The widespread application of uninterpretable machine learning systems for sensitive purposes has spurred research into elucidating the decision-making process of these systems. These efforts have their background in many different disciplines, one of which is the field of AI & law. In particular, recent works have observed that machine learning training data can be interpreted as legal cases. Under this interpretation, the formalism developed to study case law, called the theory of precedential constraint, can be used to analyze the way in which machine learning systems draw on training data—or should draw on them—to make decisions. In the present work, we advance the theory underlying these explanation methods, by relating it to order theory and logic. This allows us to write a software implementation of the theory that can be used to compute with the definitions and give automatic proofs of the properties of the model. We use this implementation to evaluate the model on a series of datasets. Through this analysis, we characterize the types of datasets that are more, or less, suitable to be described by the theory.

Hybrid Intelligence (HI) is an emerging paradigm in which artificial intelligence (AI) augments human intelligence. The current literature lacks systematic models that guide the design and evaluation of HI systems. Further, discussions around HI primarily focus on technology, neglecting the holistic human-AI ensemble. In this paper, we take the initial steps toward the development of a quality model for characterizing and evaluating HI systems from a human-AI teams perspective. We first conducted a study investigating the adequacy of properties commonly associated with effective human teams to describe HI. The study features the insights of 50 HI researchers, and shows that various human team properties, including boundedness, interdependence, competency, purposefulness, initiative, normativity, and effectiveness, are important for HI systems. Based on these results, we developed a quality model for HI teams composed of seven high-level quality attributes, further refined into 16 specific ones. To evaluate the relevance and understanding of the proposed attributes, we conducted a second empirical investigation by staging competitions in which participants used the quality model to develop and analyze HI usage scenarios. Our analysis of 48 collected scenarios, which we openly release, confirms the proposed attributes' relevance and highlights insights that emerge when designers consider the quality model in HI system design.

The popularity of an opinion in one's direct circles is not necessarily a good indicator of its popularity in one's entire community. Network structures make local information about global properties of the group potentially inaccurate, and the way a social network is wired constrains what kind of information distortion can actually occur. In this paper, we discuss which classes of networks allow for a large enough proportion of the population to get a wrong enough impression about the overall distribution of opinions. We start by focusing on the 'majority illusion', the case where one sees a majority opinion in one's direct circles that differs from the global majority. We show that no network structure can guarantee that most agents see the correct majority. We then perform computational experiments to study the likelihood of majority illusions in different classes of networks. Finally, we generalize to other types of illusions. Supplementary Information: The online version contains supplementary material available at 10.1007/s10458-025-09720-w.

Communication is a widely used mechanism to promote cooperation in multi-agent systems. In the field of emergent communication, agents are typically trained in specific environments: cooperative, competitive or mixed-motive. Motivated by the idea that real-world settings are characterized by incomplete information and that humans face daily interactions under a wide spectrum of incentives, we aim to explore the role of emergent communication when simultaneously exploited across all these contexts. In this work, we pursue this line of research by focusing on social dilemmas. To do this, we developed an extended version of the Public Goods Game, which allows us to train independent reinforcement learning agents simultaneously in different scenarios where incentives are (mis)aligned to various extents. Additionally, agents experience uncertainty in terms of the alignment of their incentives with those of others. We equip agents with the ability to learn a communication policy and study the impact of emergent communication in the face of uncertainty among agents. Our findings show that in settings where all agents have the same level of uncertainty, communication can enhance the cooperation of the whole group. However, in cases of asymmetric uncertainty, the agents that do not face uncertainty learn to use communication to deceive and exploit their uncertain peers.

This paper develops a measure of the influence of individual arguments in abstract argumentation frameworks. By applying ideas from power indices in coalitional game theory, the proposed measure—called admissibility impact value—quantifies the impact that individual arguments have on the set of admissible extensions of a given argumentation framework. It improves on existing impact measures in that it is more fine-grained and sensitive to small differences in the attack relations of argumentation frameworks. Special consideration is given to well-founded frameworks, where the improvements are particularly pronounced.

Addressing the question of how to achieve optimal decision-making under risk and uncertainty is crucial for enhancing the capabilities of artificial agents that collaborate with or support humans. In this work, we address this question in the context of Public Goods Games. We study learning in a novel multi-objective version of the Public Goods Game where agents have different risk preferences, by means of multi-objective reinforcement learning. We introduce a parametric non-linear utility function to model risk preferences at the level of individual agents, over the collective and individual reward components of the game. We study the interplay between such preference modelling and environmental uncertainty on the incentive alignment level in the game. We demonstrate how different combinations of individual preferences and environmental uncertainty sustain the emergence of cooperative patterns in non-cooperative environments (i.e., where competitive strategies are dominant), while others sustain competitive patterns in cooperative environments (i.e., where cooperative strategies are dominant).

