Results 1  10
of
10
Complete Extensions in Argumentation Coincide with ThreeValued Stable Models in Logic Programming
, 2009
"... In this paper, we prove the correspondence between complete extensions in abstract argumentation and 3valued stable models in logic programming. This result is in line with earlier work of [8] that identified the correspondence between the grounded extension in abstract argumentation and the wellf ..."
Abstract

Cited by 13 (3 self)
 Add to MetaCart
In this paper, we prove the correspondence between complete extensions in abstract argumentation and 3valued stable models in logic programming. This result is in line with earlier work of [8] that identified the correspondence between the grounded extension in abstract argumentation and the wellfounded model in logic programming, as well as between the stable extensions in abstract argumentation and the stable models in logic programming. We believe the results of this paper are not only relevant by themselves, but can also potentially be used for future work on the correspondence between argumentation and logic programming semantics.
Fibring argumentation frames.
 Studia Logica,
, 2009
"... Abstract. This paper is part of a research program centered around argumentation networks and offering several research directions for argumentation networks, with a view of using such networks for integrating logics and network reasoning. In Section 1 we introduce our program manifesto. In Section ..."
Abstract

Cited by 8 (3 self)
 Add to MetaCart
(Show Context)
Abstract. This paper is part of a research program centered around argumentation networks and offering several research directions for argumentation networks, with a view of using such networks for integrating logics and network reasoning. In Section 1 we introduce our program manifesto. In Section 2 we motivate and show how to substitute one argumentation network as a node in another argumentation network. Substitution is a purely logical operation and doing it for networks, besides developing their theory further, also helps us see how to bring logic and networks closer together. Section 3 develops the formal properties of the new kind of network and Section 4 offers general discussion and comparison with the literature.
Semantics for Higher Level Attacks in Extended Argumentation Frames
, 2009
"... In 2005 the author introduced networks which allow attacks on attacks of any level. So if a→b reads a attacks b, then this attack can itself be attacked by another node c. This attack itself can attack another node d. This situation can be iterated to any level with attacks and nodes attacking other ..."
Abstract

Cited by 5 (3 self)
 Add to MetaCart
(Show Context)
In 2005 the author introduced networks which allow attacks on attacks of any level. So if a→b reads a attacks b, then this attack can itself be attacked by another node c. This attack itself can attack another node d. This situation can be iterated to any level with attacks and nodes attacking other attacks and other nodes. In this paper we provide semantics (of extensions) to such networks. We offer three different approaches to obtaining semantics. 1. The translation approach This uses the methodology of ‘Logic by translation’. We translate faithfully the new networks into ordinary Dung networks with more nodes and extract the semantics from the translation. 2. The labelling approach This method regards the arrows as additional entities to be attacked and to mount attacks and applies a variation of the usual machinery of Camindada like labelling to the network. The new concept we need to employ here is that of ‘joint attacks’. 3. The logic programming approach We translate the higher level network into a logic program and obtain semantics for it through known semantics for logic programs. We then compare our methods with those of S. Modgil and P. M. Dung et al. 1
Logical tools for handling change in agentbased systems
, 2009
"... 1.2 Short overview of the different logics....................................... 9 ..."
Abstract

