Abstracts
Leon van der Torre
| Reasoning Under Construction: Prospective Coherence in Base Argumentation |
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| Arguments are not always complete; they may still be under construction. A reasoner may have selected inference rules while some of the premises needed to apply them remain to be established. This raises the question of whether an unfinished argument can be completed while preserving the facts and rules already selected. In this talk, we investigate this question by drawing on intention coherence, according to which an agent’s intentions should be jointly achievable. We introduce prospective coherence for arguments under construction: the requirement that an argument admits a completion in which all selected rules can be applied, while preserving consistency and avoiding redundant premises. Based on joint work with Liuwen Yu, to be presented at BNAIC 2026 in Maastricht |
Luca Redondi
| Moral Principles in ASPIC+: A Formal Analysis of Competing Views |
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| This is joint work with Aleks Knoks. In many normative theories, we find general ethical principles that are defeasibly applied to particular contexts to detach deontic verdicts. Meta-ethicists argue for different ways to make sense of their defeasibility. One option is to regard them as “contributory”: they specify what counts as a reason for (or against) an action but may be outweighed. Alternatively, one may conceive principles as “hedged”, meaning that they allow for exceptions. Finally, one can hold that principles are both contributory and hedged. We characterize these accounts of principles formally within ASPIC+. The formalization reveals a further distinction, overlooked by the informal literature, between views on principles that satisfy reinstatement and views that do not. We establish correspondences between any pair of models of principles, thus proving that they are all equally expressive. This suggests that the meta-ethical debate over which model is to be preferred should focus on other criteria instead of expressivity. We explore the differences between the models using the notion of (contrastive) deontic explanation: while all models agree on what should (or should not) be the case, they diverge on why it should be. |
Josephine Dik
| Reasoning with Values in Norm-based Argumentation |
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| This paper is joint work with Kees van Berkel. Value-based argumentation provides a well-established framework for modelling nonmonotonic reasoning, where conflicts between arguments are resolved by considering the relative importance of the values they promote. In this talk, we introduce the VAC-framework, a rule-based argumentative framework that offers an explicit and explanatory characterization of input/output logic that includes values attached to norms in order to capture judicial reasoning. Recognizing that the relative importance of values is itself context-dependent and defeasible, we introduce a novel mechanism for value aggregation that allows multiple values to jointly influence the outcome of legal reasoning. We show that values serve as a selection function that identify a relevant subset of a maximal consistent set of norms. The proposed framework is illustrated through a child custody case study. |
Réka Markovich / Liuwen Yu
| From Interpretation to Balancing: Modeling Judicial Discretionary Decision Making with Argumentation |
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| Judicial discretion gives judges room to weigh competing considerations under legal standards that leave the outcome open. This freedom is constrained by requirements to consider relevant circumstances and provide reasons that can be scrutinized on appeal. In this talk, we trace our research journey in using formal argumentation to model aspects of judicial discretionary decision making in the DISCREASON project. We begin with bipolar argumentation, examining how different meanings of support express interpretive choices in legal reasoning and affect the conclusions that follow. We then briefly introduce an argumentation model of balancing that distinguishes how reasons support an option’s permissibility from how they support ruling out its alternatives. When discussing balancing, we are often asked where the numerical weights come from. We approach the related knowledge-engineering tasks of weight assignment and model construction through two complementary investigations: using large language models to assign argument strengths based on judges’ stated reasons, and reconstructing judicial reasoning with higher-order quantitative bipolar models. We briefly introduce the latter as ongoing work at the close of the talk. |
Kees van Berkel
| Normative Narrator: Guiding and Explaining Reinforcement Learning Agents |
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| This paper is joint work with Emery Neufeld. A normative supervisor is an external module that uses a formal reasoning engine to impose normative constraints on reinforcement learning agents, by either dynamic action masking or feeding the agent additional punishments when violations of norms occur (or both). In this talk, we use a normative supervisor implemented with a solver for deontic answer set programming (ASP) — deolingo — as a basis for the construction of a normative narrator, which uses deolingo’s ability to interface with the explainable solver xclingo to construct a module capable of both regulating behaviour through action masking and additional punishments, and providing contrastive explanations of why a given action was allowed while others were not, relative to the normative system being enforced. The explanations are modelled after the two tiers — internal and external — of explanation. We demonstrate this approach’s ability to provide understandable and descriptive explanations in a scenario where a taxi driver agent must act in accordance to a normative system governing its normal duties and provisions that must be made in case of an emergency. I will also discuss open questions and the role that explainability may further play in explaining norm-guided RL agents. |
