Related papers: The matrices of argumentation frameworks
Argumentation is the process of constructing arguments about propositions, and the assignment of statements of confidence to those propositions based on the nature and relative strength of their supporting arguments. The process is modelled…
Argumentation accommodates various rhetorical devices, such as questions, reported speech, and imperatives. These rhetorical tools usually assert argumentatively relevant propositions rather implicitly, so understanding their true meaning…
Value-based argumentation enhances a classical abstract argumentation graph - in which arguments are modelled as nodes connected by directed arrows called attacks - with labels on arguments, called values, and an ordering on values, called…
Traditional treatments of formal logic provide: 1. A syntax for formulas. 2. An inference relation between sets of formulas. 3. A rule for assigning meaning to formulas (semantics) that is sound with respect to the inference relation. First…
We apply ideas from abstract argumentation theory to study cooperative game theory. Building on Dung's results in his seminal paper, we further the correspondence between Dung's four argumentation semantics and solution concepts in…
We motivate and give semantics to theory presentation combinators as the foundational building blocks for a scalable library of theories. The key observation is that the category of contexts and fibered categories are the ideal theoretical…
Convenient parameterizations of matrices in terms of vectors transform (certain classes of) matrix equations into covariant (hence rotation-invariant) vector equations. Certain recently introduced such parameterizations are tersely…
We generalize intuitionistic tense logics to the multi-modal case by placing grammar logics on an intuitionistic footing. We provide axiomatizations for a class of base intuitionistic grammar logics as well as provide axiomatizations for…
This paper introduces context algebras and demonstrates their application to combining logical and vector-based representations of meaning. Other approaches to this problem attempt to reproduce aspects of logical semantics within new…
A matrix approach to continuous iteration is proposed for general formal series. It leads, in particular, to an order{to{order iteration of the exponential function, and consequently to an algorithmic approach to tetration. Lower{order…
Deliberative processes play a vital role in shaping opinions, decisions and policies in our society. In contrast to persuasive debates, deliberation aims to foster understanding of conflicting perspectives among interested parties. The…
Random matrices now play a role in many parts of computational mathematics. To advance these applications, it is desirable to have tools that are flexible, easy to use, and powerful. Over the last 25 years, researchers have developed a…
In this note, we propose a simple-looking but broad conjecture about star-algebras over the field of real numbers. The conjecture enables many matrix decompositions to be represented by star-algebras and star-ideals. This paper is written…
The notion of argumentation and the one of belief stand in a problematic relation to one another. On the one hand, argumentation is crucial for belief formation: as the outcome of a process of arguing, an agent might come to (justifiably)…
We present a computer-supported approach for the logical analysis and conceptual explicitation of argumentative discourse. Computational hermeneutics harnesses recent progresses in automated reasoning for higher-order logics and aims at…
Interaction nets are a graphical formalism inspired by Linear Logic proof-nets often used for studying higher order rewriting e.g. \Beta-reduction. Traditional presentations of interaction nets are based on graph theory and rely on…
We translate the argumentation networks ${\cal A}=(S, R)$ into a theory $D$ of intuitionistic logic, retaining $S$ as the domain and using intuitionistic negation to model the attack $R$ in ${\cal A}$: the attack $xRy$ is translated to…
We argue that explanations for "algorithmic decision-making" (ADM) systems can profit by adopting practices that are already used in the learning sciences. We shortly introduce the importance of explaining ADM systems, give a brief overview…
This dissertation presents a multifaceted look into the structural decomposition of permutation classes. The theory of permutation patterns is a rich and varied field, and is a prime example of how an accessible and intuitive definition…
The issue of representing attacks to attacks in argumentation is receiving an increasing attention as a useful conceptual modelling tool in several contexts. In this paper we present AFRA, a formalism encompassing unlimited recursive…