We propose so called clausal tableau systems for the common modal logics K4, KD4 and S4. Basing on these systems, we give more eecient decision procedures than those hitherto known for the considered logics. In particular space requirements for our logics are reduced from the previously established bound O(n 2 : log n) to O(n: log n).

The Kostka numbers Kλμ are important in several areas of mathematics, including symmetric function theory, representation theory, combinatorics and invariant theory. The q-Kostka polynomials Kλμ(q) are the q-analogues of the Kostka numbers. They generalize and extend the mathematical meaning of the Kostka numbers. Lascoux and Schützenberger proved one can attach a non-negative integer statistic...

We study the crystal base B(∞) associated with the negative part of the quantum group for finite simple Lie algebras of types E6 and E7. We present an explicit description of B(∞) as the image of a Kashiwara embedding that is in natural correspondence with the tableau description of B(∞).

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.

We study quantized dual graded graphs, which are graphs equipped with linear operators satisfying the relation DU − qUD = rI. We construct examples based upon: the Fibonacci differential poset, permutations, standard Young tableau, and plane binary trees.

We present an approach for studying logical properties of problemsolving methods (PSMs) for knowledge-intensive tasks. It is based on semantic tableaux (a deduction-style theorem-proving technique). We show how tableaux can be manipulated in a methodical way to formalize non-deductive style PSMs.

The paper presents a novel expressive logic-based formalism intended for reasoning about numerical distances. We investigate its computational properties (in particular, show that it is EXPTIMEcomplete) and devise a tableau-based satisfiabilitychecking algorithm. To be able to express knowledge about implicit or unknown distances, we then extend the language with variables ranging over distance...

In this paper, explicit formulae for the expectation and the variance of descent functions on random standard Young tableaux are presented. Using these, it is shown that the normalized variance, V/E2, is bounded if and only if a certain inequality relating tableau shape to the descent function holds.

This paper develops and compares two tableaux-style proof systems for Peirce algebras. One is a tableau refutation proof system, the other is a proof system in the style of Rasiowa-Sikorski.

An k-noncrossing RNA structure can be identified with an k-noncrossing diagram over [n], which in turn corresponds to a vacillating tableaux having at most (k − 1) rows. In this paper we derive the limit distribution of irreducible substructures via studying their corresponding vacillating tableaux. Our main result proves, that the limit distribution of the numbers of irreducible substructures ...