The controversy surrounding COMPAS exposes a significant gap between computer science and social science in understanding bias, highlighting the need to align computational fairness metrics with humanistic interpretations. In response, we introduce the EVENS benchmark to align the Equality versus Equity Notion Spectrum in LLMs. Our contributions include constructing an equality–equity notion spectrum and generating a corresponding dataset of key fairness scenarios, evaluating models’ initial stances and test stance adjustments under external legal regulations and internal organizational regulations using Retrieval-Augmented Generation (RAG), introducing Chain-of-Thought (CoT) prompting to guide fairness reasoning, and adding an uncertain choice to assess its impact. Our findings indicate that LLMs initially favor equality over equity. Incorporating legal and organizational regulations of equity through RAG can reduce proportional equality in most models and enhance equity recognition in GPT4o significantly. CoT improves the equity reasoning of Chinese models but may also rationalize existing biases, and the uncertain option promotes more cautious responses. The links to the code and datasets: https://github.com/CrexCheng/EVEN.

We extend the formal framework of classifier models used in the legal domain. While the existing classifier framework characterises cases solely through the facts involved, legal reasoning fundamentally relies on both facts and rules, particularly the ratio decidendi. This paper presents an initial approach to incorporating sets of rules within a classifier. Our work is built on the work of Canavotto et al. (2023), which has developed the rule-based reason model of precedential constraint within a hierarchy of factors. We demonstrate how decisions for new cases can be inferred using this enriched rule-based classifier framework. Additionally, we provide an example of how the time element and the hierarchy of courts can be used in the new classifier framework

This paper examines the significance of weak permissions in criminal trials (judicial permission). It introduces a dialogue game model to systematically address judicial permissions, considering different standards of proof and argumentation semantics.

The use of machine and deep learning techniques to predict outcomes in legal proceedings is a highly debated topic among legal scholars and policymakers. These technologies have the potential for supporting judicial decision-making, assist litigants, and analyze biases within the legal process. However, challenges remain, notably in the reluctance of judges to adopt such tools due to concerns over judicial independence, the normative correctness, accuracy, and robustness of algorithmic decisions, and the transparency of AI systems. It is claimed that methods are needed to validate AI-based judicial predication mechanisms. This paper contributes to addressing these challenges by developing a rich computational normative framework for judicial case-based reasoning grounded in Defeasible Deontic Logic. We explore legal CBR, focusing on inconsistencies and incomplete knowledge within case bases, and emphasize the importance of normative explanations to ensure transparency and justification in legal decision-making. By reconstructing CBR and deontic explanations, we provide a formal mechanism for validating AI-based judicial predictions where cases are represented using a fine-grained deontic language.

This study introduces Pro-Judice, a benchmark to assess how large language models align with procedural fairness in judicial contexts. Using criminal case data from China and US legal traditions, it reveals that models’ procedural fairness perceptions vary by legal context of test dataset, model architecture and version differences, and dataset-model interaction.

This work introduces the formal framework DLRisk, based on Defeasible Deontic Logic, for assessing how fundamental rights are balanced under the EU AI Act when new systems are developed. This approach enables qualitative, scenario-aware reasoning by ordering rights, capturing demotions triggered by factual conditions, and detecting collisions between rights and deployment contexts. The result is an explainable assessment of trade-offs that supports compliance analysis and risk mitigation.

Autonomous vehicles (AVs) must abide by the Highway Code. An AV agent would make plans which incorporate legal reasoning. Such plans must account for contingencies wherein the agent chooses between following a current plan that would lead to a violation of the law or providing an alternative plan which would not lead to a violation - a diversion. The paper utilises Defeasible Deontic Logic representing norms and encoded in Answer Set Programming (ASP) which is integrated with planning in ASP. The paper introduces diversions to address contingencies ith respect to legal reasoning.

Abstract In the setting of Defeasible Logic, we deal with the problem of revising and contracting a non-monotonic theory while minimizing the number of rules to be removed from the theory itself. The process is based on the notions of a set of rules being necessary and sufficient in order to prove a claim. The substantial difference among classical and non-monotonic reasoning processes makes this issue significant in order to achieve the correct revision processes. We show that the process is however computationally hard, and can be solved in polynomial time on non-deterministic machines.