Limited Voting (LV) is an approval-based method for multi-winner elections where all ballots are required to have a same fixed size. While it appears to be used as voting method in corporate governance and has some political applications, to the best of our knowledge, no formal analysis of the rule exists to date. We provide such an analysis here, prompted by a request for advice about this voting rule by a health insurance company in the Netherlands, which uses it to elect its work council. We study conditions under which LV would improve representation over standard approval voting and when it would not. We establish the extent of such an improvement, or lack thereof, both in terms of diversity and proportionality notions. These results help us understand if, and how, LV may be used as a low-effort fix of approval voting in order to enhance representation.

In this paper we build on a formal model of reasoning with dimensions to analyze data from the COMPAS program—a widely used and studied tool for predicting recidivism. We extend the underlying theory of the model by introducing a notion of consistency and apply it to assess whether COMPAS follows this principle in its risk assessments and supervision level recommendations. Our analysis yields three key findings. First, the program’s risk score assignments appear highly inconsistent, but we argue this is due to important input features missing from the dataset. Second, the program’s recommended supervision levels do exhibit a high degree of consistency. Third, we uncover errors in the dataset related to the conversion of raw scores to decile scores. These findings cast doubts on previous studies conducted on the COMPAS dataset, and demonstrate the need for evaluation studies like ours.

The widespread application of uninterpretable machine learning systems for sensitive purposes has spurred research into elucidating the decision-making process of these systems. These efforts have their background in many different disciplines, one of which is the field of AI & law. In particular, recent works have observed that machine learning training data can be interpreted as legal cases. Under this interpretation, the formalism developed to study case law, called the theory of precedential constraint, can be used to analyze the way in which machine learning systems draw on training data—or should draw on them—to make decisions. In the present work, we advance the theory underlying these explanation methods, by relating it to order theory and logic. This allows us to write a software implementation of the theory that can be used to compute with the definitions and give automatic proofs of the properties of the model. We use this implementation to evaluate the model on a series of datasets. Through this analysis, we characterize the types of datasets that are more, or less, suitable to be described by the theory.

In recent work, theories of case-based legal reasoning have been applied to the development of explainable artificial intelligence methods, through the analogy of training examples as previously decided cases. One such theory is that of precedential constraint. A downside of this theory with respect to this application is that it performs single-step reasoning, moving directly from the case base to an outcome. For this reason we propose a generalization of the theory of precedential constraint which allows multi-step reasoning, moving from the case base through a series of intermediate legal concepts before arriving at an outcome. Our generalization revolves around the notion of factor hierarchy, so we call this hierarchical precedential constraint. We present the theory, demonstrate its applicability to case-based legal reasoning, and perform a preliminary analysis of its theoretical properties.

In recent years, a model of a fortiori argumentation, developed to describe legal reasoning based on precedent, has been successfully applied in the field of artificial intelligence to improve interpretability of data-driven decision systems. In order to make this model more broadly applicable for this purpose, work has been done to expand the knowledge representation on the basis of which it functions, as the original model accommodates only binary propositional information. In particular, two separate expansions of the original model emerged; one which accounts for non-binary input information, and a second which accommodates hierarchically structured reasoning. In the present work we unify these expansions to a single model, incorporating both dimensional and hierarchical information.

We contribute to the programme of lifting proportionality axioms from the multi-winner voting setting to participatory budgeting. We define novel proportionality axioms for participatory budgeting and test them on known proportionality-driven rules such as Phragmén and Rule X. We investigate logical implications among old and new axioms and provide a systematic overview of proportionality criteria in participatory budgeting.

We study epistemic voting on binary issues where voters are characterized by their competence, i.e., the probability of voting for the correct alternative, and can choose between two actions: voting or abstaining. In our setting voting involves the expenditure of some effort, which is required to achieve the appropriate level of competence, whereas abstention carries no effort. We model this scenario as a game and characterize its equilibria under several variations. Our results show that when agents are aware of everyone's incentives, then the addition of effort may lead to Nash equilibria where wisdom of the crowds is lost. We further show that if agents' awareness of each other is constrained by a social network, the topology of the network may actually mitigate this effect.

