Dung’s (1995) argumentation framework takes as input two abstract entities: a set of arguments and a binary relation encoding attacks between these arguments. It returns acceptable sets of arguments, called extensions, w.r.t. a given semantics. While the abstract nature of this setting is seen as a great advantage, it induces a big gap with the application that it is used to. This raises some questions about the compatibility of the setting with a logical formalism (i.e., whether it (...) is possible to instantiate it properly from a logical knowledge base), and about the significance of the various semantics in the application context. In this paper we tackle the above questions. We first propose to fill in the previous gap by extending Dung’s (1995) framework. The idea is to consider all the ingredients involved in an argumentation process. We start with the notion of an abstract monotonic logic which consists of a language (defining the formulas) and a consequence operator. We show how to build, in a systematic way, arguments from a knowledge base formalised in such a logic. We then recall some basic postulates that any instantiation should satisfy. We study how to choose an attack relation so that the instantiation satisfies the postulates. We show that symmetric attack relations are generally not suitable. However, we identify at least one ‘appropriate’ attack relation. Next, we investigate under stable, semi-stable, preferred, grounded and ideal semantics the outputs of logic-based instantiations that satisfy the postulates. For each semantics, we delimit the number of extensions an argumentation system may have, characterise the extensions in terms of subsets of the knowledge base, and finally characterise the set of conclusions that are drawn from the knowledge base. The study reveals that stable, semi-stable and preferred semantics either lead to counter-intuitive results or provide no added value w.r.t. naive semantics. Besides, naive semantics either leads to arbitrary results or generalises the coherence-based approach initially developed by Rescher and Manor (1970). Ideal and grounded semantics either coincide and generalise the free consequence relation developed by Benferhat, Dubois, and Prade (1997), or return arbitrary results. Consequently, Dung’s (1995) framework seems problematic when applied over deductive logical formalisms. (shrink)

Dung’s abstract argumentation provides us with a general framework to deal with argumentation, non-monotonic reasoning and logic programming. For the extension-based semantics, one of the basic principles is I-maximality which is in particular related with the notion of skeptical justification. Another one is directionality which can be employed for the study of dynamics of argumentation. In this paper, we introduce two new extension-based semantics into Dung’s abstract argumentation, called grounded-like semantics and initial semantics which (...) satisfy the I-maximality and directionality principles. The initial semantics has many good properties and can be expected to play a central role in studying other extension-based semantics, such as admissible, complete and preferred semantics. (shrink)

Dung’s argumentation frameworks are formalisms widely used to model interaction among arguments. Although their study has been profusely developed in the field of Artificial Intelligence, it is not common to see its treatment among those less connected to computer science within the logical-philosophical community. In this paper we propose to bring to that audience a proof-theory for argument justification based on tableaux, very similar to those the Logic students are familiar with. The tableaux enable to calculate whether an (...) argument or subset of arguments are accepted or rejected in accordance to Dung’s preferred and grounded extension-based semantics. Soundness and completeness results regarding those semantics are provided. (shrink)

We describe a tool that allows the merging of extensions of argumentation frameworks, following the approach defined by 33–42). The tool is implemented in Java, and is highly modular thanks to Object Oriented Programming principles. We describe a short experimental study that assesses the scalability of the approach, as well as the impact on runtime of using an integrity constraint.

1. Argumentation, by considering arguments and their interactions, is a way of reasoning that has proven successful in many contexts, for instance, in multi-agent applications (Carrera & Iglesias,...

