Properties of ABA+ for Non-Monotonic Reasoning

We investigate properties of ABA+, a formalism that extends the well studied structured argumentation formalism Assumption-Based Argumentation (ABA) with a preference handling mechanism. In particular, we establish desirable properties that ABA+ semantics exhibit. These pave way to the satisfaction by ABA+ of some (arguably) desirable principles of preference handling in argumentation and nonmonotonic reasoning, as well as non-monotonic inference properties of ABA+ under various semantics.Comment: This is a revised version of the paper presented at the worksho

A Plausibility Semantics for Abstract Argumentation Frameworks

We propose and investigate a simple ranking-measure-based extension semantics for abstract argumentation frameworks based on their generic instantiation by default knowledge bases and the ranking construction semantics for default reasoning. In this context, we consider the path from structured to logical to shallow semantic instantiations. The resulting well-justified JZ-extension semantics diverges from more traditional approaches.Comment: Proceedings of the 15th International Workshop on Non-Monotonic Reasoning (NMR 2014). This is an improved and extended version of the author's ECSQARU 2013 pape

On cumulativity in the context of defeasible argumentation

Las lógicas que permiten razonar de manera no-monótona suelen ser caracterizadas por la propiedad que carecen - casualmente, la monotonía - en vez de serlo por aquellas que sí gozan. Gabbay, Makinson y Kraus propusieron un conjunto de propiedades básicas de las relaciones de inferencia que toda teoría no-monótona debería satisfacer. No obstante, existen varios formalismos aparentemente razonables que no satisfacen algunos de estos principios, por caso la mayoría de los formalismos de argumentación rebatible. En este artículo determinamos el estado de estas propiedades básicas en el marco de dos populares sistemas argumentativosLogics for nonmonotonic reasoning have often been described by the property they lack—that is, monotonicity—instead of by those they do enjoy. Gabbay, Makinson and Kraus proposed a set of core properties for inference relations that every nonmonotonic theory ought to have. Yet, there are some apparently well-behaved formalisms that fail to comply with some of these principles, such as most defeasible argumentation formalisms. In this article we determine the status of these core properties in the context of two well-known argumentation frameworks.Workshop de Agentes y Sistemas Inteligentes (WASI)Red de Universidades con Carreras en Informática (RedUNCI

Argument-based Belief in Topological Structures

This paper combines two studies: a topological semantics for epistemic notions and abstract argumentation theory. In our combined setting, we use a topological semantics to represent the structure of an agent's collection of evidence, and we use argumentation theory to single out the relevant sets of evidence through which a notion of beliefs grounded on arguments is defined. We discuss the formal properties of this newly defined notion, providing also a formal language with a matching modality together with a sound and complete axiom system for it. Despite the fact that our agent can combine her evidence in a 'rational' way (captured via the topological structure), argument-based beliefs are not closed under conjunction. This illustrates the difference between an agent's reasoning abilities (i.e. the way she is able to combine her available evidence) and the closure properties of her beliefs. We use this point to argue for why the failure of closure under conjunction of belief should not bear the burden of the failure of rationality.Comment: In Proceedings TARK 2017, arXiv:1707.0825

A Framework for Combining Defeasible Argumentation with Labeled Deduction

In the last years, there has been an increasing demand of a variety of logical systems, prompted mostly by applications of logic in AI and other related areas. Labeled Deductive Systems (LDS) were developed as a flexible methodology to formalize such a kind of complex logical systems. Defeasible argumentation has proven to be a successful approach to formalizing commonsense reasoning, encompassing many other alternative formalisms for defeasible reasoning. Argument-based frameworks share some common notions (such as the concept of argument, defeater, etc.) along with a number of particular features which make it difficult to compare them with each other from a logical viewpoint. This paper introduces LDSar, a LDS for defeasible argumentation in which many important issues concerning defeasible argumentation are captured within a unified logical framework. We also discuss some logical properties and extensions that emerge from the proposed framework.Comment: 15 pages, presented at CMSRA Workshop 2003. Buenos Aires, Argentin