In response to [6], we discover the looked for inversion formula for F -nomial coefficients. Before supplying its proof, we generalize F -nomial coefficients to multi F -nomial coefficients and we give their combinatorial interpretation in cobweb posets language, as the number of maximal-disjoint blocks of the form σPk1,k2,...,ks of layer 〈Φ1 → Φn〉. Then we present inversion formula for F -nomi...

We study under which conditions the domain of-terms () and the equality theory of the-calculus () form the basis of a usable constraint logic programming language (CLP). The conditions are that the equality theory must contain axiom , and the formula language must depart from Horn clauses and accept universal quantiications and implications in goals. In short, CLP(,) must be close to Prolog.

This paper proposes a rule language for defining social expectations based on a metric interval temporal logic with past and future modalities and a current-time binding operator. An algorithm for run-time monitoring compliance of rules in this language based on formula progression is also outlined.

Third of a series of articles laying down the bases for classical first order model theory. Interpretation of a language in a universe set. Evaluation of a term in a universe. Truth evaluation of an atomic formula. Reassigning the value of a symbol in a given interpretation. Syntax and semantics of a non atomic formula are then defined concurrently (this point is explained in [16], 4.2.1). As a...

Let L be a set of regular languages of A∗. An L-polynomial is a finite union of products of the form L0a1L1 · · · anLn, where each ai is a letter of A and each Li is a language of L. We give an explicit formula for computing the intersection of two L-polynomials. Contrary to Arfi’s formula (1991) for the same purpose, our formula does not use complementation and only requires union, intersectio...

The increasing use of automatic computer processing of information re-quests a new approach in mathematical formula editors. We are used toWYSIWYG editors that produce beautiful presentation of formula. The newICT services, such as database searching or calculation web-services, requirestoring the semantic information behind a formula. This can only be donewith a new generat...

In response to [7], we discover the looked for inversion formula for F -nomial coefficients. Before supplying its proof, we generalize F -nomial coefficients to multi F -nomial coefficients and we give their combinatorial interpretation in cobweb posets language, as the number of maximal-disjoint blocks of the form σPk1,k2,...,ks of layer 〈Φ1 → Φn〉. Then we present inversion formula for F -nomi...

The aim of this study was to investigate the language development of 20 children who had been exposed to thiamine (vitamin B(1)) deficiency in infancy due to feeding with soy-based formula that was accidentally deficient of thiamine. In this case-control study, 20 children (12 males, eight females; mean age 31.8mo [SD 4.1], range 24-39mo) who were fed thiamine-deficient formula in infancy were ...

Model formulas are the standard approach for specifying the variables in statistical models in the S language. Although being eminently useful in an extremely wide class of applications, they have certain limitations including being confined to single responses and not providing convenient support for processing formulas with multiple parts. The latter is relevant for models with two or more se...