Extension-based Semantics of Abstract Dialectical Frameworks

One of the most prominent tools for abstract argumentation is the Dung's framework, AF for short. It is accompanied by a variety of semantics including grounded, complete, preferred and stable. Although powerful, AFs have their shortcomings, which led to development of numerous enrichments. Among the most general ones are the abstract dialectical frameworks, also known as the ADFs. They make use of the so-called acceptance conditions to represent arbitrary relations. This level of abstraction brings not only new challenges, but also requires addressing existing problems in the field. One of the most controversial issues, recognized not only in argumentation, concerns the support cycles. In this paper we introduce a new method to ensure acyclicity of the chosen arguments and present a family of extension-based semantics built on it. We also continue our research on the semantics that permit cycles and fill in the gaps from the previous works. Moreover, we provide ADF versions of the properties known from the Dung setting. Finally, we also introduce a classification of the developed sub-semantics and relate them to the existing labeling-based approaches.Comment: To appear in the Proceedings of the 15th International Workshop on Non-Monotonic Reasoning (NMR 2014

Dialectics and difference: against Harvey's dialectical post-Marxism

David Harvey`s recent book, Justice, nature and the geography of difference (JNGD), engages with a central philosophical debate that continues to dominate human geography: the tension between the radical Marxist project of recent decades and the apparently disempowering relativism and `play of difference' of postmodern thought. In this book, Harvey continues to argue for a revised `post-Marxist' approach in human geography which remains based on Hegelian-Marxian principles of dialectical thought. This article develops a critique of that stance, drawing on the work of Jacques Derrida, Gilles Deleuze and Felix Guattari. I argue that dialectical thinking, as well as Harvey's version of `post-Marxism', has been undermined by the wide-ranging `post-' critique. I suggest that Harvey has failed to appreciate the full force of this critique and the implications it has for `post-Marxist' ontology and epistemology. I argue that `post-Marxism', along with much contemporary human geography, is constrained by an inflexible ontology which excessively prioritizes space in the theory produced, and which implements inflexible concepts. Instead, using the insights of several `post-' writers, I contend there is a need to develop an ontology of `context' leading to the production of `contextual theories'. Such theories utilize flexible concepts in a multilayered understanding of ontology and epistemology. I compare how an approach which produces a `contextual theory' might lead to more politically empowering theory than `post-Marxism' with reference to one of Harvey's case studies in JNGD

Strong Admissibility Revisited

Preprin

Looking for complication: The case of management education

This paper argues that in face of the changes occurring in the organizational world, management education should consider the need to rethink some of its premises and adapt to the new times. The need to complicate management learning due to increased complication in competitive landscapes, is analyzed. Four possibilities of addressing organizational topics in a complicated way are contrasted: the vertical, horizontal, hypertextual, and dialectical approaches. The promises of the dialectical approach are particularly stressed as a more demanding and potentially enriching path for the creation of knowledge about organizations. The test of the four approaches in a group of undergraduate students provides some preliminary data for analyzing the strenghts and weaknesses of our proposal.

Strong Admissibility for Abstract Dialectical Frameworks

Abstract dialectical frameworks (ADFs) have been introduced as a formalism for modeling and evaluating argumentation allowing general logical satisfaction conditions. Different criteria used to settle the acceptance of arguments are called semantics. Semantics of ADFs have so far mainly been defined based on the concept of admissibility. However, the notion of strongly admissible semantics studied for abstract argumentation frameworks has not yet been introduced for ADFs. In the current work we present the concept of strong admissibility of interpretations for ADFs. Further, we show that strongly admissible interpretations of ADFs form a lattice with the grounded interpretation as top element.Comment: 9 pages, 3 Figures, SAC '21 conference: The 36th ACM/SIGAPP Symposium on Applied Computin

On the equivalence between logic programming semantics and argumentation semantics

This work has been supported by the National Research Fund, Luxembourg (LAAMI project), by the Engineering and Physical Sciences Research Council (EPSRC, UK), grant Ref. EP/J012084/1 (SAsSy project), by CNPq (Universal 2012 – Proc. 473110/2012-1), and by CNPq/CAPES (Casadinho/PROCAD 2011).Peer reviewedPreprin

Aquinas and Naturalism

Aquinas’s actual response to a naturalistic challenge at ST I.2.3 is one which most naturalists would find unimpressive. However, I shall argue that there is a stronger response latent in his philosophical system. I take Quine as an example of a methodological naturalist, examine the roots of his position and look at two critical responses to his views (those of BonJour and Boghossian). If one adjusts some of the problematical aspects of their responses and establishes a hybrid position on the epistemology and metaphysics of an antinaturalistic stance, it turns out to be the position Aquinas himself takes on meaning and knowledg