Related papers: Revisiting initial sets in abstract argumentation
In this work, we show that both logic programming and abstract argumentation frameworks can be interpreted in terms of Nelson's constructive logic N4. We do so by formalizing, in this logic, two principles that we call non-contradictory…
Transfinite set theory including the axiom of choice supplies the following basic theorems: (1) Mappings between infinite sets can always be completed, such that at least one of the sets is exhausted. (2) The real numbers can be well…
In a recent work we have shown how to construct an information algebra of coherent sets of gambles defined on general possibility spaces. Here we analyze the connection of such an algebra with the set algebra of subsets of the possibility…
In this article, we present a novel approach for parsing argumentation structures. We identify argument components using sequence labeling at the token level and apply a new joint model for detecting argumentation structures. The proposed…
In this paper we discuss contrastive explanations for formal argumentation - the question why a certain argument (the fact) can be accepted, whilst another argument (the foil) cannot be accepted under various extension-based semantics. The…
Verbs play an important role in the understanding of natural language text. This paper studies the problem of abstracting the subject and object arguments of a verb into a set of noun concepts, known as the "argument concepts". This set of…
Scaling arguments provide valuable analysis tools across physics and complex systems yet are often employed as one generic method, without explicit reference to the various mathematical concepts underlying them. A careful understanding of…
In this paper we inititate the study of abstract simplicial complexes which are initial segments of qualitative probability orders. This is a natural class that contains the threshold complexes and is contained in the shifted complexes, but…
The purpose of this paper is to outline a simple set of axioms for basic set theory from which most fundamental facts can be derived. The key to the whole project is a new axiom of set theory which I dubbed "The Law of Extremes". It allows…
Predicate abstraction provides a powerful tool for verifying properties of infinite-state systems using a combination of a decision procedure for a subset of first-order logic and symbolic methods originally developed for finite-state model…
We define a notion of an arithmetic set in an arbitrary countable group and study properties of these sets in the cases of Abelian groups and non-abelian free groups.
It is well known that the R, the set of real numbers, is an abstract set, where almost all its elements cannot be described in any finite language. We investigate possible approaches to what might be called an epi-constructionist approach…
We present a categorical framework for relating causal models that represent the same system at different levels of abstraction. We define a causal abstraction as natural transformations between appropriate Markov functors, which concisely…
We make three contributions. First, we formulate a discussion-graph semantics for first-order logic with equality, enabling reasoning about discussion and argumentation in AI more generally than before. This addresses the current lack of a…
We show that an interesting class of feed-forward neural networks can be understood as quantitative argumentation frameworks. This connection creates a bridge between research in Formal Argumentation and Machine Learning. We generalize the…
In formal argumentation, a distinction can be made between extension-based semantics, where sets of arguments are either (jointly) accepted or not, and ranking-based semantics, where grades of acceptability are assigned to arguments.…
Gradual semantics within abstract argumentation associate a numeric score with every argument in a system, which represents the level of acceptability of this argument, and from which a preference ordering over arguments can be derived.…
When faced with the question of how to represent properties in a formal proof system any user has to make design decisions. We have proved three of the theorems from Maskin's 2004 survey article on Auction Theory using the Isabelle/HOL…
Assumption-based Argumentation (ABA) is a well-established form of structured argumentation. ABA frameworks with an underlying atomic language are widely studied, but their applicability is limited by a representational restriction to…
Argumentation is a promising model for reasoning with uncertain knowledge. The key concept of acceptability enables to differentiate arguments and counterarguments: The certainty of a proposition can then be evaluated through the most…