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)

In abstract argumentation, each argument is regarded as atomic. There is no internal structure to an argument. Also, there is no specification of what is an argument or an attack. They are assumed to be given. This abstract perspective provides many advantages for studying the nature of argumentation, but it does not cover all our needs for understanding argumentation or for building tools for supporting or undertaking argumentation. If we want a more detailed formalization of arguments than is available with (...) abstract argumentation, we can turn to structured argumentation, which is the topic of this special issue of Argument and Computation. In structured argumentation, we assume a formal language for representing knowledge and specifying how arguments and counterarguments can be constructed from that knowledge. An argument is then said to be structured in the sense that normally, the premises and claim of the argument are made explicit, and the relationship between the premises and claim is formally defined (for instance, using logical entailment). In this introduction, we provide a brief overview of the approaches covered in this special issue on structured argumentation. (shrink)

Argumentation represents a way of reasoning over a knowledge base containing possibly incomplete and/or inconsistent information, to obtain useful conclusions. As a reasoning mechanism, the way an argumentation reasoning engine reaches these conclusions resembles the cognitive process that humans follow to analyze their beliefs; thus, unlike other computationally reasoning systems, argumentation offers an intellectually friendly alternative to other defeasible reasoning systems. LogicProgrammingisacomputationalparadigmthathasproducedcompu- tationallyattractivesystemswithremarkablesuccessinmanyapplications. Merging ideas from both areas, Defeasible Logic Programming offers a computational reasoning system that uses an argumentation engine (...) to obtain answers from a knowledge base represented using a logic programming language extended with defeasible rules. This combination of ideas brings about a computationally effective system together with a human-like reasoning model facilitating its use in applications. (shrink)

Mathematicians often speak of conjectures, yet unproved, as probable or well-confirmed by evidence. The Riemann Hypothesis, for example, is widely believed to be almost certainly true. There seems no initial reason to distinguish such probability from the same notion in empirical science. Yet it is hard to see how there could be probabilistic relations between the necessary truths of pure mathematics. The existence of such logical relations, short of certainty, is defended using the theory of logical probability (or objective Bayesianism (...) or non-deductive logic), and some detailed examples of its use in mathematics surveyed. Examples of inductive reasoning in experimental mathematics are given and it is argued that the problem of induction is best appreciated in the mathematical case. (shrink)

We present a formal, mathematical model of argument structure and evaluation, taking seriously the procedural and dialogical aspects of argumentation. The model applies proof standards to determine the acceptability of statements on an issue-by-issue basis. The model uses different types of premises (ordinary premises, assumptions and exceptions) and information about the dialectical status of statements (stated, questioned, accepted or rejected) to allow the burden of proof to be allocated to the proponent or the respondent, as appropriate, for each premise separately. (...) Our approach allows the burden of proof for a premise to be assigned to a different party than the one who has the burden of proving the conclusion of the argument, and also to change the burden of proof or applicable proof standard as the dialogue progresses from stage to stage. Useful for modeling legal dialogues, the burden of production and burden of persuasion can be handled separately, with a different responsible party and applicable proof standard for each. Carneades enables critical questions of argumentation schemes to be modeled as additional premises, using premise types to capture the varying effect on the burden of proof of different kinds of questions. (shrink)

This article discusses how inference to the best explanation can be justified as a practical meta - argument. It is, firstly, justified as a practical argument insofar as accepting the best explanation as true can be shown to further a specific aim. And because this aim is a discursive one which proponents can rationally pursue in — and relative to — a complex controversy, namely maximising the robustness of one’s position, IBE can be conceived, secondly, as a meta - argument. (...) My analysis thus bears a certain analogy to Sellars ’ well - known justification of inductive reasoning ; it is based on recently developed theories of complex argumentation. (shrink)

