We study theory revision and composition in the context of OLPFOL logic. In this logic, the representation of knowledge is split into two parts: writing definitions for completely known concepts (OLP part), and writing constraints and expressing partial knowledge on other concepts (FOL part). In a previous work, the composition of two OLP-FOL theories with nonintersecting sets of defined predic...

Starting with a general formula, precise but difficult to use, for the adjoint of a composition operator on a functional Hilbert space, we compute an explicit formula on the classical Hardy Hilbert space for the adjoint of a composition operator with rational symbol. To provide a foundation for this formula, we study an extension to the definitions of composition, weighted composition, and Toep...

In this paper, we study the model of stochastic timed automata and we target the definition of adequate composition operators that will allow a compositional approach to the design of stochastic systems with hard real-time constraints. This paper achieves the first step towards that goal. Firstly, we define a parallel composition operator that (we prove) corresponds to the interleaving semantic...

Let Ω be a bounded, convex domain and B a ball in R, n ≥ 2. We use σB to denote the ball with the same center as B and with diam σB σ diam B , σ > 0. We do not distinguish the balls from cubes in this paper. We use |E| to denote the n-dimensional Lebesgue measure of the set E ⊆ R. We say that w is a weight if w ∈ Lloc R and w > 0, a.e. Differential forms are extensions of functions in R. For ex...

Functional composition can be computed efficiently, robustly, and precisely over polynomials and piecewise polynomials represented in the Bézier and B-spline forms [6, 8, 20]. Nevertheless, the applications of functional composition in geometric modeling have been quite limited. In this work, as a testimony to the value of functional composition, we first recall simple applications to curve-cur...

We describe some features of the tactic language implemented in the theorem prover Ergo 5. This is a variant of the generic tactic language Angel. We have adapted the language by changing the semantics of its parallel composition operator, the operator by which diierent tactics are applied to diierent branches in a proof tree. The paper includes a denotational semantics for this operator, and a...

we introduce a new concept of general $g$-$eta$-monotone operator generalizing the general $(h,eta)$-monotone operator cite{arvar2, arvar1}, general $h-$ monotone operator cite{xiahuang} in banach spaces, and also generalizing $g$-$eta$-monotone operator cite{zhang}, $(a, eta)$-monotone operator cite{verma2}, $a$-monotone operator cite{verma0}, $(h, eta)$-monotone operator cite{fanghuang}, $h$-...