A keyH is a semi-standard tableau of partition shape whose evaluation is a permutation of the shape. We give a necessary and sufficient condition that the Knuth class of a key equals the set of shuffles of its columns. In particular, on a three-letter alphabet the Knuth class of a key equals the set of shuffles of its columns, and on a four-letter alphabet, the Knuth class of a key is either th...

Logic calculi, and Gentzen-type calculi in particular, can be categorised into two types: search-oriented and interaction-oriented calculi. Both these types have certain inherent characteristics stemming from the purpose for which they are designed. In this paper, we give a general characterisation of the two types and present two calculi that are typical representatives of their respective cla...

Let a,ß > -1 and Pla'3)(x) = (l-x)a(l+x)ßp[a'a){x), where Pjf (x) is the Jacobi function of the first kind, A > —(a + ß + l)/2, and -1 < i < 1. Let r the integral exists. It is known that for a + •>-Ä4r'<",')(*-i),£Ä<-> *J o whenever ß = 0, we have /(*) = lim 4 f fC« (x l) PÍÍ$A-*)\ . . r2(A + i/2) X sin 7rA^-:-L_¡-d\ w in J, r(A-ra + l/2)F(A + ^ + l/2) almost everywhere in [—1,1], In this pape...

The formal definition of abduction asks what needs to be added to a knowledge base to enable an observation to be entailed. TBox abduction in description logics (DLs) asks what TBox axioms need to be added to a DL knowledge base to allow a TBox axiom to be entailed. We describe a sound and complete algorithm, based on the standard DL tableau, that takes a TBox abduction problem in ALC and gener...

Let T be a standard Young tableau of shape λ ` k. We show that the probability that a randomly chosen Young tableau of n cells contains T as a subtableau is, in the limit n → ∞, equal to f/k!, where f is the number of all tableaux of shape λ. In other words, the probability that a large tableau contains T is equal to the number of tableaux whose shape is that of T , divided by k!. We give sever...

Modeling the environment of a design module under verification is a known practical problem in compositional verification. In this paper, we propose an approach to translate an ACTL specification into such an environment. Throughout the translation, we construct an efficient tableau for the full range of ACTL and synthesize the tableau into Verilog HDL behavior level program. The synthesized pr...

This article continues our study of axiom systems that can verify their own consistency and prove all Peano Arithmetic’s Π1 theorems. We will develop some new types of exceptions for the Semantic Tableaux Version of the Second Incompleteness Theorem.

We provide a general and modular framework for describing inferences in Answer Set Programming (ASP) that aims at an easy incorporation of additional language constructs. To this end, we generalize previous work characterizing computations in ASP by means of tableau methods. We start with a very basic core fragment in which rule heads and bodies consist of atomic literals. We then gradually ext...

We give a bijective proof of an identity relating primed shifted gl(n)-standard tableaux to the product of a gl(n) character in the form of a Schur function and ∏ 1≤i<j≤n(xi + yj). This result generalises a number of well–known results due to Robbins and Rumsey, Chapman, Tokuyama, Okada and Macdonald. An analogous result is then obtained in the case of primed shifted sp(2n)standard tableaux whi...

In this paper we explore the geometry of the integer points in a cone rooted at a rational point. This basic geometric object allows us to establish some links between lattice point free bodies and the derivation of inequalities for mixed integer linear programs by considering two rows of a simplex tableau simultaneously.