Formal dialogue systems model rule-based interaction between agents and as such have multiple applications in multi-agent systems and AI more generally. Their conceptual roots are in formal theories of natural argumentation, of which Hamblin’s formal systems of argumentation in Hamblin (Fallacies. Methuen, London, 1970, Theoria 37:130–135, 1971) are some of the earliest examples. Hamblin cites the medieval theory of obligationes as inspiration for his development of formal argumentation. In an obligatio, two agents, the Opponent and the Respondent, engage in an (...) alternating-move dialogue, where the Respondent’s actions are governed by certain rules, and the goal of the dialogue is establishing the consistency of a proposition. We implement obligationes in the formal dialogue system framework of Prakken (Knowl Eng Rev 21(2):163–188, 2006) using Dynamic Epistemic Logic (van Ditmarsch et al. in Dynamic epistemic logic, Synthese Library Series. Springer, Berlin, 2007). The result is a new type of inter-agent dialogue, for consistency-checking, and analyzing obligationes in this way also sheds light on interpretational and historical questions concerning their use and purpose in medieval academia. (shrink)

This paper presents a theory of reasoning with evidence in order to determine the facts in a criminal case. The focus is on the process of proof, in which the facts of the case are determined, rather than on related legal issues, such as the admissibility of evidence. In the literature, two approaches to reasoning with evidence can be distinguished, one argument-based and one story-based. In an argument-based approach to reasoning with evidence, the reasons for and against the occurrence of (...) an event, e.g., based on witness testimony, are central. In a story-based approach, evidence is evaluated and interpreted from the perspective of the factual stories as they may have occurred in a case, e.g., as they are defended by the prosecution. In this paper, we argue that both arguments and narratives are relevant and useful in the reasoning with and interpretation of evidence. Therefore, a hybrid approach is proposed and formally developed, doing justice to both the argument-based and the narrative-based perspective. By the formalization of the theory and the associated graphical representations, our proposal is the basis for the design of software developed as a tool to make sense of the evidence in complex cases. (shrink)

This paper argues that some traditional fallacies should be considered as reasonable arguments when used as part of a properly conducted dialog. It is shown that argumentation schemes, formal dialog models, and profiles of dialog are useful tools for studying properties of defeasible reasoning and fallacies. It is explained how defeasible reasoning of the most common sort can deteriorate into fallacious argumentation in some instances. Conditions are formulated that can be used as normative tools to judge whether a given defeasible (...) argument is fallacious or not. It is shown that three leading violations of proper dialog standards for defeasible reasoning necessary to see how fallacies work are: (a) improper failure to retract a commitment, (b) failure of openness to defeat, and (c) illicit reversal of burden of proof. (shrink)

This paper gives an explication of our intuitive notion of strength of justification in a controversial debate. It defines a thesis' degree of justification within the bipolar argumentation framework of the theory of dialectical structures as the ratio of coherently adoptable positions according to which that thesis is true over all coherently adoptable positions. Broadening this definition, the notion of conditional degree of justification, i.e.\ degree of partial entailment, is introduced. Thus defined degrees of justification correspond to our pre-theoretic intuitions (...) in the sense that supporting and defending a thesis t increases, whereas attacking it decreases, t's degree of justification. Moreover, it is shown that (conditional) degrees of justification are (conditional) probabilities. Eventually, the paper explains that it is rational to believe theses with a high degree of justification insofar as this strengthens the robustness of one's position. (shrink)

To create a programming environment for contract dispute resolution, we propose an extension of assumption-based argumentation into modular assumption-based argumentation in which different modules of argumentation representing different knowledge bases for reasoning about beliefs and facts and for representation and reasoning with the legal doctrines could be built and assembled together. A distinct novel feature of modular argumentation in compare with other modular logic-based systems like Prolog is that it allows references to different semantics in the same module at the (...) same time, a feature critically important for application of argumentation in legal domains like contract dispute resolution where the outcomes of court cases often depend on whether credulous or skeptical modes of reasoning were applied by the contract parties. We apply the new framework to model the doctrines of contract breach and mutual mistake. (shrink)

1. The benefits resulting from a combination of quantitative (e.g. probabilistic) and qualitative (e.g. logic-based) reasoning are widely acknowledged (e.g. see Domingos et al., 2006; Poole, 2011)....