Carneades is a recently proposed formalism for structured argumentation with varying proof standards, inspired by legal reasoning, but more generally applicable. Its distinctive feature is that each statement can be given its own proof standard, which is claimed to allow a more natural account of reasoning under burden of proof than existing formalisms for structured argumentation, in which proof standards are defined globally. In this article, the two formalisms are formally related by translating Carneades into the ASPIC+ framework (...) for structured argumentation. Since ASPIC+ is defined to generate Dung-style abstract argumentation frameworks, this in effect translates Carneades graphs into abstract argumentation frameworks. For this translation, we prove a formal correspondence and show that certain rationality postulates hold. It is furthermore proved that Carneades always induces a unique Dung extension, which is the same in all of Dung's semantics, allowing us to generalise Carneades to cycle-containing structures. (shrink)

argumentation has been shown to be a powerful tool within many fields such as artificial intelligence, logic and legal reasoning. In this paper we enhance Dung’s well-known abstract argumentation framework with explanatory capabilities. We show that an explanatory argumentation framework (EAF) obtained in this way is a useful tool for the modeling of scientific debates. On the one hand, EAFs allow for the representation of explanatory and justificatory arguments constituting rivaling scientific views. On the other hand, (...) different procedures for selecting arguments, corresponding to different methodological and epistemic requirements of theory evaluation, can be formulated in view of our framework. (shrink)

Probabilistic argumentation and neuro-argumentative systems offer new computational perspectives for the theory and applications of argumentation, but their principled construction involves two entangled problems. On the one hand, probabilistic argumentation aims at combining the quantitative uncertainty addressed by probability theory with the qualitative uncertainty of argumentation, but probabilistic dependences amongst arguments as well as learning are usually neglected. On the other hand, neuro-argumentative systems offer the opportunity to couple the computational advantages of learning and massive parallel (...) computation from neural networks with argumentative reasoning and explanatory abilities, but the relation of probabilistic argumentation frameworks with these systems has been ignored so far. Towards the construction of neuro-argumentative systems based on probabilistic argumentation, we associate a model of abstract argumentation and the graphical model of Boltzmann machines in order to (i... (shrink)

In this paper, we study conditional preferences in abstract argumentation by introducing a new generalization of Dung-style argumentation frameworks (AFs) called Conditional Preference-based AFs (CPAFs). Each subset of arguments in a CPAF can be associated with its own preference relation. This generalizes existing approaches for preference-handling in abstract argumentation, and allows us to reason about conditional preferences in a general way. We conduct a principle-based analysis of CPAFs and compare them to related generalizations of (...) AFs. Specifically, we highlight similarities and differences to Modgil’s Extended AFs and show that our formalism can capture Value-based AFs. Moreover, we show that in some cases the introduction of conditional preferences leads to an increase in computational complexity. (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)

Abstract. The notion of similarity has been studied in many areas of Computer Science; in a general sense, this concept is defined to provide a measure of the semantic equivalence between two pieces of knowledge, expressing how “close” their meaning can be regarded. In this work, we study similarity as a tool useful to improve the representation of arguments, the interpretation of the relations between arguments, and the semantic evaluation associated with the arguments in the argumentative process. In this (...) direction, we present a novel mechanism to determine the similarity between two arguments based on descriptors representing particular aspects associated with these arguments. This mechanism involves a comparison process influenced by the context in which the process develops, where this context provides the relevant aspects that need to be analyzed in the application domain. Then, we use this similarity measure as a quantity to compute the result of attacks and supports in the argumentation process. These valuations, applied to a Bipolar Argumentation Frameworks, allowed us to refine the argument relations, providing the tools to establish a family of new argumentation semantics that considers the similarity between arguments as a crucial part for the argumentation process. (shrink)

An abstract framework for structured arguments is presented, which instantiates Dung's ('On the Acceptability of Arguments and its Fundamental Role in Nonmonotonic Reasoning, Logic Programming, and n- Person Games', Artificial Intelligence , 77, 321-357) abstract argumentation frameworks. Arguments are defined as inference trees formed by applying two kinds of inference rules: strict and defeasible rules. This naturally leads to three ways of attacking an argument: attacking a premise, attacking a conclusion and attacking an inference. To resolve (...) such attacks, preferences may be used, which leads to three corresponding kinds of defeat: undermining, rebutting and undercutting defeats. The nature of the inference rules, the structure of the logical language on which they operate and the origin of the preferences are, apart from some basic assumptions, left unspecified. The resulting framework integrates work of Pollock, Vreeswijk and others on the structure of arguments and the nature of defeat and extends it in several respects. Various rationality postulates are proved to be satisfied by the framework, and several existing approaches are proved to be a special case of the framework, including assumption-based argumentation and DefLog. (shrink)