Consistency of case bases is a way to avoid the problem of retrieving conflicting constraining precedents for new cases to be decided. However, in legal practice the consistency requirements for cases bases may not be satisfied. As pointedout in [6], a model of precedential constraint should take into account the hierarchical structure of the specific legal system under consideration and the temporaldimension of cases. This article continues the research initiated in [18,9], whichestablished a connection between Boolean classifiers and legal case-based reasoning. On this basis, we enrich the classifier models with an organisational structurethat takes into account both the hierarchy of courts and which courts issue decisions that are binding/constraining on subsequent cases. We focus on common lawsystems. We also introduce a temporal relation between cases. Within this enrichedframework, we can formalise the notions of overruled cases and cases decided perincuriam: such cases are not to be considered binding on later cases. Finally, weshow under which condition principles based on the hierarchical structure and onthe temporal dimension can provide an unambiguous decision-making process fornew cases in the presence of conflicting binding precedents.

We study weak permissions in criminal trials, which require judicial determination due to the absence of explicit prohibitions. We thus sketch a dialogue game to address this issue, analyzing argumentative dynamics with common and private knowledge. By applying various argumentation semantics, we clarify the procedural implications for weak permissions.

What happens if the way in which we handle a genuine deontic conflict ---i.e., a deontic ambiguity--- matters regarding the application of other norms that are not directly affected by that conflict? We argue that the law requires sometimes propagating the ambiguity to other norms and sometimes confining it to some norms only. We explore this issue and model different reasoning patterns. The problem is addressed in a new variant of Defeasible Deontic Logic. The contribution of this paper is threefold: (a) we extend the treatment of ambiguity blocking and propagation to Defeasible Deontic Logic; (b) we discuss reasoning patterns in the law, especially in criminal law, where we need to deal with both ambiguity blocking and ambiguity propagation in the same legal system and logic; (c) we devise an annotated variant of Defeasible Deontic Logic where we distinguish literals that must be obtained through an ambiguity-blocking mechanism from those that are derived using an ambiguity-propagating mechanism.

This article continues the research initiated in [1,2], which established a connection between Boolean classifiers and legal case-based reasoning. We relax the assumption that case bases are such that all situations have been decided in favour of the defendant or the plaintiff and we introduce an inductive strategy for assigning plausible outcomes to undecided cases. Using counterfactual reasoning, we propose a method to determine whether, at each step of the induction, a feature is a factor, i.e., it consistently favours a single outcome, or is irrelevant, i.e., it is does not favour any outcome, or is ambiguous, i.e., it favours opposite outcomes.

The EU AI Act is the first step toward a comprehensive legal framework for AI. It introduces provisions for AI systems based on their risk levels in relation to fundamental rights. Providers of AI systems must conduct Conformity Assessments before market placement. Recent amendments added Fundamental Rights Impact Assessments for high-risk AI system users, focusing on compliance with EU and national laws, fundamental rights, and potential impacts on EU values. The paper suggests that automating business process compliance can help standardize these assessments and outlines some methodological guidelines.

Modelling the concept of explanation is a central matter in AI systems, as it provides methods for developing eXplainable AI (XAI). When explanation applies to normative reasoning, XAI aims at promoting normative trust in the decisions of AI systems: in fact, such a trust depends on understanding whether systems predictions correspond to legally compliant scenarios. This paper extends to normative reasoning a work by Governatori et al. (2022) on the notion of stable explanations in a non-monotonic setting: when an explanation is stable, it can be used to infer the same normative conclusion independently of other facts that are found afterwards.

This paper brings together factor-based models of case-based reasoning (CBR) and the logical specification of classifiers. Horty [8] has developed the factor-based models of precedent into a theory of precedential constraint. In this paper we combine binary-input classifier logic (BCL) to classifiers and their explanations given by Liu & Lorini [13, 14] with Horty’s account of factor-based CBR, since both a classifier and CBR map sets of features to decisions or classifications. We reformulate case bases in the language of BCL, and give several representation results. Furthermore, we show how notions of CBR can be analyzed by notions of classifier explanation.