Can argumentation form the basis for any form of reasoning, informal or formal logical reasoning? We examine this question from the particular perspective of the recent developments in logic-based Artificial Intelligence (AI). We propose that argumentation provides the wider framework encompassing uniformly all reasoning, with strict or formal logical reasoning being a special boundary case. We also attempt to link this unifying role of argumentation with Aristotle’s original investigation of methods and forrmalisms for the systematic study of human reasoning.

This paper aims at comparing and relating belief revision and argumentation as approaches to model reasoning processes. Referring to some prominent literature references in both fields, we will discuss their (implicit or explicit) assumptions on the modeled processes and hence commonalities and differences in the forms of reasoning they are suitable to deal with. The intended contribution is on one hand assessing the (not fully explored yet) relationships between two lively research fields in the broad area of defeasible reasoning and (...) on the other hand pointing out open issues and potential directions for future research. (shrink)

The Toulmin model has been proved useful in law and argumentation theory. This model describes the basic process in justifying a claim, which comprises six elements, i.e., claim (C), data (D), warrant (W), backing (B), qualifier (Q), and rebuttal (R). Specifically, in justifying a claim, one must put forward ‘data’ and a ‘warrant’, whereas the latter is authorized by ‘backing’. The force of the ‘claim’ being justified is represented by the ‘qualifier’, and the condition under which the claim cannot be (...) justified is represented as the ‘rebuttal’. To further improve the model, (Goodnight, Informal Logic 15:41–52, 1993) points out that the selection of a backing needs justification, which he calls legitimation justification. However, how such justification is constituted has not yet been clarified. To identify legitimation justification, we separate it into two parts. One justifies a backing’s eligibility (legitimation justification 1 ; LJ 1 ); the other justifies its superiority over other eligible backings (legitimation justification 2 ; LJ 2 ). In this paper, we focus on LJ 1 and apply it to the legal justification (of judgements) in hard cases for illustration purposes. We submit that LJ 1 refers to the justification of the legal interpretation of a norm by its backing, which can be further separated into several orderable subjustifications. Taking the subjustification of a norm’s existence as an example, we show how it would be influenced by different positions in the philosophy of law. Taking the position of the theory of natural law, such subjustification is presented and evaluated. This paper aims not only to inform ongoing theoretical efforts to apply the Toulmin model in the legal field, but it also seeks to clarify the process in the justification of legal judgments in hard cases. It also offers background information for the possible construction of related AI systems. In our future work, LJ 2 and other subjustifications of LJ 1 will be discussed. (shrink)

The Handbook of Formal Argumentation is a community effort aimed at providing a comprehensive and up-to-date view of the state of the art and current trends in the lively research field of formal argumentation. The first volume of the Handbook is organised into five parts, containing nineteen chapters in all, each written by leading experts in the field. The first part provides a general and historical perspective on the field. The second part gives a comprehensive coverage of the argumentation formalisms (...) available in the literature at various levels of abstraction. The third part is devoted to cover some of the many dialogical aspects of argumentation, while the fourth one deals with algorithmic, computational and implementation issues. Finally, the fifth part provides some deeper analyses on the previously introduced topics. The Handbook of Formal Argumentation is an open-ended initiative of which the present volume is the first outcome. Further volumes are planned to cover topics not included in the present one and the initiative is conceived to grow by the support and feeding it receives from the community members. (shrink)

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 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)

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)

