Crank-Nicolson finite element discretizations for a two-dimenional linear Schroedinger-type equation posed in noncylindrical domain

First published in Mathematics of Computation online 2014 (84 (2015), 1571-1598), published by the American Mathematical SocietyMotivated by the paraxial narrow–angle approximation of the Helmholtz equation in domains of variable topography, we consider an initialand boundary-value problem for a general Schr¨odinger-type equation posed on a two space-dimensional noncylindrical domain with mixed boundary conditions. The problem is transformed into an equivalent one posed on a rectangular domain, and we approximate its solution by a Crank–Nicolson finite element method. For the proposed numerical method, we derive an optimal order error estimate in the L2 norm, and to support the error analysis we prove a global elliptic regularity theorem for complex elliptic boundary value problems with mixed boundary conditions. Results from numerical experiments are presented which verify the optimal order of convergence of the method

Preliminary notions of arguments from commonsense knowledge

The field of Computational Argumentation is well-tailored to approach commonsense reasoning, due to its ability to model contradictory information. In this paper, we present preliminary work on how an argumentation framework can explicitly model commonsense knowledge, both at a logically structured and at an abstract level. We discuss the correlation with current research and present interesting future directions

Abstract Argumentation Frameworks with Domain Assignments

Argumentative discourse rarely consists of opinions whose claims apply universally. As with logical statements, an argument applies to specific objects in the universe or relations among them, and may have exceptions. In this paper, we propose an argumentation formalism that allows associating arguments with a domain of application. Appropriate semantics are given, which formalise the notion of partial argument acceptance, i.e., the set of objects or relations that an argument can be applied to. We show that our proposal is in fact equivalent to the standard Argumentation Frameworks of Dung, but allows a more intuitive and compact expression of some core concepts of commonsense and non-monotonic reasoning, such as the scope of an argument, exceptions, relevance and others

A Multi Attack Argumentation Framework

This paper presents a novel abstract argumentation framework, called Multi-Attack Argumentation Framework (MAAF), which supports different types of attacks. The introduction of types gives rise to a new family of non-standard semantics which can support applications that classical approaches cannot, while also allowing classical semantics as a special case. The main novelty of the proposed semantics is the discrimination among two different roles that attacks play, namely an attack as a generator of conflicts, and an attack as a means to defend an argument. These two roles have traditionally been considered together in the argumentation literature. Allowing some attack types to serve one of those roles only, gives rise to the different semantics presented here

Methinks: Enabling Sophisticated Comment Management in the Social Web

User reviews, comments and votes on the Social Web form the modern version of word-of-mouth communication, which has a huge impact on people’s shopping habits, businesses and the overall market. Despite that, systems have so far limited practical success in helping consumers and businesses analysing, managing and understanding Social Web content. In this paper, we present a new tool that leverages a combination of techniques from Semantic Web, Computational Argumentation and Crowdsourcing to support this activity, through an intuitive and functional user interface

A specification-based QoS-aware design framework for service-based applications

Effective and accurate service discovery and composition rely on complete specifications of service behaviour, containing inputs and preconditions that are required before service execution, outputs, effects and ramifications of a successful execution and explanations for unsuccessful executions. The previously defined Web Service Specification Language (WSSL) relies on the fluent calculus formalism to produce such rich specifications for atomic and composite services. In this work, we propose further extensions that focus on the specification of QoS profiles, as well as partially observable service states. Additionally, a design framework for service-based applications is implemented based on WSSL, advancing state of the art by being the first service framework to simultaneously provide several desirable capabilities, such as supporting ramifications and partial observability, as well as non-determinism in composition schemas using heuristic encodings; providing explanations for unexpected behaviour; and QoS-awareness through goal-based techniques. These capabilities are illustrated through a comparative evaluation against prominent state-of-the-art approaches based on a typical SBA design scenario