Cited by 3 (0 self)
 Add to MetaCart
(Show Context)
1.2 Short overview of the different logics....................................... 9
Defeasible inheritance systems and reactive diagrams ∗
, 2008
"... Inheritance diagrams are directed acyclic graphs with two types of connections between nodes: x → y (read x is a y) and x ̸ → y (read as x is not a y). Given a diagram D, one can ask the formal question of “is there a valid (winning) path between node x and node y? ” Depending on the existence of a ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
(Show Context)
Inheritance diagrams are directed acyclic graphs with two types of connections between nodes: x → y (read x is a y) and x ̸ → y (read as x is not a y). Given a diagram D, one can ask the formal question of “is there a valid (winning) path between node x and node y? ” Depending on the existence of a valid path we can answer the question “x is a y ′ ′ or ”x is not a y ′ ′. The answer to the above question is determined through a complex inductive algorithm on paths between arbitrary pairs of points in the graph. This paper aims to simplify and interpret such diagrams and their algorithms. We approach the area on two fronts. (1) Suggest reactive arrows to simplify the algorithms for the winning paths. (2) We give a conceptual analysis of (defeasible or nonmonotonic) inheritance diagrams, and compare our analysis to the “small ” and “big sets ” of preferential and related reasoning. In our analysis, we consider nodes as information sources and truth values, direct links as information,
Ideal Extensions as Logical Programming Models
, 2013
"... We show that the ideal sets of an argumentation framework can be characterized by two kinds of logical models: ideal models (2valued logical models) and pstable models (2valued logical models). We also show that the maximal ideal set of an argumentation framework can be characterized by the well ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
(Show Context)
We show that the ideal sets of an argumentation framework can be characterized by two kinds of logical models: ideal models (2valued logical models) and pstable models (2valued logical models). We also show that the maximal ideal set of an argumentation framework can be characterized by the wellfounded+ model (a 3valued logical model). These results argue for the logical foundations of the ideal sets of an argumentation framework. Moreover, these results consolidate the strong relationship between argumentation semantics and logic programming semantics with negation as failure. More accurately, we prove that the five argumentation semantics suggested by Dung et al., grounded, stable, preferred, complete and ideal semantics, can be characterized by the wellfounded model, stablemodel, pstable, Clark’s completion and wellfounded+ model semantics, respectively by using a unique mapping from argumentation frameworks into logic programs. We observe that the labellings of these argumentation semantics can be inferred by the logical models of a logic program. 1
Dov M. Gabbay Semantics for Higher Level Attacks in Extended Argumentation Frames
"... Abstract. In 2005 the author introduced networks which allow attacks on attacks of any level. So if a → b reads a attacks b, then this attack can itself be attacked by another node c. This attack itself can attack another node d. This situation can be iterated to any level with attacks and nodes att ..."
Abstract
 Add to MetaCart
(Show Context)
Abstract. In 2005 the author introduced networks which allow attacks on attacks of any level. So if a → b reads a attacks b, then this attack can itself be attacked by another node c. This attack itself can attack another node d. This situation can be iterated to any level with attacks and nodes attacking other attacks and other nodes. In this paper we provide semantics (of extensions) to such networks. We offer three different approaches to obtaining semantics. 1. The translation approach This uses the methodology of ‘Logic by translation’. We translate faithfully the new networks into ordinary Dung networks with more nodes and extract the semantics from the translation. 2. The labelling approach This method regards the arrows as additional entities to be attacked and to mount attacks and applies a variation of the usual machinery of Camindada like labelling to the network. The new concept we need to employ here is that of ‘joint attacks’. 3. The logic programming approach We translate the higher level network into a logic program and obtain semantics for it through known semantics for logic programs. We then compare our methods with those of S. Modgil and P. M. Dung et al.
2.2 Basic logical definitions............................................... 28 Contents
, 2009
"... 1.2 Short overview of the different logics....................................... 9 ..."
Abstract
 Add to MetaCart
(Show Context)
1.2 Short overview of the different logics....................................... 9
Argumentation Inference as Logic Programming Inference: An Extended Abstract
"... In this extended abstract, we present a small survey of recent results in the study of argumentation theory as logic programming. In particular, we survey recent characterizations of eight argumentation se ..."
Abstract
 Add to MetaCart
(Show Context)
In this extended abstract, we present a small survey of recent results in the study of argumentation theory as logic programming. In particular, we survey recent characterizations of eight argumentation se
unknown title
, 2013
"... A neural cognitive model of argumentation with application to legal inference and decision making ..."
Abstract
 Add to MetaCart
A neural cognitive model of argumentation with application to legal inference and decision making