Much like admissibility is the key concept underlying preferred semantics, strong admissibility is the key concept underlying grounded semantics, as membership of a strongly admissible set is sufficient to show membership of the grounded extension. As such, strongly admissible sets and labellings can be used as an explanation of membership of the grounded extension, as is for instance done in some of the proof procedures for grounded semantics. In the current paper, we present two polynomial algorithms for constructing relatively small (...) strongly admissible labellings, with associated min–max numberings, for a particular argument. These labellings can be used as relatively small explanations for the argument’s membership of the grounded extension. Although our algorithms are not guaranteed to yield an absolute minimal strongly admissible labelling for the argument (as doing so would have implied an exponential complexity), our best performing algorithm yields results that are only marginally larger. Moreover, the runtime of this algorithm is an order of magnitude smaller than that of the existing approach for computing an absolute minimal strongly admissible labelling for a particular argument. As such, we believe that our algorithms can be of practical value in situations where the aim is to construct a minimal or near-minimal strongly admissible labelling in a time-efficient way. (shrink)

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. (shrink)

In the current paper we consider theories with vocabulary containing a number of binary and unary relation symbols. Binary relation symbols represent labeled edges of a graph and unary relations represent unique annotations of the graph's nodes. Such theories, which we call annotation theories^ can be used in many applications, including the formalization of argumentation, approximate reasoning, semantics of logic programs, graph coloring, etc. We address a number of problems related to annotation theories over finite models, including satisfiability, querying problem, (...) specification of preferred models and model checking problem. We show that most of considered problems are NPTime- or co-NPTime-complete. In order to reduce the complexity for particular theories, we use second-order quantifier elimination. To our best knowledge none of existing methods works in the case of annotation theories. We then provide a new second-order quantifier elimination method for stratified theories, which is successful in the considered cases. The new result subsumes many other results, including those of [2, 28, 21]. (shrink)

ABSTRACTThis paper studies abduction in abstract argumentation frameworks. Given an argument, an agent verifies whether the argument is justified or not in its argumentation framework. If the argument is not justified in the argumentation framework, the agent seeks conditions to explain the justification state by hypothesising arguments in the universal argumentation framework. We formulate such abductive reasoning in argumentation semantics and provide its computation in logic programming. We also apply abduction to enforcement and simple dialogue games in argumentation frameworks.

The main objective of this paper is to define a logic for reasoning about distributed time-stamped claims. Such a logic is interesting for theoretical reasons, i.e. as a logic per se, but also because it has a number of practical applications, in particular when one needs to reason about a huge amount of pieces of evidence collected from different sources, where some of the pieces of evidence may be contradictory and some sources are considered to be more trustworthy than others. (...) We introduce the time-stamped claim logic including a sound and complete sequent calculus. In order to show how time-stamped claim logic can be used in practice, we consider a concrete cyber-attribution case study. (shrink)

This paper presents a comprehensive study of argumentation frameworks with necessities (AFNs), a bipolar extension of Dung Abstract argumentation frameworks (AFs) where the support relation captures a positive interaction between arguments having the meaning of necessity: the acceptance of an argument may require the acceptance of other argument(s). The paper discusses new main acceptability semantics for AFNs and their characterization both by a direct approach and a labelling approach. It examines the relationship between AFNs and Dung AFs and shows the (...) gain provided by the former in terms of concision. Finally, the paper shows how to represent an AFN as a normal logic program (LP) and vice versa and in both cases establishes a one-to-one correspondence between extensions under the main acceptability semantics (except for semi-stable semantics where the correspondence is not completely full) of an AFN and particular cases of 3-valued stable models of normal LPs. (shrink)

We study instantiated abstract argumentation frames of the form, where is an abstract argumentation frame and where the arguments x of S are instantiated by I as well formed formulas of a well known logic, for example as Boolean formulas or as predicate logic formulas or as modal logic formulas. We use the method of conceptual analysis to derive the properties of our proposed system. We seek to define the notion of complete extensions for such systems and provide algorithms for (...) finding such extensions. We further develop a theory of instantiation in the abstract, using the framework of Boolean attack formations and of conjunctive and disjunctive attacks. We discuss applications and compare critically with the existing related literature. (shrink)