Preference relations are at the heart of many fundamental concepts in artificial intelligence, ranging from utility comparisons, to defeat among strategies and relative plausibility among states, just to mention a few. Reasoning about such relations has been the object of extensive research and a wealth of formalisms exist to express and reason about them. One such formalism is conditional logic, which focuses on reasoning about the “best” alternatives according to a given preference relation. A “best” alternative is normally interpreted as an alternative that is either maximal (no other alternative is preferred to it) or optimal (it is at least as preferred as all other alternatives). And the preference relation is normally assumed to satisfy strong requirements (typically transitivity and some kind of well-foundedness assumption). Here, we generalize this existing literature in two ways. Firstly, in addition to maximality and optimality, we consider two other interpretations of “best”, which we call unmatchedness and acceptability. Secondly, we do not inherently require the preference relation to satisfy any constraints. Instead, we allow the relation to satisfy any combination of transitivity, totality and anti-symmetry. This allows us to model a wide range of situations, including cases where the lack of constraints stems from a modeled agent being irrational (for example, an agent might have preferences that are neither transitive nor total nor anti-symmetric) or from the interaction of perfectly rational agents (for example, a defeat relation among strategies in a game might be anti-symmetric but not total or transitive). For each interpretation of “best” (maximal, optimal, unmatched or acceptable) and each combination of constraints (transitivity, totality and/or anti-symmetry), we study the sets of valid inferences. Specifically, in all but one case we introduce a sound and strongly complete axiomatization, and in the one remaining case we show that no such axiomatization exists.

We study a setting in which a community wishes to identify a strongly supported proposal from a large space of alternatives, in order to change the status quo. We describe a deliberation process in which agents dynamically form coalitions around proposals that they prefer over the status quo. We formulate conditions on the space of proposals and on the ways in which coalitions are formed that guarantee deliberation to succeed, that is, to terminate by identifying a proposal with the largest possible support. Our results provide theoretical foundations for the analysis of deliberative processes in systems for democratic deliberation support, such as, e.g., LiquidFeedback or Polis.

The paper develops a theory of power for delegable proxy voting systems. We define a power index able to measure the influence of both voters and delegators. Using this index, which we characterize axiomatically, we extend an earlier game-theoretic model by incorporating power-seeking behavior by agents. We analytically study the existence of pure strategy Nash equilibria in such a model. Finally, by means of simulations, we study the effect of several parameters on the emergence of power inequalities in the model.

Stare decisis is a fundamental principle of case-based reasoning. Yet its application varies in complexity and depends, in particular, on whether relevant past decisions agree, or exist at all. The contribution of this paper is a formal treatment of types of the hardness of case-based decisions. The typology of hardness is defined in terms of the arguments for and against the issue to be decided, and their kind of validity (conclusive, presumptive, coherent, incoherent). We apply the typology of hardness to Berman and Hafner's research on the dynamics of case-based reasoning and show formally how the hardness of decisions varies with time.

Formalizing case-based reasoning is an important topic in AI and Law, which has been discussed using various approaches, such as formal dialogue games, abstract dialectical frameworks.In this paper we model case-based reasoning by using the formal argument semantics of case models.With the precedent models we present, the validity of legal arguments in the case-based reasoning process can be shown formally.We also present a case study of precedent models in a real legal domain and evaluate the validity of arguments in case-based reasoning.

We outline a formalization of precedent comparison in the precedent model formalism.

Well-behaved preferences (e.g., total pre-orders) are a cornerstone of several areas in artificial intelligence, from knowledge representation, where preferences typically encode likelihood comparisons, to both game and decision theories, where preferences typically encode utility comparisons. Yet weaker (e.g., cyclical) structures of comparison have proven important in a number of areas, from argumentation theory to tournaments and social choice theory. In this paper we provide logical foundations for reasoning about this type of preference structures where no obvious best elements may exist. Concretely, we compare and axiomatize a number of ways in which the concepts of maximality and optimality can be generalized in this general class of preferences. We thereby expand the scope of the long-standing tradition of the logical analysis of preference.

Liquid democracy is a proxy voting method where proxies are delegable. We propose and study a game-theoretic model of liquid democracy to address the following question: when is it rational for a voter to delegate her vote? We study the existence of pure-strategy Nash equilibria in this model, and how group accuracy is affected by them. We complement these theoretical results by means of agent-based simulations to study the effects of delegations on group’s accuracy on variously structured social networks.