A legal procedure in court proceedings is a sequence of actions in which the last action is (the creation of) a(n individual) norm, where the court settles that it is obligatory in the interest of some agents that other agents bring about a certain state of affairs. This paper models legal procedures by using a variant of Propositional Dynamic Logic (PDL) enriched with a preference operator for prioritising procedural actions. The key reason towards the usage of PDL is that, in procedural law, claims and resolutions resemble programs to be executed. Requests are organised in a preference order and resolutions have their own dynamics of execution (either spontaneously by the one obliged and/or by force of law).

Normative concepts can play a crucial role in modelling the behaviour and interaction of artificial agents. Investigations are still relatively underdeveloped in robotics while interesting ideas come from related fields, such as multi-agent systems (MAS).

This paper develops a new comprehensive computational framework for reasoning about private international law that encompasses the reasoning patterns modeled by previous works [3,8,9]. The framework is a multi-modal extension of [10] preserving some nice properties of the original system, including some efficient algorithms to compute the extensions of normative theories representing legal systems.

Free Choice Permission is one of the challenges for the formalisation of norms. In this paper, we follow a novel approach that accepts Free Choice Permission in a restricted form. The intuition behind the guarded form is strongly aligned with the idea of defeasibility. Accordingly, we investigate how to model the guarded form in Defeasible Deontic Logic extended with disjunctive permissions.

This paper presents a framework for modelling legislative deliberation in the form of dialogues. Roughly, in legislative dialogues coalitions can dynamically change and propose rule-based theories associated with different utility functions, depending on the legislative theory the coalitions are trying to determine.

This paper extends previous work by presenting a framework for modelling legislative deliberation in the form of dialogues with incomplete information.Roughly, in such legislative dialogues coalitions are initially equipped with different theories which constitute their private knowledge.Under this assumption they can dynamically change and propose new legislation associated with different utility functions.

We introduce a computational model based on Deontic Defeasible Logic to handle the issue of Pragmatic Oddity. The key idea is that a conjunctive obligation is allowed only when each individual obligation is independent of the violation of the other obligations. The solution makes essential use of the constructive proof theory of the logic.

In this work we enrich a formalism for argumentation by including a formal characterization of features related to the knowledge, in order to capture proper reasoning in legal domains. We add meta-data information to the arguments in the form of labels representing quantitative and qualitative data about them. These labels are propagated through an argumentative graph according to the relations of support, conflict, and aggregation between arguments.

We study how the non-classical n-ary operator ⊗, originally intended to capture the concept of reparative obligation, can be used in the context of social choice theory to model preferences. A novel possible-world model-theoretic semantics, called sequence semantics, was proposed for the operator. In this paper, we propose a sound and complete axiomatisation of a minimal modal logic for the operator, and we extend it with axioms suitable to model social choice consistency principles such as extension consistency and contraction consistency. We provide completeness results for such extensions.

Normative systems accommodate temporary norms of several types, which can also be modified in different, and codified ways. In this paper we address the problem of modifying temporary norms that are represented by means of the combination of two known formalisms in the current literature. The framework evolves from a known one, which provides a system of norms at two distinct layers, and represents changes at the two layers as means to provide room for the codified change types. This results in four novel operators that anticipate and extend norms in two different combined ways, by preserving or not the effects of the norms in the period of time generated by the temporal modifications. We study these new operators and show how they relate to the operators of annulment and abrogation analysed elsewhere.

The interpretation of a norm is often uncertain and conflicting. In this paper we propose a model for arguing about legal interpretation, which considers the problems of vagueness. After motivating our adoption of graded categories as a tool to tackle the problem of open texture in legal interpretation, we introduce a model based on fuzzy logic and argumentation. Then, we conduct a case study by using an example from medically assisted reproduction.

This paper presents a belief revision operator for legal systems that considers time intervals. This model relates techniques about belief revision formalisms and time intervals with temporalised rules for legal systems. Our goal is to formalise a temporalised belief base and corresponding timed derivation, together with a proper revision operator. This operator may remove rules when needed or adapt intervals of time when contradictory norms are added in the system.

In this paper we extend a formal framework presented in [6] to model reasoning across legal systems. In particular, we propose a logical system that encompasses the various interpretative interactions occurring between legal systems in the context of private international law. This is done by introducing meta-rules to reason with interpretive canons.

