301 research outputs found
Letter to the editor: Consistency of LPC+Ch
summary:In his paper [Kybernetika 31, No. 1, 99â106 (1995; Zbl 0857.03042)], E. Turunen says in the corollary on p. 106:
âNotice that the third last line on page 195 in [J. K. Mattila, âModifier logicâ, in: J. Kacprzyk (ed.) et al., Fuzzy logic for the management of uncertainty. New York: Wiley. 191â209 (1992)] stating that LPC+Ch calculus is consistent is not correct.â
The system LPC+Ch is consistent, which can be seen quite trivially
Coordination of Dynamic Software Components with JavaBIP
JavaBIP allows the coordination of software components by clearly separating
the functional and coordination aspects of the system behavior. JavaBIP
implements the principles of the BIP component framework rooted in rigorous
operational semantics. Recent work both on BIP and JavaBIP allows the
coordination of static components defined prior to system deployment, i.e., the
architecture of the coordinated system is fixed in terms of its component
instances. Nevertheless, modern systems, often make use of components that can
register and deregister dynamically during system execution. In this paper, we
present an extension of JavaBIP that can handle this type of dynamicity. We use
first-order interaction logic to define synchronization constraints based on
component types. Additionally, we use directed graphs with edge coloring to
model dependencies among components that determine the validity of an online
system. We present the software architecture of our implementation, provide and
discuss performance evaluation results.Comment: Technical report that accompanies the paper accepted at the 14th
International Conference on Formal Aspects of Component Softwar
Bialgebraic Semantics for Logic Programming
Bialgebrae provide an abstract framework encompassing the semantics of
different kinds of computational models. In this paper we propose a bialgebraic
approach to the semantics of logic programming. Our methodology is to study
logic programs as reactive systems and exploit abstract techniques developed in
that setting. First we use saturation to model the operational semantics of
logic programs as coalgebrae on presheaves. Then, we make explicit the
underlying algebraic structure by using bialgebrae on presheaves. The resulting
semantics turns out to be compositional with respect to conjunction and term
substitution. Also, it encodes a parallel model of computation, whose soundness
is guaranteed by a built-in notion of synchronisation between different
threads
PRECONDITIONERS AND TENSOR PRODUCT SOLVERS FOR OPTIMAL CONTROL PROBLEMS FROM CHEMOTAXIS
In this paper, we consider the fast numerical solution of an optimal control
formulation of the Keller--Segel model for bacterial chemotaxis. Upon
discretization, this problem requires the solution of huge-scale saddle point
systems to guarantee accurate solutions. We consider the derivation of
effective preconditioners for these matrix systems, which may be embedded
within suitable iterative methods to accelerate their convergence. We also
construct low-rank tensor-train techniques which enable us to present efficient
and feasible algorithms for problems that are finely discretized in the space
and time variables. Numerical results demonstrate that the number of
preconditioned GMRES iterations depends mildly on the model parameters.
Moreover, the low-rank solver makes the computing time and memory costs
sublinear in the original problem size.Comment: 23 page
A Framework for Defining Logical Frameworks
In this paper, we introduce a General Logical Framework, called GLF, for defining Logical Frameworks, based on dependent types, in the style of the well known Edinburgh Logical Framework LF. The framework GLF features a generalized form of lambda abstraction where beta-reductions fire provided the argument satisfies a logical predicate and may produce an n-ary substitution. The type system keeps track of when reductions have yet to fire. The framework GLF subsumes, by simple instantiation, LF as well as a large class of generalized constrained-based lambda calculi, ranging from well known restricted lambda calculi, such as Plotkin's call-by-value lambda calculus, to lambda calculi with patterns. But it suggests also a wide spectrum of completely new calculi which have intriguing potential as Logical Frameworks. We investigate the metatheoretical properties of the calculus underpinning GLF and illustrate its expressive power. In particular, we focus on two interesting instantiations of GLF. The first is the Pattern Logical Framework (PLF), where applications fire via pattern-matching in the style of Cirstea, Kirchner, and Liquori. The second is the Closed Logical Framework (CLF) which features, besides standard beta-reduction, also a reduction which fires only if the argument is a closed term. For both these instantiations of GLF we discuss standard metaproperties, such as subject reduction, confluence and strong normalization. The GLF framework is particularly suitable, as a metalanguage, for encoding rewriting logics and logical systems, where rules require proof terms to have special syntactic constraints, e.g. logics with rules of proof, in addition to rules of derivations, such as, e.g., modal logics, and call-by-value lambda calculus
Limit sets as examples in noncommutative geometry
The fundamental group of a hyperbolic manifold acts on the limit set, giving
rise to a cross-product C^* algebra. We construct nontrivial K-cycles for the
cross-product algebra, thereby extending some results of Connes and Sullivan to
higher dimensions. We also show how the Patterson-Sullivan measure on the limit
set can be interpreted as a center-valued KMS state.Comment: final versio
The Bloch Transform on Lp-Spaces
We investigate the Bloch Transform on Bochner Lebesgue Spaces. A decomposition in terms of vector valued Fourier Series leads to the study of translation invariant operators on sequence spaces. These operators act like multiplication operators. We proof multiplier theorems for the Bloch Transform, which are used to derive the band gap structure of the spectrum for general periodic operators. The results are applied to partial differential operators
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