We revisit the notion of initial sets by Xu and Cayrol 2016), i. e., non-empty minimal admissible sets in abstract argumentation frameworks. Initial sets are a simple concept for analysing conflicts in an abstract argumentation framework and to explain why certain arguments can be accepted. We contribute with new insights on the structure of initial sets and devise a simple non-deterministic construction principle for any admissible set, based on iterative selection of initial sets of the (...) original framework and its induced reducts. In particular, we characterise many existing admissibility-based semantics via this construction principle, thus providing a constructive explanation on the structure of extensions. We also investigate certain problems related to initial sets with respect to their computational complexity. (shrink)

dialectical frameworks have been introduced as a formalism for modeling argumentation allowing general logical satisfaction conditions and the relevant argument evaluation. Different criteria used to settle the acceptance of arguments are called semantics. Semantics of ADFs have so far mainly been defined based on the concept of admissibility. However, the notion of strongly admissible semantics studied for abstract argumentation frameworks has not yet been introduced for ADFs. In the current work we present the concept of (...) strong admissibility of interpretations for ADFs. Further, we show that strongly admissible interpretations of ADFs form a lattice with the grounded interpretation as the maximal element. We also present algorithms to answer the following decision problems: whether a given interpretation is a strongly admissible interpretation of a given ADF, and whether a given argument is strongly acceptable/deniable in a given interpretation of a given ADF. In addition, we show that the strongly admissible semantics of ADFs forms a proper generalization of the strongly admissible semantics of AFs. (shrink)

dialectical frameworks constitute a recent and powerful generalisation of Dung's argumentation frameworks, where the relationship between the arguments can be specified via Boolean formulas. Recent results have shown that this enhancement comes with the price of higher complexity compared to AFs. In fact, acceptance problems in the world of ADFs can be hard even for the third level of the polynomial hierarchy. In order to implement reasoning problems on ADFs, systems for quantified Boolean formulas thus are suitable (...) engines to be employed. In this paper we give complexity sensitive QBF encodings of ADF problems generalising recent work on QBFs for AF labellings. Our encodings provide a uniform and modular way of translating reasoning in ADFs to QBFs, that can be used as the basis for novel systems for ADF reasoning. (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. (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)

Over the last decade, several extensions of Dung’s Abstract Argumentation Frameworks (AFs) have been introduced in the literature. Some of these extensions concern the nature of the attack relation, such as the consideration of recursive attacks, whereas others incorporate additional interactions, such as a support relation. Recently, the Attack–Support Argumentation Framework (ASAF) was proposed, which accounts for recursive attacks and supports, attacks to supports and supports to attacks, at any level, where the support relation is interpreted (...) as necessity. Currently, to determine the accepted elements of an ASAF (which may be arguments, attacks, and supports) it is required to translate such an ASAF into a Dung’s AF. In this work, we provide a formal characterization of acceptability semantics directly on the ASAF, without requiring such a translation. We prove that our characterization is sound since it satisfies different results from Dung’s argumentation theory; moreover, we formally show that the approach proposed here for addressing acceptability is equivalent to the preexisting one, in which the ASAF was translated into an AF. Also, we formalize the relationship between the ASAF and other frameworks on which it is inspired: the Argumentation Framework with Recursive Attacks (AFRA) and the Argumentation Framework with Necessities (AFN). (shrink)

This work introduces the Attack-Support Argumentation Framework (ASAF), an approach to abstract argumentation that allows for the representation and combination of attack and support relations. This framework extends the argumentation Framework with Recursive Attacks (AFRA) in two ways. Firstly, it adds a support relation enabling to express support for arguments; this support can also be given to attacks, and to the support relation itself. Secondly, it extends AFRA’s attack relation by allowing attacks to the aforementioned support (...) relation. Moreover, since the support relation of the ASAF has a necessity interpretation, the ASAF also extends the Argumentation Framework with Necessities (AFN). Thus, the ASAF provides a unified framework for representing attack and support for arguments, as well as attack and support for the attack and support relations at any level. (shrink)

