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)

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)

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)

This paper provides equational semantics for Dung's argumentation networks. The network nodes get numerical values in [0,1], and are supposed to satisfy certain equations. The solutions to these equations correspond to the ?extensions? of the network. This approach is very general and includes the Caminada labelling as a special case, as well as many other so-called network extensions, support systems, higher level attacks, Boolean networks, dependence on time, and much more. The equational approach has its conceptual roots in the nineteenth (...) century following the algebraic equational approach to logic by George Boole, Louis Couturat, and Ernst Schroeder. (shrink)

In this paper we show that some versions of Dung’s abstract argumentation frames are equivalent to classical propositional logic. In fact, Dung’s attack relation is none other than the generalised Peirce–Quine dagger connective of classical logic which can generate the other connectives ${\neg, \wedge, \vee, \to}$ of classical logic. After establishing the above correspondence we offer variations of the Dung argumentation frames in parallel to variations of classical logic, such as resource logics, predicate logic, etc., etc., and create resource argumentation (...) frames, predicate argumentation frames, etc., etc. We also offer the notion of logic proof as a geometrical walk along the nodes of a Dung network and thus we are able to offer a geometrical abstraction of the notion of inference based argumentation. Thus our paper is also a contribution to the question: “What is a logical system” in as much as it integrates logic with abstract argumentation networks. (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...

Formal models of argumentation have been investigated in several areas, from multi-agent systems and artificial intelligence (AI) to decision making, philosophy and law. In artificial intelligence, logic-based models have been the standard for the representation of argumentative reasoning. More recently, the standard logic-based models have been shown equivalent to standard connectionist models. This has created a new line of research where (i) neural networks can be used as a parallel computational model for argumentation and (ii) neural networks can be used (...) to combine argumentation, quantitative reasoning and statistical learning. At the same time, non-standard logic models of argumentation started to emerge. In this paper, we propose a connectionist cognitive model of argumentation that accounts for both standard and non-standard forms of argumentation. The model is shown to be an adequate framework for dealing with standard and non-standard argumentation, including joint-attacks, argument support, ordered attacks, disjunctive attacks, meta-level attacks, self-defeating attacks, argument accrual and uncertainty. We show that the neural cognitive approach offers an adequate way of modelling all of these different aspects of argumentation. We have applied the framework to the modelling of a public prosecution charging decision as part of a real legal decision making case study containing many of the above aspects of argumentation. The results show that the model can be a useful tool in the analysis of legal decision making, including the analysis of what-if questions and the analysis of alternative conclusions. The approach opens up two new perspectives in the short-term: the use of neural networks for computing prevailing arguments efficiently through the propagation in parallel of neuronal activations, and the use of the same networks to evolve the structure of the argumentation network through learning (e.g. to learn the strength of arguments from data). (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)

In this paper, we introduce the methodology and techniques of metaargumentation to model argumentation. The methodology of meta-argumentation instantiates Dung's abstract argumentation theory with an extended argumentation theory, and is thus based on a combination of the methodology of instantiating abstract arguments, and the methodology of extending Dung's basic argumentation frameworks with other relations among abstract arguments. The technique of meta-argumentation applies Dung's theory of abstract argumentation to itself, by instantiating Dung's abstract arguments with meta-arguments using a technique called flattening. (...) We characterize the domain of instantiation using a representation technique based on soundness and completeness. Finally, we distinguish among various instantiations using the technique of specification languages. (shrink)

Dung’s argumentation frameworks have been applied for over twenty years to the analysis of argument justification. This representation focuses on arguments and the attacks among them, abstracting away from other features like the internal structure of arguments, the nature of utterers, the specifics of the attack relation, etc. The model is highly attractive because it reduces most of the complexities involved in argumentation processes. It can be applied to different settings, like the argument evaluation of an individual agent or the (...) case of dialectic disputes between two agents (pro and con), or even in multi-agent collective argumentation. The latter case involves agents with possibly different arguments and/or opinions on how to evaluate them, leading to the possibility of considering multiple sets of arguments and attack relations. Two basic questions can be asked here, namely ‘what to aggregate’ and ‘how to aggregate’. The former concerns what kinds of entities do the agents intend to choose (arguments, attacks, assessments, etc.), while the second one focuses on which aggregation mechanisms yield rational choices (voting on arguments, merging procedures to obtain a common argumentation framework, deliberation processes, etc.). In particular, the question about the rationality of a collective argument choice relates this topic to Social Choice and Judgment Aggregation theories, while its associated strategic issues relate it to Game Theory. The research efforts on the disparate problems elicited by collective argumentation have generated a considerable corpus of literature that deserves an orderly evaluation. This survey is intended as a contribution to that end. (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)

This paper studies general numerical networks with support and attack. Our starting point is argumentation networks with the Caminada labelling of three values 1=in, 0=out and ½=undecided. This is generalised to arbitrary values in [01], which enables us to compare with other numerical networks such as predator?prey ecological networks, flow networks, logical modal networks and more. This new point of view allows us to see the place of argumentation networks in the overall landscape of networks and import and export ideas (...) to and from argumentation networks. We make a special effort to make clear how general concepts in general networks relate to the special case of argumentation networks. We pay special attention to the handling of loops and to the special features of numerical support. We find surprising connections with the Dempster?Shafer rule and with the cross-ratio in projective geometry. This paper is an expansion of our 2005 paper and so we also consider higher level features such as numerical attacks on attacks, and propagation of numerical values.We conclude with a brief view of temporal numerical argumentation and with a detailed comparison with related papers published since 2005. (shrink)

The article develops and justifies, on the basis of the epistemological argumentation theory, two central pieces of the theory of evaluative argumentation interpretation: 1. criteria for recognizing argument types and 2. rules for adding reasons to create ideal arguments. Ad 1: The criteria for identifying argument types are a selection of essential elements from the definitions of the respective argument types. Ad 2: After presenting the general principles for adding reasons (benevolence, authenticity, immanence, optimization), heuristics are proposed for finding missing (...) reasons, for deductive arguments, e.g., semantic tableaux are suggested. (shrink)