Dominik Pichler
| Beyond Global Invariance: S4 Semantics for Conditional Obligation |
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| The central question of this talk is whether the global modal background of Åqvist’s system F can be weakened while preserving its deontic principles. To investigate this, a semantic framework is introduced that combines a state-dependent selection function with a standard Kripke accessibility relation. Suitable conditions on the selection function and its interaction with accessibility preserve the relevant deontic axioms while allowing the S5 modal base to be replaced by weaker modal logics. This separation makes the framework modular: the modal structure can vary while the deontic principles remain fixed. In particular, the framework yields S4 and KD4 variants of system F that are sound and strongly complete. The S4 variant can also be described by a generalised preference semantics with state-dependent preference relations. The classical preference semantics of F is recovered when accessibility is global and the preference relation is state-independent. |
Blaž Istenič Urh
| On Tipping Scales: a Two-Level Semantics for Balancing Constitutional Rights |
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| An influential view in legal theory (mostly associated with Robert Alexy) sees balancing of constitutional rights (principles) as reducible to the balancing of case-specific reasons. This means that the strengths of reasons for some legal effects applying or not are compared and if the reasons associated with some legal outcome prevail, its effects are to hold. To model this balancing for the case where reasons are independent, we present the semantics of a novel preference- and truthmaker-based conditional logic. It distinguishes two kinds of statements expressing that a particular combination of case-specific circumstances favors a particular outcome: (1) strong support, which is taken to represent the balancing justified by established case law or by constraints from a higher court, and (2) weak support, which represents the balancing done by the court itself (challenged more easily). In addition, strengths of reasons can be compared. We also relate the formalism to Horty's reason model for precedential reasoning. This is joint work with Luca Redondi and Réka Markovich. |
Ovidio Manteiga Moar
| Explainable Normative Reasoning based on Deontic Equilibrium Logic with Deolingo |
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| Deolingo is based on Deontic Equilibrium Logic with eXplicit negation (DELX), a formalism that was shown to provide a simple representational solution to many of the main deontic reasoning challenges in the literature, like the use of defeasible obligations, the distinction between explicit and implicit permissions, a proper treatment of dilemmas versus contrary-to-duty (CTD), or the formalisation of deontic and factual detachment, to name the most relevant ones. In the talk, we describe the basic syntax of Deolingo, deontic logic programs, and explain how these programs are translated into regular ASP, by using the ASP solver Clingo. Apart from producing the models (answer sets) generated by Clingo containing the derived obligations, Deolingo can also provide explanations in terms of derivation trees using natural language statements. To this aim, Deolingo has been extended with rule annotations that are interpreted using the ASP explanation tool Xclingo. Deolingo is also being extended to support deontic temporal reasoning by leveraging the existing tool Telingo, in particular, the operators proposed on the paper ”Tackling Temporal Deontic Challenges with Equilibrium Logic” (DeoTEL). Finally, we briefly introduce a new modal deontic formalism called Modal Deontic Equilibrium Logic (MDEL), which is more expressive than DELX, allowing for a proper representation of complex formulas, like obligations of disjunctions, and will eventually be implemented in Deolingo as well. |
Apostolos Tzimoulis
| Formal models for information extraction, persuasion, and strategic reasoning |
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| This talk introduces formal tools for analyzing how agents extract reliable information from narratives and strategic communication. Building on models of persuasion by Rubinstein and Glazer and Baruch Halpern’s Tiglath-Pileser principle, we develop a relational approach to understanding how communicated claims can remain connected to the truth despite systematic bias and manipulation. We investigate the structural and dynamic properties of these relations and illustrate their application to persuasion. |
Christian Straßer
| Ignorance is not Bliss: Deontic Risk and the Asking of Questions |
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| This is joint work with Isabella Cissell (TU Vienna), Leander Hirschsteiner (RUB) and Hauke Krugmeier (RUB). When reasoning with incomplete information, we often face situations where it is unclear whether the premises of certain inferences hold or whether defeaters are available. Reasoning with norms adds urgency to this problem: if you are obliged to act only if certain conditions do and others do not obtain, you should not just act without knowing whether those conditions are met. Act too quickly, and you might violate norms inadvertently. Investigate everything, and you waste resources. The real challenge is knowing when an inquiry is actually warranted: when finding out more would genuinely change what you ought to do, and when you should just act on what you already know. In this paper, we extend Default Argumentation Calculi (DAC) to model exactly this kind of normative reasoning under uncertainty. Our extension, DACQ, adds inference rules that generate inquiry warrants and lets them compete with deontic arguments through defeasible attack relations. We evaluate the system using standard argumentation semantics, prove correspondence results between extensions and normative outcomes, and ground the design in rationality desiderata, such as affirmative openness, and the new condition of deontic relevance. The result is a formal framework that does not just compute what to do, but explains why an agent asks a question, suspends an obligation, or revises its commitments when new information arrives. |
