Beishui Liao

AAMAS Conference 2026 Conference Paper

Disobedience in Normative Multi-agent Systems

• Marija Slavkovik
• Liuwen Yu
• Leon van der Torre
• Réka Markovich
• Beishui Liao

An intelligent agent should be able to disobey the norms of its environment. We define disobedience as an act of intentional norm violation and we postulate the distinctions among four types of disobedience: direct violation, justified exception, civil disobedience, and trolling. Each type requires a distinct monitoring workflow: direct violations are sanctioned, exceptions are waived, civil disobedience is sanctioned but also logged as a reform signal, and trolls are sanctioned but excluded from reform processes. To capture this, we formalize a compliance management architecture that separates monitoring of observable behaviour, assessment of disobedience type, and dispatching to the appropriate enforcement workflow. This separation clarifies the dual perspective: agents use reasonbased practical reasoning to decide whether to obey or disobey, while the governance framework processes observable outcomes and routes them into differentiated institutional responses.

FLAP Journal 2025 Journal Article

Formal Argumentation and Modal Logic

• Carlos Iván Chesñevar
• Jürgen Dix
• Beishui Liao
• Jieting Luo
• Carlo Prioetti
• Antonio Yuste-Ginel

The interrelationship between defeasible argumentation and modal logic is rooted in their shared goal of capturing and modelling reasoning under uncer- tainty and changing conditions. In the last years, researchers have explored different ways to combine these two formalizations to create more robust sys- tems for handling complex reasoning tasks, in which modal operators can be incorporated into argumentation systems.

NeurIPS Conference 2025 Conference Paper

IneqSearch: Hybrid Reasoning for Olympiad Inequality Proofs

• Zhaoqun Li
• Beishui Liao
• Qiwei Ye

Mathematicians have long employed decomposition techniques to prove inequalities, yet automating this process remains a significant challenge in computational mathematics. We introduce IneqSearch, a hybrid reasoning system that integrates symbolic computation with large language models (LLMs) to address this challenge. IneqSearch reformulates inequality proving as a structured search problem: identifying appropriate combinations of theorems that decompose expressions into non-negative components. The system combines a symbolic solver for deductive reasoning with an LLM-based agent for constructive proof exploration, effectively implementing methodologies observed in formal mathematical practice. A key contribution of IneqSearch is its iterative learning mechanism that systematically incorporates newly proven results into its theorem database, enabling knowledge acquisition during practice that enhances its capabilities without requiring human intervention. In empirical evaluation on 437 Olympiad-level inequalities, IneqSearch successfully proves 342 problems, significantly outperforming existing methods and demonstrating the effectiveness of integrating symbolic and neural approaches for mathematical reasoning.

ECAI Conference 2025 Conference Paper

LLM-ASPIC +: A Neuro-Symbolic Framework for Defeasible Reasoning

• Xiaotong Fang
• Zhaoqun Li
• Chen Chen
• Beishui Liao

Large language models (LLMs) excel at complex reasoning and achieve human-like performance in many natural language processing tasks. However, they still struggle to reason effectively when faced with inconsistent or contradictory information. This capability gap raises significant concerns for real-world applications where reliable decision-making depends on reconciling conflicting evidence, such as legal analysis, medical diagnosis, and commonsense reasoning. In this paper, we focus on defeasible reasoning in natural language, a task that challenges LLMs to handle and resolve contradictory information. To improve the defeasible reasoning capability of LLMs, we propose LLM-ASPIC+, a framework combining neural language understanding with formal argumentation. Our framework harnesses LLMs’ capacity for grounding and contextual reasoning while integrating formal argumentation frameworks to establish systematic conflict resolution mechanisms lacking in LLMs. We also create MineQA, a newly synthesized dataset designed to evaluate multi-step defeasible reasoning under both strict and defeasible rules. LLM-ASPIC+ achieves state-of-the-art results on multi-step defeasible reasoning, with 87. 1% accuracy on BoardGameQA-2 and 82. 6% on BoardGameQA-3. These results show that integrating neural language models with formal argumentation effectively supports defeasible reasoning in natural language.

