A Translation-Based Approach for Revision of Argumentation Frameworks

Dung's argumentation framework is an abstract framework based on a set of arguments and a binary attack relation defined over the set. One instantiation, among many others, of Dung's framework consists in constructing the arguments from a set of propositional logic formulas. Thus an argument is seen as a reason for or against the truth of a particular statement. Despite its advantages, the argumentation approach for inconsistency handling also has important shortcomings. More precisely, in some applications what one is interested in are not so much only the conclusions supported by the arguments but also the precise explications of such conclusions. We show that argumentation framework applied to classical logic formulas is not suitable to deal with this problem. On the other hand, intuitionistic logic appears to be a natural alternative candidate logic (instead of classical logic) to instantiate Dung's framework. We develop constructive argumentation framework. We show that intuitionistic logic offers nice and desirable properties of the arguments. We also provide a characterization of the arguments in this setting in terms of minimal inconsistent subsets when intuitionistic logic is embedded in the modal logic S4.

The Attack-Support Argumentation Framework (ASAF) is an abstract argumentation framework that provides a unified setting for representing attack and support for arguments, as well as attack and support for the attack and support relations at any level. Currently, the extensions of the ASAF are obtained by translating it into a Dung's Argumentation Framework (AF). In this work we provide the ASAF with the ability of determining its extensions without requiring such a translation. We follow an extension-based approach for characterizing the acceptability semantics directly on the ASAF, considering the complete, preferred, stable and grounded semantics. Finally, we show that the proposed characterization satisfies different results from Dung's argumentation theory.

Credulous acceptance in high-order argumentation frameworks with necessities: An incremental approach

The propositional revision operator is a special theory change operator. In this paper we give examples for the generalized propositional revision operator in the weighted case. The examples are new not only from the point of view of the technique of the construction of a concrete revision operator for weighted knowledge bases, but also in their semantics. Furthermore, the application shows that under the given semantic the usage of a revision operator for weighted knowledge bases can solve also the update problem in some cases.

We propose a logical encoding of extended abstract argumentation frameworks, that is frameworks with higher-order attacks (i.e. attacks whose targets are other attacks). Our purpose is to separate the logical expression of the meaning of an attack (simple or higher-order) from the logical expression of acceptability semantics. We consider semantics which specify the conditions under which the arguments (resp. the attacks) are considered as accepted, directly on the extended framework, without translating the original framework into a Dung's argumentation framework. We characterize the output of a given framework in logical terms (namely as particular models of a logical theory). Our proposal applies to the particular case of Dung's frameworks, enabling to recover standard extensions.

The system ASPARTIX is a tool for computing acceptable extensions for a broad range of formalizations of Dung's argumentation framework and generalizations thereof. ASPARTIX relies on a fixed disjunctive datalog program which takes an instance of an argumentation framework as input, and uses the answer-set solver DLV for computing the type of extension specified by the user.

Argumentative reasoning and taxonomic analysis for the identification of medical errors

This paper reconsiders Modgil's Extended Argumentation Frameworks EAFs that extend Dung's abstract argumentation frameworks by attacks on attacks. This allows to encode preferences directly in the framework and thus also to reason about the preferences themselves. As a first step to reduction-based approaches to implement EAFs, we give an alternative but equivalent characterization of acceptance in EAFs. Then we use this characterization to provide EAF encodings for answer set programming and propositional logic. Moreover, we address an open complexity question and the expressiveness of EAFs.

Claim-augmented argumentation frameworks (CAFs) constitute a generic formalism for conflict resolution of conclusion-oriented problems in argumentation. CAFs extend Dung argumentation frameworks (AFs) by assigning a claim to each argument. So far, semantics for CAFs are defined with respect to the underlying AF by interpreting the extensions of the respective AF semantics in terms of the claims of the accepted arguments; we refer to them as inherited semantics of CAFs.<br>A central concept of many argumentation semantics is maximization, which can be done with respect to arguments as in preferred semantics, or with respect to the range as in semi-stable semantics. However, common instantiations of argumentation frameworks require maximality on the claim-level and inherited semantics often fail to provide maximal claim-sets even if the underlying AF semantics yields maximal argument sets. To address this issue, we investigate a different approach and introduce claim-level semantics (cl-semantics) for CAFs where maximization is performed on the claim-level. We compare these two approaches for five prominent semantics (preferred, naive, stable, semi-stable, and stage) and relate in total eleven CAF semantics to each other. Moreover, we show that for a certain subclass of CAFs, namely well-formed CAFs, the different versions of preferred and stable semantics coincide, which is not the case for the remaining semantics. We furthermore investigate a recently established translation between well-formed CAFs and SETAFs and show that, in contrast to the inherited naive, semi-stable and stage semantics, the cl-semantics correspond to the respective SETAF semantics. Finally, we investigate the expressiveness of the considered semantics in terms of their signatures.

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.

In this paper we further progress the analysis of the recently introduced multi-valued argumentation frameworks (MVAFs). MVAFs are an extension of Dung's abstract argumentation, where arguments have a degree of truth associated with them. Here we describe a list of properties of MVAFs considering the major multi-valued logics such as those proposed by Gödel, Zadeh and Łukasiewicz. We then propose a computational framework that joins multi-valued and probabilistic argumentation frameworks to handle situations where arguments affected by vagueness and/or probabilities coexist. The findings are a contribution to the field of non-monotonic approximate reasoning and they also represent a well-grounded proposal towards the introduction of gradualism in argumentation systems.