This paper introduces a multi-agent dynamic epistemic logic for abstract argumentation. Its main motivation is to build a general framework for modelling the dynamics of a debate, which entails reasoning about goals, beliefs, as well as policies of communication and information update by the participants. After locating our proposal and introducing the relevant tools from abstract argumentation, we proceed to build a three-tiered logical approach. At the first level, we use the language of propositional logic to (...) encode states of a multi-agent debate. This language allows to specify which arguments any agent is aware of, as well as their subjective justification status. We then extend our language and semantics to that of epistemic logic, in order to model individuals’ beliefs about the state of the debate, which includes uncertainty about the information available to others. As a third step, we introduce a framework of dynamic epistemic logic and its semantics, which is essentially based on so-called event models with factual change. We provide completeness results for a number of systems and show how existing formalisms for argumentation dynamics and unquantified uncertainty can be reduced to their semantics. The resulting framework allows reasoning about subtle epistemic and argumentative updates—such as the effects of different levels of trust in a source—and more in general about the epistemic dimensions of strategic communication. (shrink)

Discussion among individuals about a given issue often induces polarization and bipolarization effects, i.e. individuals radicalize their initial opinion towards either the same or opposite directions. Experimental psychologists have put forward Persuasive Arguments Theory as a clue for explaining polarization. PAT claims that adding novel and persuasive arguments pro or contra the debated issue is the major cause for polarization. Recent developments in abstract argumentation provide the tools for capturing these intuitions on a formal basis. Here Bipolar (...) class='Hi'>Argumentation Frameworks are employed as a tool for encoding the information of agents in a debate relative to a given issue a. A probabilistic extension of BAF allows to encode the likelihood of the opinions pro or contra a before and after information exchange. It is shown, by a straightforward example, how these measures provide the basis to capture the intuitions of PAT. (shrink)

Discussion among individuals about a given issue often induces polarization and bipolarization effects, i.e. individuals radicalize their initial opinion towards either the same or opposite directions. Experimental psychologists have put forward Persuasive Arguments Theory as a clue for explaining polarization. PAT claims that adding novel and persuasive arguments pro or contra the debated issue is the major cause for polarization. Recent developments in abstract argumentation provide the tools for capturing these intuitions on a formal basis. Here Bipolar (...) class='Hi'>Argumentation Frameworks are employed as a tool for encoding the information of agents in a debate relative to a given issue a. A probabilistic extension of BAF allows to encode the likelihood of the opinions pro or contra a before and after information exchange. It is shown, by a straightforward example, how these measures provide the basis to capture the intuitions of PAT. (shrink)

This paper presents a methodology to design and implement programs intended to decide cases, described as sets of factors, according to a theory of a particular domain based on a set of precedent cases relating to that domain. We useDialectical Frameworks, a recent development in AI knowledge representation, as the central feature of our design method. ADFs will play a role akin to that played by Entity–Relationship models in the design of database systems. First, we explain how the factor (...) hierarchy of the well-known legal reasoning system CATO can be used to instantiate an ADF for the domain of US Trade Secrets. This is intended to demonstrate the suitability of ADFs for expressing the design of legal cased based systems. The method is then applied to two other legal domains often used in the literature of AI and Law. In each domain, the design is provided by the domain analyst expressing the cases in terms of factors organised into an ADF from which an executable program can be implemented in a straightforward way by taking advantage of the closeness of the acceptance conditions of the ADF to components of an executable program. We evaluate the ease of implementation, the performance and efficacy of the resulting program, ease of refinement of the program and the transparency of the reasoning. This evaluation suggests ways in which factor based systems, which are limited by taking as their starting point the representation of cases as sets of factors and so abstracting away the particular facts, can be extended to address open issues in AI and Law by incorporating the case facts to improve the decision, and by considering justification and reasoning using portion of precedents. (shrink)

