This paper considers various aspects of representing arguments and logical argumentation frameworks. We investigate different approaches to address consistency and minimality within such frameworks, arguing that these properties can, and in some cases should, be omitted from the definition of an argument. We analyze the relationship between how consistency is verified and the selection of attack rules, showing that this choice should align with the underlying logic. Based on these results, we propose compact representations of logical argumentation frameworks and examine methods for transforming one framework into another (e.g., a more concise version) without losing logical entailments.

In this paper, we introduce novel methods for drawing conclusions from inconsistent information in a highly cautious manner. While standard paraconsistent approaches typically rely on the formulas in the intersection of maximally consistent subsets, known as the free formulas, we argue that not all these formulas share the same degree of reliability. Our refined reasoning frameworks distinguish between free formulas, based on their actual involvement in the inconsistency, an so enabling inference only when conclusions are robustly supported. These methods are particularly valuable in high-stakes contexts where decisions carry irreversible or far-reaching consequences. We present several implementation techniques grounded in multi-valued semantics and syntactic independence, analyze their fundamental logical properties, and establish a hierarchy of their inferential strength.

This paper continues an established line of research about the relations between argumentation theory, particularly assumption-based argumentation, and different kinds of logic programs. In particular, we extend known result of Bondarenko, Dung, Kowalski and Toni, and of Caminada and Schulz, by showing that assumption-based argumentation can represent not only normal logic programs, but also disjunctive logic programs under the stable model semantics. For this, we consider some inference rules for disjunction that the core logic of the argumentation frameworks should respect, and show the correspondence to the handling of disjunctions in the heads of the logic programs’ rules.

Logic-based argumentation is a formal method for constructing, evaluating and comparing arguments. In this paper we address two (related) key issues concerning the representation of logical argumentation frameworks: how to describe them in a compact way, and how to move from one framework to another while preserving their basic logical characteristics. The results are applied to various forms of attack rules and different kinds of argumentative semantics, and are demonstrated for transitions between several 3-valued logics and classical logic. As a byproduct, our results are also used for converting logic-based argumentation frameworks to assumption-based argumentation frameworks.

In this paper, we consider assumption-based argumentation frameworks that are based on contrapositive logics and partially-ordered preference functions. It is shown that these structures provide a general and solid platform for representing and reasoning with conflicting and prioritized arguments. Two useful properties of the preference functions are identified (selectivity and max-lower-boundedness), and extended forms of attack relations are supported (there exists-attacks and for all-attacks), which assure several desirable properties and a variety of formal settings for argumentation-based conclusion drawing. These two variations of attacks maybe further extended to collective attacks. Such (existential or universal) collective attacks allow to challenge a collective of assertions rather than single assertions. We show that these extensions not only enhance the expressive power of the framework, but in certain cases also enable more rational patterns of reasoning with conflicting assertions.

Approximation fixpoint theory (AFT) is an abstract and general algebraic framework for studying the semantics of nonmonotonic logics. It provides a unifying study of the semantics of different formalisms for nonmonotonic reasoning, such as logic programming, default logic and autoepistemic logic. In this paper, we extend AFT to dealing with non-deterministic constructs that allow to handle indefinite information, represented e.g. by disjunctive formulas. This is done by generalizing the main constructions and corresponding results of AFT to non-deterministic operators, whose ranges are sets of elements rather than single elements. The applicability and usefulness of this generalization is illustrated in the context of disjunctive logic programming.

Conflicts in argumentation-based frameworks are usually described in terms of attacks of arguments, or sets of arguments, on specific counter-arguments. In this paper we consider (assumption-based) argumentation frameworks, in which attacks have a more general form: they are performed on a collective of arguments that cannot stand together with the attacking arguments. We show that not only that this generalized form of attacks increases the expressive power of the argumentation frameworks, but in certain cases it also allows more sensible patterns of reasoning with conflicting considerations. Along the way, we also provide a novel characterization of the grounded semantics in prioritized argumentation frameworks.

Assumption-based argumentation (ABA) is an argumentative formalism that allows for reasoning on the basis of defeasible assumptions and strict rules. Standard semantics for this formalism sometimes give rise to problematic behaviour in the presence of rules with assumptions in their heads. In this paper, we introduce a six-valued labelling semantics that overcomes these shortcomings while preserving all the usual properties of the standard Dung-style three-valued semantics for ABA frameworks, including existence of the complete semantics, uniqueness of the grounded semantics and preservation of the computational complexity of all main reasoning processes.

We present a novel computational approach to resolving conflicts among norms by nonmonotonic normative reasoning (in constrained I/O logics). Our approach extends standard sequent-based proof systems and makes them more adequate to nonmonotonic reasoning by adding to the sequents annotations that keep track of what is known about the defeasible status of the derived sequents. This makes transparent the reasons according to which norms should be applicable or inapplicable, and accordingly the sequents that make use of such norms are accepted or retracted. We also show that this proof theoretic method has tight links to the semantics of formal argumentation frameworks. The outcome of this paper is thus a threefold characterization result that relates, in the context of nonmonotonic normative reasoning, three traditional ingredients of AI-based reasoning methods: maximally consistent sets of premises (in constrained I/O logics), derived sequents (which are accepted in corresponding annotated sequent calculi), and logical arguments (that belong to the grounded extensions of the induced logical argumentation frameworks).