The paper develops a formal theory of the degree of justification of arguments, which relies solely on the structure of an argumentation framework, and which can be successfully interfaced with approaches to instantiated argumentation. The theory is developed in three steps. First, the paper introduces a graded generalization of the two key notions underpinning Dung's semantics: self-defense and conflict-freeness. This leads to a natural generalization of Dung's semantics, whereby standard extensions are weakened or strengthened depending on the level of self-defense and conflict-freeness they meet. The paper investigates the fixpoint theory of these semantics, establishing existence results for them. Second, the paper shows how graded semantics readily provide an approach to argument rankings, offering a novel contribution to the recently growing research programme on ranking-based semantics. Third, this novel approach to argument ranking is applied and studied in the context of instantiated argumentation frameworks, and in so doing is shown to account for a simple form of accrual of arguments within the Dung paradigm. Finally, the theory is compared in detail with existing approaches.

We study voting games on binary issues, where voters hold an objective over the outcome of the collective decision and are allowed, before the vote takes place, to negotiate their ballots with the other participants. We analyse the voters' rational behaviour in the resulting two-phase game when ballots are aggregated via non-manipulable rules and, more specifically, quota rules. We show under what conditions undesirable equilibria can be removed and desirable ones sustained as a consequence of the pre-vote phase.

Abstract We develop a logic for reasoning about semi-public environments , i.e. environments in which a process is executing, and where agents in the environment have partial and potentially different views of the process. Previous work on this problem illustrated that it was problematic to obtain both an adequate semantic model and a language for reasoning about semi-public environments. We here use program models for representing the changes that occur during the execution of a program. These models serve both as syntactic objects and as semantic models, and are a modification of action models in Dynamic Epistemic Logic, in the sense that they allow for ontic change (i.e. change in the world or state). We show how program models can elegantly capture a notion of observation of the environment. The use of these models resolves several difficulties identified in earlier work, and admit a much simpler treatment than was possible in previous work on semi-public environments.

We provide an in-depth study of the knowledge-theoretic aspects of communication in so-called gossip protocols. Pairs of agents communicate by means of calls in order to spread information—so-called secrets—within the group. Depending on the nature of such calls knowledge spreads in different ways within the group. Systematizing existing literature, we identify 18 different types of communication, and model their epistemic effects through corresponding indistinguishability relations. We then provide a classification of these relations and show its usefulness for an epistemic analysis in presence of different communication types. Finally, we explain how to formalise the assumption that the agents have common knowledge of a distributed epistemic gossip protocol.

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The fourth international workshop on Logic Rationality and Interaction (LORI-4) took place in Hangzhou, China on October 9th–12th 2013, hosted by the Center for the Study of Language and Cognition (CSLC) of Zhejiang University. 1 The event brought together an international group of logicians, computer scientists, decision and game theorists, linguists and AI researchers. Along with the contributed papers and posters, the workshop featured seven invited talks—by Giuseppe Dari-Mattiacci, Valentin Goranko, Hannes Leitgeb, Beishui Liao, Christian List, Sonja Smets and Dongmo Zhang. 2 The articles in this special issue were selected among the papers of the workshop proceedings [ 2 ]. The selected papers were revised and extended, and went through the same extensive review process as all regular submissions to the JLC . The result is a collection of papers that accurately represents the width and depth of the ideas contributed to LORI-4. We are confident that you will appreciate them.

In this paper we attempt to shed light on the concept of an agent’s knowledge after a non-deterministic action is executed. We start by making a comparison between notions of non-deterministic choice, and between notions of sequential composition, of settings with dynamic and/or epistemic character; namely Propositional Dynamic Logic (PDL), Dynamic Epistemic Logic (DEL), and the more recent logic of Semi-Public Environments (SPE). These logics represent two different approaches for defining the aforementioned actions, and in order to provide unified frameworks that encompass both, we define the logics DELVO (DEL+Vision+Ontic change) and PDLVE (PDL+Vision+Epistemic operators). DELVO is given a sound and complete axiomatisation.

We present a simple Ceteris Paribus Logic (CP) and study its relationship with existing logics that deal with the representation of choice and power in games in normal form including atemporal STIT, Coalition Logic of Propositional Control (CL-PC) and Dynamic Logic of Propositional Assignments (DL-PA). Thanks to the polynomial reduction of the satisfiability problem for atemporal STIT in the satisfiability problem for CP, we obtain a complexity result for the latter problem.