Answer-set programming (ASP) has emerged as a declarative programming paradigm where problems are encoded as logic programs, such that the so-called answer sets of theses programs represent the solutions of the encoded problem. The efficiency of the latest ASP solvers reached a state that makes them applicable for problems of practical importance. Consequently, problems from many different areas, including diagnosis, data integration, and graph theory, have been successfully tackled via ASP. In this work, we present such ASP-encodings for problems associated (...) to abstract argumentation frameworks (AFs) and generalisations thereof. Our encodings are formulated as fixed queries, such that the input is the only part depending on the actual AF to process. We illustrate the functioning of this approach, which is underlying a new argumentation system called ASPARTIX in detail and show its adequacy in terms of computational complexity. (shrink)

We explore the computational complexity of justification, stability and relevance in incomplete argumentation frameworks (IAFs). IAFs are abstract argumentation frameworks that encode qualitative uncertainty by distinguishing between certain and uncertain arguments and attacks. These IAFs can be completed by deciding for each uncertain argument or attack whether it is present or absent. Such a completion is an abstract argumentation framework, for which it can be decided which arguments are acceptable under a given semantics. (...) The justification status of an argument in a completion then expresses whether the argument is accepted (in), not accepted because it is attacked by an accepted argument (out) or neither (undec). For a given IAF and certain argument, the justification status of that argument need not be the same in all completions. This is the issue of stability, where an argument is stable if its justification status is the same in all completions. For arguments that are not stable in an IAF, the relevance problem is of interest: which uncertain arguments or attacks should be investigated for the argument to become stable? In this paper, we define justification, stability and relevance for IAFs and provide a complexity analysis for these problems under grounded, complete, preferred and stable semantics. (shrink)

Argumentation Frameworks provide a fruitful basis for exploring issues of defeasible reasoning. Their power largely derives from the abstract nature of the arguments within the framework, where arguments are atomic nodes in an undifferentiated relation of attack. This abstraction conceals different senses of argument, namely a single-step reason to a claim, a series of reasoning steps to a single claim, and reasoning steps for and against a claim. Concrete instantiations encounter difficulties and complexities as a result of (...) conflating these senses. To distinguish them, we provide an approach to instantiating AFs in which the nodes are restricted to literals and rules, encoding the underlying theory directly. Arguments in these senses emerge from this framework as distinctive structures of nodes and paths. As a consequence of the approach, we reduce the effort of computing argumentation extensions, which is in contrast to other approaches. Our framework retains the theoretical and computational bene.. (shrink)

argumentation, as originally defined by Dung, is a model that allows the description of certain information about arguments and relationships between them: in an abstract argumentation framework, the agent knows for sure whether a given argument or attack exists. It means that the absence of an attack between two arguments can be interpreted as “we know that the first argument does not attack the second one”. But the question of uncertainty in abstract argumentation has received (...) much attention in the last years. In this paper, we survey approaches that allow to express information like “There may be an attack between these arguments”. We describe the main models that incorporate qualitative uncertainty in abstract argumentation, as well as some applications of these models. We also highlight some open questions that deserve some attention in the future. (shrink)

This paper studies a fundamental mechanism by which conflicts between arguments are drawn from sentiments regarding acceptability of the arguments. Given sets of arguments, an inverse abstract argumentation problem seeks attack relations between arguments such that acceptability semantics interprets each argument in the sets of arguments as being acceptable in each of the attack relations. It is an inverse problem of the traditional problem we refer to as the forward abstract argumentation problem. Given an attack relation, (...) the forward abstract argumentation problem seeks sets of arguments such that acceptability semantics interprets each argument in the sets of arguments as being acceptable in the attack relation. We give a probabilistic model of argumentation-theoretic inference. It is a generative model formalising the process by which acceptability semantics interprets acceptability of arguments in a given attack relation. We show that it gives a broad view of solutions to the forward and inverse abstract argumentation problems. Specifically, solutions to the inverse and forward abstract argumentation problems are shown to be equivalent to a maximum likelihood estimate and maximum likelihood prediction, respectively, which are both available with the generative model. In addition, they are shown to be special cases of the posterior distribution and the evidence, respectively, which are both obtained by probabilistic inference on the generative model. We report an experiment result and application example of the generative model in the inverse problems. (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 this paper, I propose a logical-cognitive approach to argumentation and advocate an idea that argumentation presupposes that intelligent agents engaged in it are cognitively diverse. My approach to argumentation allows drawing distinctions between justification, conviction and persuasion as its different kinds. In justification agents seek to verify weak or strong coherency of an agent’s position in a dialogue. In conviction they argue to modify their partner’s position by means of demonstrating weak or strong cogency of their (...) positions before a ‘rational judge’. My approach to argumentation employs a ‘light’ version of Dung’s abstract argumentative frameworks. It is based on Stich’s idea of agents’ cognitive diversity the epistemic aspect of which is argued to be close to Pavilionis’s conception of meaning continuum. To illustrate my contributions I use an example based on the Kitchen Debate (1959) between Khrushchev and Nixon. (shrink)