AIJ Journal 2024 Journal Article

Bisimulation between base argumentation and premise-conclusion argumentation

• Jinsheng Chen
• Beishui Liao
• Leendert van der Torre

The structured argumentation system that represents arguments by premise-conclusion pairs is called premise-conclusion argumentation (PA) and the one that represents arguments by their premises is called base argumentation (BA). To assess whether BA and PA have the same ability in argument evaluation by extensional semantics, this paper defines the notion of extensional equivalence between BA and PA. It also defines the notion of bisimulation between BA and PA and shows that bisimulation implies extensional equivalence. To illustrate how base argumentation, bisimulation and extensional equivalence can contribute to the study of PA, we prove some new results about PA by investigating the extensional properties of a base argumentation framework and exporting them to two premise-conclusion argumentation frameworks via bisimulation and extensional equivalence. We show that there are essentially three kinds of extensions in these frameworks and that the extensions in the two premise-conclusion argumentation frameworks are identical.

JAIR Journal 2023 Journal Article

The Jiminy Advisor: Moral Agreements among Stakeholders Based on Norms and Argumentation

• Beishui Liao
• Pere Pardo
• Marija Slavkovik
• Leendert van der Torre

An autonomous system is constructed by a manufacturer, operates in a society subject to norms and laws, and interacts with end users. All of these actors are stakeholders affected by the behavior of the autonomous system. We address the challenge of how the ethical views of such stakeholders can be integrated in the behavior of an autonomous system. We propose an ethical recommendation component called Jiminy which uses techniques from normative systems and formal argumentation to reach moral agreements among stakeholders. A Jiminy represents the ethical views of each stakeholder by using normative systems, and has three ways of resolving moral dilemmas that involve the opinions of the stakeholders. First, the Jiminy considers how the arguments of the stakeholders relate to one another, which may already resolve the dilemma. Secondly, the Jiminy combines the normative systems of the stakeholders such that the combined expertise of the stakeholders may resolve the dilemma. Thirdly, and only if these two other methods have failed, the Jiminy uses context-sensitive rules to decide which of the stakeholders take preference over the others. At the abstract level, these three methods are characterized by adding arguments, adding attacks between arguments, and revising attacks between arguments. We show how a Jiminy can be used not only for ethical reasoning and collaborative decision-making, but also to provide explanations about ethical behavior.

AAMAS Conference 2023 Conference Paper

What Do You Care About: Inferring Values from Emotions

• Jieting Luo
• Mehdi Dastani
• Thomas Studer
• Beishui Liao

Observers can glean information from others’ emotional expressions through the act of drawing inferences from another individual’s emotional expressions. It is important for socially aware artificial systems to be capable of doing that as it can facilitate social interaction among agents, and is particularly important in humanrobot interaction for supporting a more personalized treatment of users. In this short paper, we propose a methodology for developing a formal model that allows agents to infer another agent’s values from her emotion expressions.

FLAP Journal 2022 Journal Article

Defeasible Deontic Logic: Arguing about Permission and Obligation.

• Huimin Dong
• Beishui Liao
• Réka Markovich
• Leendert van der Torre

Defeasible deontic logic uses techniques from non-monotonic logic to address various challenges in normative reasoning, such as prima facie permissions and obligations, moral dilemmas, deontic detachment, contrary-to-duty reasoning and legal interpretation. In this article, we use formal argumentation to design defeasible deontic logics, based on two classical deontic logics. In particular, we use the ASPIC+ structured argumentation theory to define non-monotonic variants of well-understood monotonic modal logics. We illustrate the ASPIC+ based approach and the resulting defeasible deontic logics using argumentation about strong permission.

IS Journal 2021 Journal Article

An Optimized Quantitative Argumentation Debate Model for Fraud Detection in E-Commerce Transactions

• Haixiao Chi
• Yiwei Lu
• Beishui Liao
• Liaosa Xu
• Yaqi Liu

Since the existing machine-learning-based approaches for fraud detection are incapable of providing explanations, we propose a fraud detection method based on quantitative argumentation, which is intrinsically interpretable. First, we construct an argumentative tree by combining human-level knowledge and the knowledge learned from data. Second, we extend the existing quantitative argumentation debates (QuAD) frameworks by adding correlation strength between arguments and exploit the particle swarm optimization algorithm (PSO) to identify the correlation strength between arguments. Third, the performance of the new method is investigated by an empirical study, using the data from Ant Financial, the Alibaba Group's financial services provider. The results show that the new method has better performance than the existing DF-QuAD algorithm and is competitive with other machine learning methods, including Xgboost, ANN, SVM, and LR.

