Related papers: The matrices of argumentation frameworks

A general theorem on factorization of matrices with polynomial entries is proven and it is used to reduce polynomial Darboux matrices to linear ones. Some new examples of linear Darboux matrices are discussed.

We consider multi-agent argumentation, where each agent's view of the arguments is encoded as an argumentation framework (AF). Then we study deliberative processes than can occur on this basis. We think of a deliberative process as taking…

Drawing from research on computational models of argumentation (particularly the Carneades Argumentation System), we explore the graphical representation of arguments in a dispute; then, comparing two different traditions on the limits of…

We obtain a canonical representation for block matrices. The representation facilitates simple computation of the determinant, the matrix inverse, and other powers of a block matrix, as well as the matrix logarithm and the matrix…

This paper introduces combinatorial representations, which generalise the notion of linear representations of matroids. We show that any family of subsets of the same cardinality has a combinatorial representation via matrices. We then…

In many real-life situations that involve exchanges of arguments, individuals may differ on their assessment of which supports between the arguments are in fact justified, i.e., they put forward different support-relations. When confronted…

There is a generic way to add any new feature to a system. It involves 1) identifying the basic units which build up the system and 2) introducing the new feature to each of these basic units. In the case where the system is argumentation…

There are various interesting semantics' (extensions) designed for argumentation frameworks. They enable to assign a meaning, e.g., to odd-length cycles. Our main motivation is to transfer semantics' proposed by Baroni, Giacomin and Guida…

Represented spaces form the general setting for the study of computability derived from Turing machines. As such, they are the basic entities for endeavors such as computable analysis or computable measure theory. The theory of represented…

In this position paper, we propose a reasoning framework that can model the reasoning process underlying natural language inferences. The framework is based on the semantic tableau method, a well-studied proof system in formal logic. Like…

Translations between different nonmonotonic formalisms always have been an important topic in the field, in particular to understand the knowledge-representation capabilities those formalisms offer. We provide such an investigation in terms…

Based on ideas of quantum theory of open systems we propose the consistent approach to the formulation of logic of plausible propositions. To this end we associate with every plausible proposition diagonal matrix of its likelihood and…

Argumentation has proved a useful tool in defining formal semantics for assumption-based reasoning by viewing a proof as a process in which proponents and opponents attack each others arguments by undercuts (attack to an argument's premise)…

Distributed representations (such as those based on embeddings) and discrete representations (such as those based on logic) have complementary strengths. We explore one possible approach to combining these two kinds of representations. We…

Argumentation is a central subarea of Artificial Intelligence (AI) for modeling and reasoning about arguments. The semantics of abstract argumentation frameworks (AFs) is given by sets of arguments (extensions) and conditions on the…

For a representation of a Lie algebra, one can construct a diagram of the representation, i. e. a directed graph with edges labeled by matrix elements of the representation. This article explains how to use these diagrams to describe normal…

This paper defines an argumentation semantics for extended logic programming and shows its equivalence to the well-founded semantics with explicit negation. We set up a general framework in which we extensively compare this semantics to…

The representation of graphs is commonly based on the adjacency matrix concept. This formulation is the foundation of most algebraic and computational approaches to graph processing. The advent of deep learning language models offers a wide…

We propose a new, structured, logic-based framework for legal reasoning and argumentation: Instead of using a single, unstructured meaning space, theory graphs organize knowledge and inference into collections of modular meaning spaces…

Over the recent twenty years, argumentation has received considerable attention in the fields of knowledge representation, reasoning, and multi-agent systems. However, argumentation in dynamic multi-agent systems encounters the problem of…