Complete Assumption Labellings
نویسندگان
چکیده
Recently, argument labellings have been proposed as a new (equivalent) way to express the extension semantics of Abstract Argumentation (AA) frameworks. Here, we introduce a labelling approach for the complete semantics in Assumption-Based Argumentation (ABA), where labels are assigned to assumptions rather than whole arguments. We prove that the complete assumption labelling corresponds to the complete extension semantics in ABA, as well as to the complete extension semantics and the complete argument labelling in AA.
منابع مشابه
Graphical Representation of Assumption-Based Argumentation
Since Assumption-Based Argumentation (ABA) was introduced in the nineties, the structure and semantics of an ABA framework have been studied exclusively in logical terms without any graphical representation. Here, we show how an ABA framework and its complete semantics can be displayed in a graph, clarifying the structure of the ABA framework as well as the resulting complete assumption labelli...
متن کاملSome Sequence of Wrapped Δ-Labellings for the Complete Bipartite Graph
The design of large disk array architectures leads to interesting combinatorial problems. Minimizing the number of disk operations when writing to consecutive disks leads to the concept of “cluttered orderings” which were introduced for the complete graph by Cohen et al. (2001). Mueller et al. (2005) adapted the concept of wrapped Δ-labellings to the complete bipartite case. In this paper, we g...
متن کاملTriangular embeddings of complete graphs from graceful labellings of paths
We show that to each graceful labelling of a path on 2s + 1 vertices, s ≥ 2, there corresponds a current assignment on a 3-valent graph which generates at least 22s cyclic oriented triangular embeddings of a complete graph on 12s + 7 vertices. We also show that in this correspondence, two distinct graceful labellings never give isomorphic oriented embeddings. Since the number of graceful labell...
متن کاملEdge-Magic Group Labellings of Countable Graphs
We investigate the existence of edge-magic labellings of countably infinite graphs by abelian groups. We show for that for a large class of abelian groups, including the integers Z, there is such a labelling whenever the graph has an infinite set of disjoint edges. A graph without an infinite set of disjoint edges must be some subgraph of H + I, where H is some finite graph and I is a countable...
متن کاملConnections between labellings of trees
There are many long-standing conjectures related with some labellings of trees. It is important to connect labellings that are related with conjectures. We find some connections between known labellings of simple graphs.
متن کامل