Conflicts are inherent to normative systems. In this paper, we explore a novel approach to normative reasoning by quantifying the amount of conflicts within normative systems. We refine the idea from classical logic, according to which a formula is a consequence of a knowledge base in case its negation renders the knowledge base inconsistent. In our approach, whether a formula is a logical consequence depends, for instance, on its negation's marginal contribution to the inconsistency of the given knowledge base. Accordingly, various inconsistency measures and corresponding (nonmonotonic and paraconsistent) normative entailment relations are analyzed relative to a number of logical properties. To illustrate our approach, we adopt Input/Output logic, a renowned formalism in deontic logic, specifically designed for defeasible normative reasoning. As an application, the resulting entailment relations provide recommendations to agents for minimizing norm conflicts, and may be incorporated in a number of implementations (like the Tweety libraries and the LogiKey framework) by involving inconsistency measurements in normative reasoning.

We show that assumption-based argumentation frameworks, based on contrapositive logics and partially-ordered preference functions, provide a solid platform for argumentation-based reasoning. Two useful properties of the preference functions are identified (selectivity and max-lower-boundedness), and extended forms of attacks relations are supported (exists-attacks and forall-attacks), which assure several desirable properties and a variety of reasoning modes.

Logical argumentation is a well-known approach to modeling non-monotonic reasoning with conflicting information. In this paper we provide a comprehensive postulate-based study of properties of logical argumentation frameworks and a full characterization of their semantics and inference relations. In this way we identify well-behaved formal argumentative models of drawing logically justified inferences from a given set of possibly conflicting defeasible, as well as strict assumptions. Given some desiderata in terms of rationality postulates, we consider the conditions that an argumentation framework should fulfill for the desiderata to hold. One purpose of this approach is to assist designers to “plug-in” pre-defined formalisms according to actual needs. To this end, we present a classification of argumentation frameworks relative to the types of attacks they implement. In turn, for each class we determine which desiderata are satisfied. Our study is highly abstract, supposing only a minimal set of requirements on the considered underlying deductive systems, and in this way covering a broad range of formalisms, including classical, intuitionistic and modal logics.

We introduce annotated sequent calculi, which are extensions of standard sequent calculi, where sequents are combined with annotations that represent their derivation statuses. Unlike in ordinary calculi, sequents that are derived in annotated calculi may still be retracted in the presence of conflicting sequents, thus inferences are made under stricter conditions. Conflicts in the resulting systems are handled like in adaptive logics and argumentation theory. The outcome is a robust family of proof systems for non-monotonic reasoning with inconsistent information, where revision considerations are fully integrated into the object level of the proofs. These systems are shown to be strongly connected to logical argumentation.

Explainable artificial intelligence (XAI) has gained increasing interest in recent years in the argumentation community. In this paper we consider this topic in the context of logic-based argumentation, showing that the latter is a particularly promising paradigm for facilitating explainable AI. In particular, we provide two representations of abductive reasoning by sequent-based argumentation frameworks and show that such frameworks successfully cope with related challenges, such as the handling of synonyms, justifications, and logical equivalences.

We show that logic-based argumentation, and in particular sequent-based frameworks, is a robust argumentative setting for abductive reasoning and explainable artificial intelligence.

Simple contrapositive assumption-based argumentation frameworks are a general setting for structured argumentation, providing a robust approach to reasoning with arguments and counter-arguments. In this paper we extend these frameworks with priorities and introduce some new results concerning the Dung's semantics of the resulting formalisms.

In this paper we provide a detailed analysis of the inference process induced by logical argumentation frameworks. The frameworks may be defined with respect to any propositional language and logic, different arguments that represent deductions in the logic, various support-based attack relations between arguments, and all the complete Dung-style semantics for the frameworks. We show that, ultimately, for characterizing the inference process with respect to a given framework, extension-based semantics may be divided into two types: single-extension and multiple-extension, which induce respective kinds of entailment relations. These entailments are further classified by the way they tolerate new information (nonmonotonicity-related properties) and maintain conflicts among arguments (inconsistency-related properties).

In this paper we make a contribution to the unification of formal models of defeasible reasoning. We present several translations between formal argumentation frameworks and nonmonotonic logics for reasoning with plausible assumptions. More specifically, we translate adaptive logics into assumption-based argumentation and ASPIC+, ASPIC+ into assumption-based argumentation and a fragment of assumption-based argumentation into adaptive logics. Adaptive logics are closely related to Makinson's default assumptions and to a significant class of systems within the tradition of preferential semantics in the vein of KLM and Shoham. Thus, our results also provide close links between formal argumentation and the latter approaches.

We recall some of the better known approaches to non-classical logics, with an emphasis on the contributions of Arnon Avron to the subject and in relation to the papers in this volume.

We examine different methods of handling argument consistency and minimality in logical argumentation frameworks, showing that both properties may (and sometimes even should) be omitted from the definition of arguments. In process, we consider the adequacy of attack rules to the underlying logics.