In 2005 the author introduced networks which allow attacks on attacks of any level. So if a → b reads a attacks 6, 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. (shrink)

In 2005 the author introduced networks which allow attacks on attacks of any level. So if a → b reads a attacks 6, 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 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. (shrink)

There is a generic way to add any new feature to a system. It involves identifying the basic units which build up the system and introducing the new feature to each of these basic units. In the case where the system is argumentation and the feature is probabilistic we have the following. The basic units are: the nature of the arguments involved; the membership relation in the set S of arguments; the attack relation; and the choice of extensions. Generically to (...) add a new aspect to an argumentation network \ can be done by adding this feature to each component. This is a brute-force method and may yield a non-intuitive or meaningful result. A better way is to meaningfully translate the object system into another target system which does have the aspect required and then let the target system endow the aspect on the initial system. In our case we translate argumentation into classical propositional logic and get probabilistic argumentation from the translation. Of course what we get depends on how we translate. In fact, in this paper we introduce probabilistic semantics to abstract argumentation theory based on the equational approach to argumentation networks. We then compare our semantics with existing proposals in the literature including the approaches by M. Thimm and by A. Hunter. Our methodology in general is discussed in the conclusion. (shrink)

1. The last 25 years have seen an increasing interest in the area of formal argumentation. The ultimate goal of the field is to come up with computational models of how we make decisions, based on...

The connection between logic programming and formal argumentation has been studied starting from the landmark 1995 paper of Dung. Subsequent work has identified a standard translation from logic programs to argumentation frameworks, under which pairwise correspondences hold between various logic programming semantics and various formal argumentation semantics. This includes the correspondence between 3-valued stable and complete semantics, between well-founded and grounded semantics and between 2-valued stable and stable semantics. In the current paper, we show that the existing translation is able (...) to yield the additional correspondence between ideal semantics for logic programming and ideal semantics for formal argumentation. We also show that correspondence does not hold between eager semantics for logic programming and eager semantics for formal argumentation, at least when translating from logic programming to formal argumentation. Overall, the current work should be seen as completing the analysis of correspondences between mainstream admissibility-based argumentation semantics and their logic programming counterparts. (shrink)

In the current paper, we re-examine how abstract argumentation can be formulated in terms of labellings, and how the resulting theory can be applied in the field of modal logic. In particular, we are able to express the (complete) extensions of an argumentation framework as models of a set of modal logic formulas that represents the argumentation framework. Using this approach, it becomes possible to define the grounded extension in terms of modal logic entailment.

In this paper we introduce hypersequent-based frameworks for the modelling of defeasible reasoning by means of logic-based argumentation and the induced entailment relations. These structures are an extension of sequent-based argumentation frameworks, in which arguments and the attack relations among them are expressed not only by Gentzen-style sequents, but by more general expressions, called hypersequents. This generalization allows us to overcome some of the known weaknesses of logical argumentation frameworks and to prove several desirable properties of the entailments that are (...) induced by the extended frameworks. It also allows us to incorporate as the deductive base of our formalism some well-known logics, which lack cut-free sequent calculi, and so are not adequate for standard sequent-based argumentation. We show that hypersequent-based argumentation yields robust defeasible variants of these logics, with many desirable properties. (shrink)

We consider the problem of learning argumentation frameworks from a given set of labelings such that every input is a σ-labeling of these argumentation frameworks. Our new algorithm takes labelings and computes attack constraints for each argument that represent the restrictions on argumentation frameworks that are consistent with the input labelings. Having constraints on the level of arguments allows for a very effective parallelization of all computations. An important element of this approach is maintaining a representation of all argumentation frameworks (...) that satisfy the input labelings instead of simply finding any suitable argumentation framework. This is especially important, for example, if we receive additional labelings at a later time and want to refine our result without having to start all over again. The developed algorithm is compared to previous works and an evaluation of its performance has been conducted. (shrink)