Abstract The paper proposes a fresh look at the concept of goal and advances that motivational attitudes like desire, goal and intention are just facets of the broader notion of (acceptable) outcome. We propose to encode the preferences of an agent as sequences of “alternative acceptable outcomes”. We then study how the agent's beliefs and norms can be used to filter the mental attitudes out of the sequences of alternative acceptable outcomes. Finally, we formalise such intuitions in a novel Modal Defeasible Logic and we prove that the resulting formalisation is computationally feasible.

This paper offers a new logical machinery for reasoning about interpretive canons. We identify some options for modelling reasoning about interpretations and show that interpretative argumentation has a distinctive structure where the claim that a legal text ought or may be interpreted in a certain way can be supported or attacked by arguments, whose conflicts may have to be assessed according to further arguments.

We study the complexity of the Strategic Argumentation Problem for 2-player dialogue games where a player should decide what move (set of rules) to play at each turn in order to prove (disprove) a given thesis. We show that this is an NP-complete problem.

In strategic argumentation players exchange arguments to prove or reject a claim. This paper discusses and reports on research about two basic issues regarding the game-theoretic understanding of strategic argumentation games in the law: whether such games can be reasonably modelled as zero-sum games and as games with complete information.

This paper shows how defeasible argumentation schemes can be used to represent the logical structure of the arguments used in statutory interpretation. In particular we shall address the eleven kinds of argument identified MacCormick and Summers [6] and the thirteen kinds of argument by Tarello [11]. We show that interpretative argumentation has a distinctive structure where the claim that a legal text ought or may be interpreted in a certain way can be supported or attacked by arguments, whose conflicts may have to be assessed according to further arguments.

This paper systematically investigates how to model legal contraction in an expressive variant of Defeasible Deontic Logic. We argue that legal contraction is an umbrella concept that includes operations which are conceptually and technically different: removing rules, adding exceptions, and modifying rule priorities. The peculiarities of deleting legal conclusions show that an extension of those operations is sometimes needed, which works on the indirect conclusions from which the target effect of the contraction is obtained. The proposed techniques are discussed in the context of a new version for the logic of AGM postulates of contraction.

We propose a model of vicarious reinforcement in rule-based learning agents. The influence of this reinforcement is investigated in a population where a law is enforced ex ante. The norm-governed population of learning agents is formalised and simulated in an executable probabilistic rule-based argumentation framework. Vicarious experiences are expressed with rules and their learning effects are integrated into reinforcement learning. So, agents learn not only from their own experiences but also by taking into account the experiences of others. We show that simulation results differ from traditional calculus based on expected utilities.

In the Web of Data, the absence of clarity about the licensing terms under which the data is released prevents data reuse, and thus data publication and interlinking at the expenses of the Web of Data itself. In addition, even when terms are clear, the absence of automated processing of the licenses prevents scaling data reuse and integration. In this paper, we provide a semantic model of licenses for the Web of Data. The key idea of our approach consists first in verifying the compatibility and compliance of the licensing terms associated to the data queried by the consumer, and second, if compatibility arises, in composing the single licenses into a unique license which provides the terms of reuse for the whole data consumed during the query solving. In particular, we propose a deontic logic semantics which is able to (i) formally define the deontic components of the licenses, i.e., Permissions, Obligations, and Prohibitions, and reason over them, (ii) verify the compatibility of the elements composing the single licenses, and return those elements which can be included into the composite license, and (iii) provide a formal account of the heuristics proposed to guide the composition.

The Web of Data is assisting to a growth of interest with respect to the open challenge of representing and reasoning in an automated way over licenses and copyright. In this paper, we deal with the problem of checking the composing together a set of licensing terms associated to a single query result on the Web of Data to create a so called composite license. More precisely, we analyze two composition heuristics, AND-composition and OR-composition, showing how they can be used to combine the deontic components specified by the licenses, i.e., permissions, obligations, and prohibitions, and which are the most suitable combinations depending on the starting licenses. Such heuristics are evaluated using the SPINdle logic reasoner.

There are occasions in which an agent lengthens its own action through the implementation of a foreign activity for its own interests. We focus on the occasional dependence relation between a principal agent and a helper agent. In particular, we are interested in the helper's harmful performance that has its origin in extra contractual situations e.g. factual and/or occasional situations based on trust or courtesy which may lead to the emergence of an obligation to compensate third parties.