In the 1980s, Pollock’s work on default reasons started the quest in the AI community for a formal system of defeasible argumentation. The main goal of this paper is to provide a logic of structured defeasible arguments using the language of justification logic. In this logic, we introduce defeasible justification assertions of the type t : F that read as “t is a defeasible reason that justifies F”. Such formulas are then interpreted as arguments and their acceptance semantics is (...) given in analogy to Dung’s abstract argumentation framework semantics. We show that a large subclass of Dung’s frameworks that we call “warranted” frameworks is a special case of our logic in the sense that Dung’s frameworks can be obtained from justification logic-based theories by focusing on a single aspect of attacks among justification logic arguments and Dung’s warranted frameworks always have multiple justification logic instantiations called “realizations”. We first define a new justification logic that relies on operational semantics for default logic. One of the key features that is absent in standard justification logics is the possibility to weigh different epistemic reasons or pieces of evidence that might conflict with one another. To amend this, we develop a semantics for “defeaters”: conflicting reasons forming a basis to doubt the original conclusion or to believe an opposite statement. This enables us to formalize non-monotonic justifications that prompt extension revision already for normal default theories. Then we present our logic as a system for abstract argumentation with structured arguments. The format of conflicting reasons overlaps with the idea of attacks between arguments to the extent that it is possible to define all the standard notions of argumentation framework extensions. Using the definitions of extensions, we establish formal correspondence between Dung’s original argumentation semantics and our operational semantics for default theories. One of the results shows that the notorious attack cycles from abstract argumentation cannot always be realized as justification logic default theories. (shrink)

In this article the argumentation structure of the court’s decision in the Popov v. Hayashi case is formalised in Prakken’s (Argument Comput 1:93–124; 2010) abstract framework for argument-based inference with structured arguments. In this framework, arguments are inference trees formed by applying two kinds of inference rules, strict and defeasible rules. Arguments can be attacked in three ways: attacking a premise, attacking a conclusion and attacking an inference. To resolve such conflicts, preferences may be used, which leads to (...) three corresponding kinds of defeat, after which Dung’s (Artif Intell 77:321–357; 1995) abstract acceptability semantics can be used to evaluate the arguments. In the present paper the abstract framework is instantiated with strict inference rules corresponding to first-order logic and with defeasible inference rules for defeasible modus ponens and various argument schemes. The main techniques used in the formal reconstruction of the case are rule-exception structures and arguments about rule validity. Arguments about socio-legal values and the use of precedent cases are reduced to arguments about rule validity. The tree structure of arguments, with explicit subargument relations between arguments, is used to capture the dependency relations between the elements of the court’s decision. (shrink)

