Two ways to approximate a proximity relation R (i.e. a reflexive and symmetric fuzzy relation) by a T -transitive one where T is a continuous archimedean t-norm are given. The first one aggregates the transitive closure R of R with a (maximal) T -transitive relation B contained in R. The second one modifies the values of R or B to better fit them with the ones of R.

In this work, we present a fast stochastic context-free parsing algorithm that is based on a stochastic version of the Valiant algorithm. First, the problem of computing the string probability is reduced to a transitive closure problem. Then, the closure problem is reduced to a matrix multiplication problem of matrices of a special type. Afterwards, some fast algorithm can be used to solve the ...

In this paper, we study the decomposition of semirings with a semilattice additive reduct. For, we introduce the notion of principal left $k$-radicals $Lambda(a)={x in S | a stackrel{l}{longrightarrow^{infty}} x}$ induced by the transitive closure $stackrel{l}{longrightarrow^{infty}}$ of the relation $stackrel{l}{longrightarrow}$ which induce the equivalence relation $lambda$. Again non-transit...

Classical structure of rough set theory was first formulated by Z. Pawlak in [6]. The foundation of its object classification is an equivalence binary relation and equivalence classes. The upper and lower approximation operations are two core notions in rough set theory. They can also be seenas a closure operator and an interior operator of the topology induced by an equivalence relation on a u...

We introduce a recursive query evaluation method whose main goal is to obtain recursive query cost estimate without performing the query. In particular, we show that the execution estimate of the parallel processing of recursive queries can be done by exploiting the characteristics of the database profile during the evaluation process for request optimization. As many recursive queries involve ...

In this paper we show that it is possible to eliminate inverse roles and functional restrictions from ALCFI knowledge bases, while preserving the soundness and completeness of inference. Specifically, we present two polynomial encodings, the first from ALCFI knowledge bases intoALCI ones, and the second fromALCI knowledge bases into ALC ones. These encodings eliminate functional restrictions an...

Let I denote a homogeneous R+-primary ideal in a twodimensional normal standard-graded domain over an algebraically closed field of characteristic zero. We show that a homogeneous element f belongs to the solid closure I∗ if and only if eHK(I) = eHK((I, f)), where eHK denotes the (characteristic zero) Hilbert-Kunz multiplicity of an ideal. This provides a version in characteristic zero of the w...

We consider involutory antimorphisms θ of a free monoid A∗ and their fixed points, called θ-palindromes or pseudopalindromes. A θ-palindrome reduces to a usual palindrome when θ is the reversal operator. For any word w ∈ A∗ the right (resp. left) θ-palindrome closure of w is the shortest θ-palindrome having w as a prefix (resp. suffix). We prove some results relating θ-palindrome closure operat...

Using recent results of the second author which explicitly identify the “(1, 2, 1, 2)avoiding” GL(p,C)×GL(q,C)-orbit closures on the flag manifold GL(p+q,C)/B as certain Richardson varieties, we give combinatorial criteria for determining smoothness, lci-ness, and Gorensteinness of such orbit closures. (In the case of smoothness, this gives a new proof of a theorem of W.M. McGovern.) Going a st...

For a polytope P , the Chvátal closure P ′ ⊆ P is obtained by simultaneously strengthening all feasible inequalities cx ≤ β (with integral c) to cx ≤ ⌊β⌋. The number of iterations of this procedure that are needed until the integral hull of P is reached is called the Chvátal rank. If P ⊆ [0, 1], then it is known that O(n log n) iterations always suffice (Eisenbrand and Schulz (1999)) and at lea...