sound and complete with respect to the semantics, thus establishing both cut elimination and equivalence with the axiomatic formulation.

In this paper we present new time and size bounds for satissability in modal K. This is done by means of a simpliied SAT based procedure. Then, as a direct consequence, we provide theoretical support to the claim of superior eeciency for the SAT based decision procedures, with respect to the \classic" tableau based procedures.

Satallax is an automatic higher-order theorem prover that generates propositional clauses encoding (ground) tableau rules and uses MiniSat to test for unsatisfiability. We describe the implementation, focusing on flags that control search and examples that illustrate how the

In this paper we reduce the question of validity of a first-order intuitionistic formula without equality to generating ground instances of this formula and then checking whether the instances are deducible in a propositional intuitionistic tableaux calculus, provided that the propositional proof is compatible with the way how the instances were generated. This result can be seen as a form of t...