In the domain of Linked Open Data a need is emerging for developing automated frameworks able to generate the licensing terms associated to data coming from heterogeneous distributed sources. This paper proposes and evaluates a deontic logic semantics which allows us to define the deontic components of the licenses, i.e., permissions, obligations, and prohibitions, and generate a composite license compliant with the licensing items of the composed different licenses. Some heuristics are proposed to support the data publisher in choosing the licenses composition strategy which better suits her needs w.r.t. the data she is publishing. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

We propose a framework for reconstructing the arguments supporting the restrictive interpretations of legal provisions. The idea is that the interpretation of legal concepts may require to change the counts-as rules defining them. Some connections with revision theory techniques are considered.

This paper proposes to integrate an argumentation framework with techniques from Temporal Constraint Satisfaction. Temporal constraints are thus embedded into legal argumentation to account for temporal aspects of legal reasoning. Through the accommodation of temporal constraints, the validity of arguments and of their conclusions is made relative to the time-points when the applied norms are alive, according to the adopted temporal perspective. A fixed-point semantics and an associated dialogue game are given.

This paper shows how belief revision techniques can be used in Defeasible Logic to change rulebased theories characterizing the deliberation process of cognitive agents. We discuss intention reconsideration as a strategy to make agents compliant with the norms regulating their behavior.

In this paper we propose an extension of Defeasible Logic to represent different concepts of defeasible permission. Special attention is paid in particular to permissive norms that work as exceptions to opposite obligations.

We address some forms of temporal reasoning within normative MAS, focusing on the combination of temporal logics with multi-modal multi-agent logics. We suggest perspectives on how these combinations can be used for modelling aspects of time within lawful provisions, obligations, and legal principles. The main contributions are the new variant of deontic tense logic using hybrid logic, and the combination of time and obligations.

This contribution introduces a novel approach to study legal interactions, legal professions, and legal institutions, by combining argumentation, game theory and evolution. We consider a population of lawyers, having different postures, who engage in adversarial argumentation with other lawyers, obtaining outcomes according the existing context and their chosen strategies. We examine the resulting games and analyse the evolution of the population.

This paper provides a novel mechanism to check whether business processes are compliant with business rules regulating them. The key point is that compliance is a relationship between two sets of specifications: the specifications for executing a business process and the specifications regulating it.

This paper proposes some variants of Temporal Defeasible Logic (TDL) to reason about normative modifications. These variants make it possible to differentiate cases in which, for example, modifications at some time change legal rules but their conclusions persist afterwards from cases where also their conclusions are blocked.

Argumentation is modelled as a game where the payoffs are measured in terms of the probability that the claimed conclusion is, or is not, defeasibly provable, given a history of arguments that have actually been exchanged, and given the probability of the factual premises. The probability of a conclusion is calculated using a standard variant of Defeasible Logic, in combination with standard probability calculus. It is a new element of the present approach that the exchange of arguments is analysed with game theoretical tools, yielding a prescriptive and to some extent even predictive account of the actual course of play. A brief comparison with existing argument-based dialogue approaches confirms that such a prescriptive account of the actual argumentation has been almost lacking in the approaches proposed so far.

We propose a computationally oriented non-monotonic multi-modal logic arising from the combination of temporalised agency and temporalised normative positions. We argue about the defeasible nature of these notions and then we show how to represent and reason with them in the setting of Defeasible Logic.

In this paper we present a labelled proof method for computing nonmonotonic consequence relations in a conditional logic setting. The method exploits the strong connection between these deductive relations and conditional logics, and it is based on the usual possible world semantics devised for the latter. The label formalism KEM, introduced to account for the semantics of normal modal logics, is easily adapted to the semantics of conditional logic by simply indexing labels with formulas. The basic inference rules are provided by the propositional system KE+—a tableau‐like analytic proof system devised to be used both as a refutation method and a direct method of proof—that is the classical core of KEM which is thus enlarged with suitable elimination rules for the conditional connective. The resulting algorithmic framework is able to compute cumulative consequence relations in so far as they can be expressed as conditional implications.