We propose a formal theory built upon an abstract argumentation framework for handling argumentation dynamics. To that end, we analyze the acceptability dynamics of arguments through the proposal of two different kinds of sets of arguments which are somehow responsible for the acceptability/rejection of a given argument. We develop a study of the consequences of breaking the construction of such sets towards the acceptance of an analyzed argument. This brings about the proposal of a novel change operation (...) which allows to determine which arguments should be removed from the framework so that another particular argument becomes accepted. Finally, the proposed model is formalized in the light of the theory of belief revision by characterizing the corresponding operations through constructive definition and an axiomatic characterization, connecting them through the corresponding representation theorem. The theoretical proposal constitutes the fundamentals for a system implementation in many dynamic domains of application. In particular, we show its application for handling the dynamics of legal interpretation. In that sense, this proposal constitutes a fundamental approach and theoretical justification to handle the dynamics of legal arguments through changes of interpretative canons. We show a possible concretisation of our abstract theory for the legal domain by analysing a real legal case from the Argentinean jurisprudence. Such a system would be capable of suggesting alternative critical points in the current state of affairs of a legal case towards pursuing a specific goal for which the case is being investigated. (shrink)

The International Competition on Computational Models of Argumentation (ICCMA) focuses on reasoning tasks in abstract argumentation frameworks. Submitted solvers are tested on a selected collection of benchmark instances, including artificially generated argumentation frameworks and some frameworks formalizing real-world problems. This paper presents the novelties introduced in the organization of the Third (2019) and Fourth (2021) editions of the competition. In particular, we proposed new tracks to competitors, one dedicated to dynamic solvers (i.e., solvers (...) that incrementally compute solutions of frameworks obtained by incrementally modifying original ones) in ICCMA’19 and one dedicated to approximate algorithms in ICCMA’21. From the analysis of the results, we noticed that i) dynamic recomputation of solutions leads to significant performance improvements, ii) approximation provides much faster results with satisfactory accuracy, and iii) classical solvers improved with respect to previous editions, thus revealing advancement in state of the art. (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)

In this paper, we introduce the methodology and techniques of meta-argumentation 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)

In this paper, we introduce the methodology and techniques of meta-argumentation 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)

ABSTRACT: Rudolf Carnap’s “Empiricism, Semantics and Ontology” (ESO) has received a good deal of sympathetic interest over the years from philosophers who are not particularly sympathetic to verificationism, or suspicious of metaphysics in general. Recent work has favorably cited ESO in connection with doubts about the genuine content of debates in the metaphysics of material objects. But, when we look at how Carnap introduces his central notion of a ‘framework’, and the questions he wants to use it to deflate, (...) there seem to be significant differences in his approach and aim from that of contemporary deflationists about the metaphysics of material objects. This paper first looks at some of these differences, and suggests a way of seeing them as arising more from differences in focus and interest than fundamental approach. However, a further question is whether philosophers who may entirely disagree with Carnap about abstract entities, or the substantiveness of the debate between Realists and Idealists – possibly all of his negative conclusions in ESO - can really be seen as heirs to his approach and argument therein. We look first at his discussion of the Realism/Idealism debate, to sort out different aspects of his analysis, and determine to what extent one can disagree with it while not thinking this undermines other analyses using the same general strategy. In the course of this, we are able to distinguish the basic Carnapian analysis of metaphysical disputes, from the question of whether, if the analysis is correct, this actually subverts the disputes. I suggest that, if we put verificationism aside, ESO really provides us with an approach and a type of skeptical challenge more than an argument, and it is open to contemporary philosophers to think that this skeptical challenge can (or can’t) be met, or can be supplemented by further argument, on a case by case basis. (shrink)

Structured argumentation systems, and their implementation, represent an important research subject in the area of Knowledge Representation and Reasoning. Structured argumentation advances over abstract argumentation frameworks by providing the internal construction of the arguments that are usually defined by a set of (strict and defeasible) rules. By considering the structure of arguments, it becomes possible to analyze reasons for and against a conclusion, and the warrant status of such a claim in the context of a (...) knowledge base represents the main output of a dialectical process. Computing such statuses is a costly process, and any update to the knowledge base could potentially have a huge impact if done naively. In this work, we investigate the case of updates consisting of both additions and removals of pieces of knowledge in the Defeasible Logic Programming (DeLP) framework, first analyzing the complexity of the problem and then identifying conditions under which we can avoid unnecessary computations—central to this is the development of structures (e.g. graphs) to keep track of which results can potentially be affected by a given update. We introduce a technique for the incremental computation of the warrant statuses of conclusions in DeLP knowledge bases that evolve due to the application of (sets of) updates. We present the results of a thorough experimental evaluation showing that our incremental approach yields significantly faster running times in practice, as well as overall fewer recomputations, even in the case of sets of updates performed simultaneously. (shrink)

