Extensions in graph normal form

Doing Argumentation using Theories in Graph Normal Form

We explore some links between abstract argumentation, logic and kernels in digraphs. Viewing argumentation frameworks as propositional theories in graph normal form, we observe that the stable semantics for argumentation can be given equivalently in terms of satisfaction and logical consequence in classical logic. We go on to show that the complete semantics can be formulated using Lukasiewicz ...

Graph Color Extensions :

Graph Orientations and Linear Extensions

Given an underlying undirected simple graph, we consider the set of all acyclic orientations of its edges. Each of these orientations induces a partial order on the vertices of our graph and, therefore, we can count the number of linear extensions of these posets. We want to know which choice of orientation maximizes the number of linear extensions of the corresponding poset, and this problem w...

NORMAL FIELD EXTENSIONS Kjk AND

Throughout the paper Kjk is a field extension and p is the exponent characteristic. In this paper I introduce the notion of .K/fc-bialgebra (coalgebra over K and algebra over k) and describe a theory of finite dimensional normal field extensions Kjk based on a ^-measuring A /̂A:-bialgebra H(Kjk) (see 1.2, 1.6 and 1.10). This approach to studying Kjk was inspired by my conviction that a successfu...

Graph Kernels Exploiting Weisfeiler-Lehman Graph Isomorphism Test Extensions

In this paper we present a novel graph kernel framework inspired the by the Weisfeiler-Lehman (WL) isomorphism tests. Any WL test comprises a relabelling phase of the nodes based on test-specific information extracted from the graph, for example the set of neighbours of a node. We defined a novel relabelling and derived two kernels of the framework from it. The novel kernels are very fast to co...