AIJ Journal 2020 Journal Article

An approach for combining ethical principles with public opinion to guide public policy

• Edmond Awad
• Michael Anderson
• Susan Leigh Anderson
• Beishui Liao

We propose a framework for incorporating public opinion into policy making in situations where values are in conflict. This framework advocates creating vignettes representing value choices, eliciting the public's opinion on these choices, and using machine learning to extract principles that can serve as succinct statements of the policies implied by these choices and rules to guide the behavior of autonomous systems.

LORI Conference 2019 Conference Paper

From Classical to Non-monotonic Deontic Logic Using ASPIC +

• Huimin Dong
• Beishui Liao
• Réka Markovich
• Leendert W. N. van der Torre

Abstract In this paper we use formal argumentation to design non-monotonic deontic logics, based on two monotonic deontic logics. In particular, we use the structured argumentation theory ASPIC \(^+\) to define non-monotonic variants of well-understood modal logics. We illustrate the approach using argumentation about free-choice permission.

AIJ Journal 2018 Journal Article

A general semi-structured formalism for computational argumentation: Definition, properties, and examples of application

• Pietro Baroni
• Massimiliano Giacomin
• Beishui Liao

In the field of computational argumentation several formalisms featuring different levels of abstraction and focusing on different aspects of the argumentation process have been developed. Their combined use, necessary to achieve a comprehensive formal coverage of the argumentation phenomenon, gives rise to a nontrivial interplay between different abstraction levels, so that counterintuitive or undesirable outcomes may result from the combination of formalisms which appear to be well-behaved when considered in isolation. To address this problem we introduce a semi-structured formalism for argumentation, called LAF-ensembles, capturing a set of essential features of structured arguments and define a class of set based argumentation frameworks appropriate to support a semantic assessment of arguments for LAF-ensembles. It is shown that, under suitable assumptions, the combination of a LAF-ensemble and of an appropriate argumentation framework is guaranteed to produce justification outcomes satisfying a set of essential requirements. The generality and usefulness of the proposed approach are demonstrated by illustrating its ability to capture as instances and enhance two structured argumentation formalisms from the literature, namely Vreeswijk's abstract argument systems and Modgil and Prakken's ASPIC +. In particular, a revised version of the latter formalism, properly dealing with generic contrariness and solving significant technical limitations of ASPIC +, is proposed.

KR Conference 2018 Conference Paper

Probabilistic Abstract Argumentation based on SCC Decomposability

• Tjitze Rienstra
• Matthias Thimm
• Beishui Liao
• Leendert van der Torre

In this paper we introduce a new set of general principles for probabilistic abstract argumentation. The main principle is a probabilistic analogue of SCC decomposability, which ensures that the probabilistic evaluation of an argumentation framework complies with the probabilistic (in)dependencies implied by the graph topology. We introduce various examples of probabilistic semantics and determine which principles they satisfy. Our work also provides new insights into the relationship between abstract argumentation and the theory of Bayesian networks.

FLAP Journal 2017 Journal Article

Handling Norms in Multi-agent Systems by Means of Formal Argumentation.

• Célia da Costa Pereira
• Beishui Liao
• Alessandra Malerba
• Antonino Rotolo
• Andrea G. B. Tettamanzi
• Leendert W. N. van der Torre
• Serena Villata

IJCAI Conference 2015 Conference Paper

Dealing with Generic Contrariness in Structured Argumentation

• Pietro Baroni
• Massimiliano Giacomin
• Beishui Liao

The adoption of a generic contrariness notion in ASPIC+ substantially enhances its expressiveness with respect to other formalisms for structured argumentation. In particular, it opens the way to novel investigation directions, like the use of multivalued logics in the construction of arguments. This paper points out however that in the current version of ASPIC+ a serious technical difficulty related with generic contrariness is present. With the aim of preserving the same level of generality, the paper provides a solution based on a novel notion of closure of the contrariness relation at the level of sets of formulas and an abstract representation of conflicts between sets of arguments. The proposed solution is shown to satisfy the same rationality postulates as ASPIC+ and represents a starting point for further technical and conceptual developments in structured argumentation.

LORI Conference 2015 Conference Paper

Formulating Semantics of Probabilistic Argumentation by Characterizing Subgraphs

• Beishui Liao
• Huaxin Huang

Abstract The existing approaches to formulate the semantics of probabilistic argumentation are based on the notion of possible world. Given a probabilistic argument graph with n nodes, 2 n subgraphs are constructed and their extensions under a given semantics are computed. Then, the probability of a set of arguments E being an extension is equal to the sum of the probabilities of all subgraphs each of which has the extension E. Since in many cases, computing the extensions of a subgraph is computationally expensive, these approaches are fundamentally inefficient or infeasible. In order to cope with this problem, the present paper proposes a novel approach to formulate the semantics of probabilistic argumentation by charactering subgraphs w. r. t. an extension. The results show that under some semantics (admissible, complete, stable), the probability of a set of arguments E being an extension can be obtained without computing the extensions of subgraphs, while under some other semantics (preferred, grounded), only partial computation of extensions is needed.