In this paper we extend the traditional Dung argumentation framework with cardinality constraints over the set of warranted arguments. This results in a new definition for argumentation semantics wherein arguments within an extension are both in some sense consistent and compliant with the constraints imposed on the system. After discussing the theoretical aspects of such a resource-bounded argumentation framework we describe its utility via an application to a concrete application domain: the scheduling of demand responsive transport.

BOOK REVIEWS Prior, A.N., Formal Logic. Oxford: The Clarendon Press, 1955. Pp. ix—329. $5.60. In the preface, the author indicates that this book is designed primarily as a textbook, though he hopes that it will prove to be of interest to others who are not Logic students. The content, which includes; Part I — The Classical Prepositional and Functional Calculi; Part II — The Traditional Logic of Terms; and Part HI — Modal, Three-valued and Extensional Systems ; is of such a nature that it should attract a variety of critico-analytical, perceptive readers other than those solely interested in Logic. Part I of the triparted arrangement commences with 'Truth-Functions and Tautologies' and is a systematic study of tautologous implications derived from fixed rules of transformation or inference and their relation to systems of tautologous alterations and conjunctions. In the axiomatizations of the Propositional Calculus to obtain a mechanical accuracy, a rigorously fixed symbolism is employed to express the laws laid down and established, as well as to represent the processes of proof. Using axioms and rules the author shows that these axioms are 'complete' and sufficient, not only to prove all tautologous formulae in the propositional calculus, but also to disprove all non-tautologous ones. Besides the fundamental axioms found in the Principia Mathematica of Whitehead and Russell, the newer and more economical ones derived by Lukasiewicz, and Hubert and Ackerman are employed. In answer to the question 'Why should the logician, whose primary interest is in inference, study other tautologous formulae beside those which are implications ?', the chapter entitled 'System with Propositional Constants and Functional Variables', is an attempt to show that all other tautologous formulae are either implications or definitional abbreviations for them. In defense of this thesis there are sections about The Implicational Calculus and Wajsberg's System in C and 0; Quine's Completeness Proof for the Full Calculus; Wajsberg's Completeness Proof for the Restricted Calculus; and Logic, Metalogic, and the Functorial Variables. Especially well expressed and explained in connection with the Theory of Quantification is the portion of the text on propositional operators, which form propositions, not out of other propositions, but out of names. The author illucidates the manner in which these new types of propositional formulae are introduced, and substituted for propositional variables in theses of the propositional calculus. With keen and astute logical acumen, he draws attention to the fact that there is a close resemblance (1) between the laws of equipollence and the principles now known as de Morgan Laws ; and (2) between universal quantification and conjunction, and existential quantification and alteration. 407 4o8Book-Reviews A. N. Prior's critical ability is especially pronounced in connection with 'Quantification and Equivalential Calculi: Definition Re-examined.' The work on extension, by the use of quantifiers and functional variables, of versions of the propositional calculus in which the only undefined truth-factor is E, 'If and only if,' includes the interesting note that Leániewski's special interest in a protothenic with an 'equivalential' basis arose from the personal view that he held about the nature of definition in formal systems. The author's account of definitions as assertions of equivalence include the contributions of Leániewski, Tarski and Sobocinski, who espoused the theory in its entirety, and of Lukasiewicz and Meredith, who partially adopted it. Despite the opinions of this distinguished company, the author clearly states that the conclusion of the account is wrong-headed and he shows that it makes it difficult to distinguish the definitions of a system from additional axioms. Indeed worthy of critical study, is Part II which is a truly remarkable synthesis of the Traditional Logic of Terms, that commences with the Aristotelian Syllogistic; is followed by a comprehensive treatment of Categorical Forms with Negative, Complex, and Quantified Terms; and concludes with Singular and Existential Propositions. When Professor Prior discusses Singulars and Generals in Traditional and Modern Logic, he explains with keen perception that there is a large element of anachronism in attributing to Aristotle any satisfactory way of interpreting his forms in the modern functional calculus and at the same time 'saving' all or most of his laws. The elaborate body of thought of...

One goal of normative multi-agent system theory is to formulate principles for normative system change that maintain the rule-like structure of norms and preserve links between norms and individual agent obligations. A central question raised by this problem is whether there is a framework for norm change that is at once specific enough to capture this rule-like behavior of norms, yet general enough to support a full battery of norm and obligation change operators. In this paper we propose an answer to this question by developing a bimodal logic for norms and obligations called NO. A key to our approach is that norms are treated as propositional formulas, and we provide some independent reasons for adopting this stance. Then we define norm change operations for a wide class of modal systems, including the class of NO systems, by constructing a class of modal revision operators that satisfy all the AGM postulates for revision, and constructing a class of modal contraction operators that satisfy all the AGM postulates for contraction. More generally, our approach yields an easily extendable framework within which to work out principles for a theory of normative system change.

Argument-based reasoning offers promising interaction and computation mechanisms for multi-agent negotiation and deliberation. Arguments in this context are typically statements of beliefs or actions related to agents' subjective values, preferences and so on. Consequences of such arguments can and should be evaluated using various criteria, and therefore it is desirable that semantics supports these criteria as principles for accepting arguments. This article gives an instance of Dung's abstract argumentation framework to deal with Pareto optimality, i.e. a fundamental criterion for social welfare. We show that the instance allows Dung's acceptability semantics to interpret Pareto optimal arguments, without loss of generality. We discuss the prospects of justified Pareto optimal arguments and Pareto optimal extensions.