The article introduces a ceteris paribus modal logic, called CP, interpreted on the equivalence classes induced by finite sets of propositional atoms. This logic is studied and then used to embed three logics of strategic interaction, namely atemporal STIT, the coalition logic of propositional control (CL−PC) and the starless fragment of the dynamic logic of propositional assignments (DL−PA). The embeddings highlight a common ceteris paribus structure underpinning the key operators of all these apparently very different logics and show, we argue, remarkable similarities behind some of the most influential formalisms for reasoning about strategic interaction

The purpose of this contribution is to set up a language to evaluate the results of concerted action among interdependent agents against predetermined properties that we can recognize as desirable from a deontic point of view. Unlike the standard view of logics to reason about coalitionally rational action, the capacity of a set of agents to take a rational decision will be restricted to what we will call agreements, which can be seen as solution concepts to a dependence structure present in a certain game. The language will identify those agreements that act accordingly or disaccordingly with the desirable properties arbitrarily set up in the beginning, and will reveal, by logical reasoning, a variety of structural properties of this type of collective action.

A well-studied phenomenon in network theory are optimal schedules to distribute information by one-to-one communication between nodes. One can take these communicative actions to be ‘telephone calls’, and this process of spreading information is known as gossiping [4]. It is typical to assume a global scheduler who simply executes a possibly non-deterministic protocol. Such a protocol can be seen as consisting of a sequence of instructions “first, agent a calls b, then c, next, d calls b ...”. We investigate epistemic gossip protocols, where an agent a will call another agent not because it is so instructed but based on its knowledge or ignorance of the factual information that is distributed over the network. Such protocols therefore don't need a central schedular, but they come at a cost: they may take longer to terminate than non-epistemic, globally scheduled, protocols. We describe various epistemic protocols, we give their logical properties, and we model them in a number of ways.

The paper proposes a framework---the Debate Graph Extraction (DGE) framework---for extracting debate graphs from transcripts of political debates. The idea is to represent the structure of a debate as a graph with speakers as nodes and "exchanges" as links. Links between nodes are established according to the semantic similarity between the speeches and indicate an alignment of content between them. Nodes are labelled according to the "attitude" (sentiment) of the speakers, positive or negative, using a lexicon based technique founded on SentiWordNet. The attitude of the speakers is then used to label the graph links as being either "supporting" or "opposing". If both speakers have the same attitude (both negative or both positive) the link is labelled as being supporting; otherwise the link is labelled as being opposing. The resulting graphs capture the abstract representation of a debate as two opposing fractions exchanging arguments on related content.

Multi-agent systems are viewed as consisting of individual agents whose behaviours are regulated by an organization-oriented normative artefact. This article presents a simplified version of a programming language that is designed to implement normative artefacts. Such artefacts are specified in terms of norms being enforced by monitoring, regimenting and sanctioning mechanisms. The syntax and operational semantics of the programming language are introduced and discussed. A logic is presented that can be used to specify and verify properties of programs developed in this language.

In the multi-agent systems community, dependence theory and game theory are often presented as two alternative perspectives on the analysis of agent interaction. The paper presents a formal analysis of a notion of dependence between players, given in terms of standard game-theoretic notions of rationality such as dominant strategy and best response. This brings the notion of dependence within the realm of game theory providing it with the sort of mathematical foundations which still lacks. Concretely, the paper presents two results: first, it shows how the proposed notion of dependence allows for an elegant characterization of a property of reciprocity for outcomes in strategic games; and second, it shows how the notion can be used to define new classes of coalitional games, where coalitions can force outcomes only in the presence of reciprocal dependencies.

The paper presents a logic-based approach to legislative meta-drafting. A class of meta-data, corresponding to specific classes of legal provisions, is introduced and discussed. Such meta-data are then formalized using a simple and tractable Description Logic, and the reasoning tasks available in the formalism are described.

The article investigates the logic underlying statements of the form ‘X counts as Y in context C’ which are commonly considered to represent the paradigmatic syntax of constitutive rules, i.e. the non-regulative component of normative systems. The analytical thesis backing the whole work consists in interpreting such statements as contextual classifications. This reading of counts-as is thoroughly investigated in two variants which we call the contextual classificatory reading and the proper contextual classificatory reading. The formal analysis of these readings, which we carry out making use of modal logic, disentangles two possible senses in which counts-as statements can be interpreted within a classificatory perspective, and clarifies the logical relations holding between them. The proposal is then compared in detail with previous work on the topic, in order to shed light on similarities, differences and their grounds.

The work investigates the logic underlying the representation of the non-regulative component of normative systems, the so-called counts-as. The analytic thesis we hold here is to view counts-as statements as statements which yield classifications and which hold only with respect to a context. These two aspects of the semantics of counts-as-the classificatory flavor, and the contextual character-are then investigated by means of modal logic techniques from a semantics-driven perspective, and a formalization of counts-as statements is thus proposed. The result is then compared in detail with previous work on the topic, and related with work which, despite developed in different areas of applied and philosophical logic, shares interesting technical and theoretical similarities with our proposal.