FLAP Journal 2015 Journal Article

Going Forth and Drawing Back: An Intensional Approach in Nonmonotonic Inference.

• Yi Mao
• Beihai Zhou
• Beishui Liao

We decompose a nonmonotonic inference Γ |∼ α into two stages: going forth to deduce all default conclusions in a logic system named DC (short for Default Conclusions), and drawing back less preferable conclusions in the face of conflicting default conclusions, based on a binary “more preferable” relation defined on those subformulas of Γ that are also its deductive consequences. Under the possible-world semantics framework, we construct a set selection function and build up a theory of semantics, as a variant of traditional selection function semantics. We prove that the underlying logic system DC is sound and complete with respect to set selection function semantics. Using this two-layer mechanism, we account for benchmark examples including the Nixon Diamond and the Penguin Principle.

EUMAS Conference 2015 Conference Paper

Probabilistic Argumentation, a Small Step for Uncertainty, a Giant Step for Complexity

• Xin Sun 0001
• Beishui Liao

Abstract In this paper we study how the restrictions of probability function affects the complexity in probabilistic argumentation. Our results show that the complexity of computing the probability of acceptance can only become tractable when we impose very strong restrictions on the probability function. Even a tiny relaxation of the restriction dramatically increases the complexity.

AIJ Journal 2014 Journal Article

On topology-related properties of abstract argumentation semantics. A correction and extension to Dynamics of argumentation systems: A division-based method

• Pietro Baroni
• Massimiliano Giacomin
• Beishui Liao

This research note provides novel results concerning the incremental computation of the stable and ideal argumentation semantics, by extending the division-based method presented in [1] and correcting a flawed claim given there. As a basis for these results, the note synthetically reviews and discusses the topology-related properties of directionality and SCC-recursiveness in abstract argumentation semantics and analyzes their relationships with the division-based method.

AIJ Journal 2011 Journal Article

Dynamics of argumentation systems: A division-based method

• Beishui Liao
• Li Jin
• Robert C. Koons

The changing of arguments and their attack relation is an intrinsic property of a variety of argumentation systems. So, it is very important to efficiently figure out how the status of arguments in a system evolves when the system is updated. However, unlike other areas of argumentation that have been deeply explored, such as argumentation semantics, proof theories, and algorithms, etc. , dynamics of argumentation systems has been comparatively neglected. In this paper, we formulate a general theory (called a division-based method) to cope with this problem based on a new concept: the division of an argumentation framework. When an argumentation framework is updated, it is divided into three parts: an unaffected, an affected, and a conditioning part. The status of arguments in the unaffected sub-framework remains unchanged, while the status of the affected arguments is computed in a special argumentation framework (called a conditioned argumentation framework, or briefly CAF) that is composed of an affected part and a conditioning part. We have proved that under a certain semantics that satisfies the directionality criterion (complete, preferred, ideal, or grounded semantics), the extensions of the updated framework are equal to the result of a combination of the extensions of an unaffected sub-framework and sets of the extensions of a set of assigned CAFs. Due to the efficiency of the division-based method, it is expected to be very useful in various kinds of argumentation systems where arguments and attacks are dynamics.

LORI Conference 2011 Conference Paper

Partial Semantics of Argumentation

• Beishui Liao
• Huaxin Huang

Abstract In various argumentation systems, under most of situations, only the justification status of some arguments of the systems should be evaluated, while that of other arguments is not necessary to be figured out. Based on this observation, we introduce an efficient method to evaluate the status of a part of arguments in an argumentation framework. This method is based on the notion of unattacked sets of an argumentation framework and the directionality criterion of argumentation semantics. Given an argumentation framework and a subset of arguments within it, we firstly identify the minimal set of arguments that are relevant to the arguments in this subset (called the minimal unattacked set ). Then, under an argumentation semantics satisfying the directionality criterion, the set of extensions of the sub-framework induced by the minimal unattacked set (called a partial semantics of the original argumentation framework) can be evaluated independently. Then, we analyze two basic properties of the partial semantics of argumentation: monotonicity and combinability.