In [11], Lascoux and Schützenberger introduced a notion of key associated to any Young tableau. More recently Lascoux [9] defined the key of an alternating sign matrix by recursively removing all −1’s in such matrices. But alternating sign matrices are in bijection with monotone triangles, which form a subclass of Young tableaux. We show that in this case these two notions of keys coincide. Mor...

Even though it is not very often admitted, partial functions do play a signiicant role in many practical applications of deduction systems. Kleene has already given a semantic account of partial functions using a three-valued logic decades ago, but there has not been a satisfactory mechanization. Recent years have seen a thorough investigation of the framework of many-valued truth-functional lo...

In this paper we show that the problem of checking consistency of a knowledge base in the Description Logic ALCM is ExpTime-complete. The M stands for meta-modelling as defined by Motz, Rohrer and Severi. To show our main result, we define an ExpTime Tableau algorithm as an extension of an algorithm for checking consistency of a knowledge base in ALC by Nguyen and Szalas.

We present the design of Tableau Machine (TM), an AIbased, interactive, visual art generator for shared living spaces. TM is an instance of what we call “alien presence”: an ambient, non-human, embodied, intelligent agent. From overhead video in key public spaces, TM interprets its environment, including its human audience, and expresses its interpretation by displaying a sequence of abstract i...

Calculi for propositional dynamic logics have been investigated since the introduction of this logic in the late seventies. Only in recent years have practical procedures been suggested and implemented. In this paper, we compare three such systems, namely, the Tableau Workbench by Abate, Goré, and Widmann (2009), the pdlProver system by Goré and Widmann (2009), and the MLSolver system by Friedm...

We give complete sequent-like tableau systems for the modal logics KB, KDB, K5, and KD5. Analytic cut rules are used to obtain the completeness. The systems have the analytic superformula property and can thus give a decision procedure.

This paper solves an open problem posed by a number of researchers: the construction of a complete calculus for matrix-based methods with rigid E-uniication. The use of rigid E-uniication and simultaneous rigid E-uniication for such methods has been proposed in (Gallier et al., 1987). After our proof of the undecidability of simultaneous rigid E-uniication (Degtyarev and Voronkov, 1996e) it has...

Contextual reasoning has been proposed as a tool for solving the problem of generality in AI and for effectively handling huge knowledge bases, while approximate reasoning has been developed to overcome the computational barrier of classical deduction. This paper combines these approaches to provide an intuitive representation of knowledge and an effective deduction. Its semantics and a tableau...

We elaborate upon a bijection discovered by Cools et al. in [CDPR10] between, on the one hand, rectangular standard Young tableaux, and, on the other hand, representatives, known as G-parking functions, of chip configurations on certain graphs modulo the chip-firing equivalence relation. We present an explcit formula for computing the G-parking function associated to a given tableau, and prove ...

For example “i” is a YT of shape (4, 3, 1). The YT is said to be standard (an SYT) if the integers in the tableau are 1, 2,..., n as in “. A partition p = (pl, p2 ,..., pt) is strict if p1 > t+ > ... > pt > 0. A generalized Shzyted Young Tableau (abbreviated ST) of shape p is an array of n-integers into t rows with row i containing pi integers and indented i 1 spaces, such that the rows are non...