The Schur function indexed by a partition λ with at most n parts is the sum of the weight monomials for the Young tableaux of shape λ. Let π be an npermutation. We give two descriptions of the tableaux that contribute their monomials to the key polynomial indexed by π and λ. (These polynomials are the characters of the Demazure modules for GL(n).) The “atom” indexed by π is the sum of weight mo...

X iv :0 80 3. 22 53 v2 [ m at h. C O ] 4 F eb 2 00 9 DIAGONAL VECTORS OF SHIFTED YOUNG TABLEAUX DORIAN CROITORU Abstra t. We study ve tors formed by entries on the diagonal of standard Young tableaux of shifted shapes. Su h ve tors are in bije tion with integer latti e points of ertain integral polytopes, whi h are Minkowski sums of simpli es. We also des ribe verti es of these polytopes, and o...

n-tableaux [1] and δ-resolution [2], which are based, respectively, on semantic tableaux and resolution, have been properly used for the resolution of abductive problems. The tool we present is a Prolog implementation of an abductive solver which combines both calculi to attack first order abductive problems by reducing them to finite versions, that is, propositional rewritings of the problems ...

This paper establishes the decidability of SR⊔IQ which has composition-based role Inclusion axioms (RIAs) of the form R1 ◦ · · · ◦ Rn⊑̇T1 ⊔ · · · ⊔ Tm. Also the consistency of an Abox A of SR⊔IQ DL w.r.t. Rbox R is established. Motivation for this kind of RIAs comes from applications in the field of manufactured products as well as other conceptual modeling applications such as family relationsh...

This article uses combinatorial objects called labeled abaci to give direct combinatorial proofs of many familiar facts about Schur polynomials. We use abaci to prove the Pieri rules, the Littlewood–Richardson rule, the equivalence of the tableau definition and the determinant definition of Schur polynomials, and the combinatorial interpretation of the inverse Kostka matrix (first given by Eğec...

Following the approach [Schwind, Risch, 91] to Reiter’s default logic, tiffs paper attempts to define a general tableaux-based framework for tt~c cornlmtation of tile extensions for several known default k)gics. The idea is to qualify the differences b(;twecn the wlriants under considcration inside a single process that can switcil easily from one variant to another. Indeed, the approach is rel...

This paper presents a labelled tableau approach for deciding interrogative-epistemic logics (IEL). Tableau calculi for these logics have been derived using a recently introduced tableau synthesis method. We also consider an extension of the framework for a setting with questioning modalities over sequences of formulae called sequential questioning logic (SQL). We have implemented the calculi us...