We address the issue of defining a semantics for deontic argumentation that supports weak permission. Some recent results show that grounded semantics do not support weak permission when there is a conflict between two obligations. We provide a definition of Deontic Argumentation Theory that accounts for weak permission, and we recall the result about grounded semantics. Then, we propose a new semantics that supports weak permission.

In cooperative human decision-making, agreements are often not total; a partial degree of agreement is sufficient to commit to a decision and move on, as long as one is somewhat confident that the involved parties are likely to stand by their commitment in the future, given no drastic unexpected changes. In this paper, we introduce the notion of agreement scenarios that allow artificial autonomous agents to reach such agreements, using formal models of argumentation, in particular abstract argumentation and value-based argumentation. We introduce the notions of degrees of satisfaction and (minimum, mean, and median) agreement, as well as a measure of the impact a value in a value-based argumentation framework has on these notions. We then analyze how degrees of agreement are affected when agreement scenarios are expanded with new information, to shed light on the reliability of partial agreements in dynamic scenarios. An implementation of the introduced concepts is provided as part of an argumentation-based reasoning software library.

In recent years, large language models (LLMs) have made significant advancements in neuro-symbolic computing. However, the combination of LLM with argumentation computation remains an underexplored domain, despite its considerable potential for real-world applications requiring defeasible reasoning. In this paper, we aim to investigate the capability of LLMs in determining the extensions of various abstract argumentation semantics. To achieve this, we develop and curate a benchmark comprising diverse abstract argumentation frameworks, accompanied by detailed explanations of algorithms for computing extensions. Subsequently, we fine-tune LLMs on the proposed benchmark, focusing on two fundamental extension-solving tasks. As a comparative baseline, LLMs are evaluated using a chain-of-thought approach, where they struggle to accurately compute semantics. In the experiments, we demonstrate that the process explanation plays a crucial role in semantics computation learning. Models trained with explanations show superior generalization accuracy compared to those trained solely with question-answer pairs. Furthermore, by leveraging the self-explanation capabilities of LLMs, our approach provides detailed illustrations that mitigate the lack of transparency typically associated with neural networks. Our findings contribute to the broader understanding of LLMs' potential in argumentation computation, offering promising avenues for further research in this domain.

We consider the notion of a vacuous reduct semantics for abstract argumentation frameworks, which, given two abstract argumentation semantics {\sigma} and {\tau}, refines {\sigma} (base condition) by accepting only those {\sigma}-extensions that have no non-empty {\tau}-extension in their reduct (vacuity condition). We give a systematic overview on vacuous reduct semantics resulting from combining different admissibility-based and conflict-free semantics and present a principle-based analysis of vacuous reduct semantics in general. We provide criteria for the inheritance of principle satisfaction by a vacuous reduct semantics from its base and vacuity condition for established as well as recently introduced principles in the context of weak argumentation semantics. We also conduct a principle-based analysis for the special case of undisputed semantics.

This volume contains revised versions of the papers selected for the fourth volume of the Online Handbook of Argumentation for AI (OHAAI). Previously, formal theories of argument and argument interaction have been proposed and studied, and this has led to the more recent study of computational models of argument. Argumentation, as a field within artificial intelligence (AI), is highly relevant for researchers interested in symbolic representations of knowledge and defeasible reasoning. The purpose of this handbook is to provide an open access and curated anthology for the argumentation research community. OHAAI is designed to serve as a research hub to keep track of the latest and upcoming PhD-driven research on the theory and application of argumentation in all areas related to AI.

An approach for encoding abstract dialectical frameworks and their semantics into classical higher-order logic is presented. Important properties and semantic relationships are formally encoded and proven using the proof assistant Isabelle/HOL. This approach allows for the computer-assisted analysis of abstract dialectical frameworks using automated and interactive reasoning tools within a uniform logic environment. Exemplary applications include the formal analysis and verification of meta-theoretical properties, and the generation of interpretations and extensions under specific semantic constraints.

In this paper we introduce a novel semantics, called defense semantics, for Dung's abstract argumentation frameworks in terms of a notion of (partial) defence, which is a triple encoding that one argument is (partially) defended by another argument via attacking the attacker of the first argument. In terms of defense semantics, we show that defenses related to self-attacked arguments and arguments in 3-cycles are unsatifiable under any situation and therefore can be removed without affecting the defense semantics of an AF. Then, we introduce a new notion of defense equivalence of AFs, and compare defense equivalence with standard equivalence and strong equivalence, respectively. Finally, by exploiting defense semantics, we define two kinds of reasons for accepting arguments, i.e., direct reasons and root reasons, and a notion of root equivalence of AFs that can be used in argumentation summarization.

A gradual semantics takes a weighted argumentation framework as input and outputs a final acceptability degree for each argument, with different semantics performing the computation in different manners. In this work, we consider the problem of attack inference. That is, given a gradual semantics, a set of arguments with associated initial weights, and the final desirable acceptability degrees associated with each argument, we seek to determine whether there is a set of attacks on those arguments such that we can obtain these acceptability degrees. The main contribution of our work is to demonstrate that the associated decision problem, i.e., whether a set of attacks can exist which allows the final acceptability degrees to occur for given initial weights, is NP-complete for the weighted h-categoriser and cardinality-based semantics, and is polynomial for the weighted max-based semantics, even for the complete version of the problem (where all initial weights and final acceptability degrees are known). We then briefly discuss how this decision problem can be modified to find the attacks themselves and conclude by examining the partial problem where not all initial weights or final acceptability degrees may be known.

In this paper we propose a general approach to define a many-valued preferential interpretation of gradual argumentation semantics. The approach allows for conditional reasoning over arguments and boolean combination of arguments, with respect to a class of gradual semantics, through the verification of graded (strict or defeasible) implications over a preferential interpretation. As a proof of concept, in the finitely-valued case, an Answer set Programming approach is proposed for conditional reasoning in a many-valued argumentation semantics of weighted argumentation graphs. The paper also develops and discusses a probabilistic semantics for gradual argumentation, which builds on the many-valued conditional semantics.

We study the computational complexity of abstract argumentation semantics based on  weak admissibility, a recently introduced concept to deal with arguments of self-defeating  nature. Our results reveal that semantics based on weak admissibility are of much higher  complexity (under typical assumptions) compared to all argumentation semantics which  have been analysed in terms of complexity so far. In fact, we show PSPACE-completeness  of all non-trivial standard decision problems for weak-admissible based semantics. We then  investigate potential tractable fragments and show that restricting the frameworks under  consideration to certain graph-classes significantly reduces the complexity. We also show  that weak-admissibility based extensions can be computed by dividing the given graph into  its strongly connected components (SCCs). This technique ensures that the bottleneck  when computing extensions is the size of the largest SCC instead of the size of the graph  itself and therefore contributes to the search for fixed-parameter tractable implementations  for reasoning with weak admissibility.