A paramount, yet unresolved issue in personalised medicine is that of automated reasoning with clinical guidelines in multimorbidity settings. This entails enabling machines to use computerised generic clinical guideline recommendations and patient-specific information to yield patient-tailored recommendations where interactions arising due to multimorbidities are resolved. This problem is further complicated by patient management desiderata, in particular the need to account for patient-centric goals as well as preferences of various parties involved. We propose to solve this problem of automated reasoning with (...) interacting guideline recommendations in the context of a given patient by means of computational argumentation. In particular, we advance a structured argumentation formalism ABA+G (short for Assumption-Based Argumentation with Preferences (ABA+) and Goals) for integrating and reasoning with information about recommendations, interactions, patient’s state, preferences and prioritised goals. ABA+G combines assumption-based reasoning with preferences and goal-driven selection among reasoning outcomes. Specifically, we assume defeasible applicability of guideline recommendations with the general goal of patient well-being, resolve interactions (conflicts and otherwise undesirable situations) among recommendations based on the state and preferences of the patient, and employ patient-centered goals to suggest interaction-resolving, goal-importance maximising and preference-adhering recommendations. We use a well-established Transition-based Medical Recommendation model for representing guideline recommendations and identifying interactions thereof, and map the components in question, together with the given patient’s state, prioritised goals, and preferences over actions, to ABA+G for automated reasoning. In this, we follow principles of patient management and establish corresponding theoretical properties as well as illustrate our approach in realistic personalised clinical reasoning scenaria. (shrink)

The principle-based approach is a methodology to classify and analyse argumentation semantics. In this paper we classify seven of the main alternatives for argumentation semantics using a set of new robustness principles. These principles complement Baroni and Giacomin’s original classification and deal with the behaviour of a semantics when the argumentation framework changes due to the addition or removal of an attack between two arguments. We distinguish so-called persistence principles and monotonicity principles, where the former deal with the question of (...) whether a labelling or extension of an argumentation framework under a given semantics persists after a change, and the latter with the question of whether new labellings or extensions are created after a change. We furthermore show in which sense labelling-based and extension-based semantics lead to subtly different principles and results. Our results can be used for choosing a semantics for a particular application, or to guide the search for new argumentation semantics, but they have been used also in the design of algorithms. (shrink)

Structured argumentation formalisms, such as ASPIC +, offer a formal model of defeasible reasoning. Usually such formalisms are highly parametrized and modular in order to provide a unifying framework in which different forms of reasoning can be expressed. This generality comes at the price that, in their most general form, formalisms such as ASPIC + do not satisfy important rationality postulates, such as non-interference. Similarly, links to other forms of knowledge representation, such as reasoning with maximal consistent sets of rules, (...) are insufficiently studied for ASPIC + although such links have been established for other, less complex forms of structured argumentation where defeasible rules are absent. Clearly, for a formal model of defeasible reasoning it is important to understand for which range of parameters the formalism displays a behavior that adheres to common standards of consistency, logical closure and logical relevance and can be adequately described in terms of other well-known forms of knowledge representation. In this paper we answer this question positively for a fragment of ASPIC + without the attack form undercut by showing that it satisfies all standard rationality postulates of structured argumentation under stable and preferred semantics and is adequate for reasoning with maximal consistent sets of defeasible rules. The study is general in that we do not impose any other requirements on the strict rules than to be contrapositable and propositional and in that we also consider priorities among defeasible rules, as long as they are ordered by a total preorder and lifted by weakest link. In this way we generalize previous similar results for other structured argumentation frameworks and so shed further light on the close relations between assumption-based argumentation and ASPIC +. (shrink)

According to the argument scheme approach, to evaluate a given scheme-saturating instance completely does entail asking all critical questions relevant to it. Although this is a central task for argumentation theorists, the field currently lacks a method for providing a complete argument evaluation. Approaching this task at the meta-level, we combine a logical with a substantive approach to the argument schemes by starting from Toulmin’s schema: ‘data, warrant, so claim’. For the yet more general schema: ‘premise; if premise, then conclusion; (...) so conclusion’, we forward a meta-level CQ-list that is arguably both complete and applicable. This list should inform ongoing theoretical efforts at generating appropriate object-level CQs for specific argument schemes. (shrink)