Rather than the art of putting forward logically valid arguments leading to Truth, argumentation is here viewed as the use of verbal means ensuring an agreement on what can be considered reasonable by a given group, on a more or less controversial matter. What is acceptable and plausible is always coconstructed by subjects engaging in verbal interaction. It is the dynamism of this exchange, realized not only in natural language, but also in a specific cultural framework, that has to (...) be accounted for. From this perspective, it is not enough to reconstruct patterns of reasoning. As logos is by definition both Reason and Language, abstract schemata have to be examined in their verbal realization in a given situation of discourse. Such an approach to arguments allows for a “thick” description taking into account their discursive and communicational aspects, as well as argumentation’s constitutive dialogism and its inscription in a set of common representations, opinions and beliefs (a doxa). This approach, exemplified by the analysis of a short text on stock options borrowed from the French newspaper Libération, is an attempt at establishing a dialogue between disciplines like argumentation theories, rhetorical criticism and discourse analysis. (shrink)

This paper studies the relation between persuasive argumentation and the speaker’s epistemic attitude. Dung-style abstract argumentation and dynamic epistemic logic provide the necessary tools to characterize the notion of persuasion. Within abstract argumentation, persuasive argumentation has been previously studied from a game-theoretic perspective. These approaches are blind to the fact that, in real-life situations, the epistemic attitude of the speaker determines which set of arguments will be disclosed by her in the context of a (...) persuasive dialogue. This work is a first step to fill this gap. For this purpose we extend one of the logics of Schwarzentruber et al. with dynamic operators, designed to capture communicative phenomena. A complete axiomatization for the new logic via reduction axioms is provided. Within the new framework, a distinction between actual persuasion and persuasion from the speaker’s perspective is made. Finally, we explore the relationship between the two notions. (shrink)

In this paper, we explore the relation between an agent’s doxastic attitude and her arguments in support of a given claim. Our main contribution is the design of a logical setting that allows us reason about binary arguments which are either in favour or against a certain claim. This is a setting in which arguments and propositions are the basic building blocks so that the concept of argument-based belief emerges in a straightforward way. We work against the background of Dung’s (...) abstract argumentation framework, extending it to a new setting in which we can study the formal properties of binary arguments as well as the larger structures they establish. This paper introduces a formal ‘two-dimensional’ language to talk about propositions and arguments, for which a sound and complete axiom system is provided. (shrink)

Much of the formal study of algorithmic concerns with respect to semantics for abstract argumentation frameworks has focused on the issue of computational complexity. In contrast matters regarding computability have been largely neglected. Recent trends in semantics have, however, started to concentrate not so much on the formulation of novel semantics but more on identifying common properties: for example, from basic ideas such as conflict-freeness through to quite sophisticated ideas such as serializability. The aim of this paper (...) is to look at the implications these more recent studies have for computability rather than computational complexity. (shrink)

In this paper, we propose an argumentation formalism that allows for both deductive and abductive argumentation, where ‘deduction’ is used as an umbrella term for both defeasible and strict ‘forward’ inference. Our formalism is based on an extended version of our previously proposed information graph formalism, which provides a precise account of the interplay between deductive and abductive inference and causal and evidential information. In the current version, we consider additional types of information such as abstractions which allow (...) domain experts to be more expressive in stating their knowledge, where we identify and impose constraints on the types of inferences that may be performed with the different types of information. A new notion of attack is defined that captures a crucial aspect of abductive reasoning, namely that of competition between abductively inferred alternative explanations. Our argumentation formalism generates an abstract argumentation framework and thus allows arguments to be formally evaluated. We prove that instantiations of our argumentation formalism satisfy key rationality postulates. (shrink)