Xavier Parent
| From Betterness to Threshold Utility in Dyadic Deontic Logic |
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| The standard account of conditional ought is qualitative: it is formulated in terms of preference models, where a binary relation ranks possible worlds according to their betterness. This paper investigates the question of whether a quantitative analysis in terms of threshold sensitive utility models can be developed. I report positive axiomatization results as well as a negative one. |
Pere Pardo
| The Jiminy moral advisor: a Python implementation |
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| Jiminy is a recent argumentation-based agent architecture for moral decision-making (Beishui et al. 2023). It features non-monotonic reasoning about institutional facts, obligations and permissions, using (possibly conflicting) norms provided by multiple stakeholders, and contextual meta-norms on the relative authoritativeness of stakeholders in different scenarios. In this talk, we will present a Python implementation of the Jiminy moral advisor (Rodríguez Lera et al. 2026) aimed for an embedding into a robotic architecture system. |
Ali Farjami
| Logic-Parametric Neuro-Symbolic Explanation Refinement: Controlling Logical Formalisms for Verifiable LLM Reasoning |
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| Large language models (LLMs) and theorem provers (TPs) can be effectively combined for the verification and refinement of explanations for natural language inference (NLI). However, existing approaches rely on a fixed logical formalism, a feature that limits robustness and adaptability. We propose a logic-parametric neuro-symbolic framework that treats the underlying logic not as a static background, but as a controllable component. Using the LogiKEy methodology, we embed a range of classical and non-classical formalisms into higher-order logic (HOL), enabling a systematic comparison of inference quality and proof behavior. We study both ontic (descriptive) and deontic (normative) reasoning, where the choice of logical formalism has significant implications for explanation refinement. In particular, we compare logic-external approaches, where normative information is represented through explicit axioms, with logic-internal approaches, where normative structure is directly encoded within the logical formalism itself. Extensive experiments demonstrate that the effectiveness of logical formalisms is strongly domain-dependent: first-order logic performs best in ontic (descriptive) reasoning, while modal and deontic logics consistently achieve superior performance in deontic (normative) settings. These findings highlight the importance of treating logic as a first class, parametric component in neuro-symbolic systems. |
Emil Weydert
| Back to the Future |
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| Reflections on Logic, Uncertainty and Belief in the Age of AI (with historical annotations) |
Hans Rott
| The Difference Semantics for Conditionals |
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| A number of recent authors have argued forcefully that the meaning of a conditional, as typically used in natural language, requires its antecedent to be relevant to its consequent (i.e., the former supports the latter, or makes a difference to it). While endorsing the general idea, we argue that existing accounts of this relevance relation are inadequate. To properly understand such conditionals, we need not only orderings of similarity or plausibility but crucially also a representation of the distances between similarities or plausibilities. Roughly, the idea is that a conditional "If 𝐴, then 𝐵" is true if and only if, within the set of 𝐴-worlds, the worlds not satisfying 𝐵 are more remote than within the set of all worlds overall. We provide a purely qualitative semantics based on quaternary relations and identify the resulting logic, thereby refining, correcting, and partially justifying existing accounts of support conditionals. (This is joint work with Hannes Leitgeb.) |
David Fuenmayor
| Quantifiers in LogiKEy: a discussion |
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| One of the killer features of using higher-order logic as a meta-language for the design of object-logical languages is the possibility to introduce semantically-motivated quantifiers to existing non-classical propositional formalisms. We will discuss our experiences and insights, as well as the possibility of a systematic approach. |
Alexander Stage
| ModalLens: Countermodel Analysis for Normative Theory Engineering with LogiKEy |
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| This paper is joint work with Christoph Benzmüller, Matteo Magnini and Luca Pasetto. The LogiKEy framework for logic and knowledge engineering supports the iterative development and assessment of normative modal theories through shallow semantical embeddings in Higher-Order Logics (HOL). Although a single countermodel establishes non-entailment, comparing multiple countermodels can reveal recurring structures that help users understand and, where appropriate, revise their theories. We present ModalLens, a tool-supported workflow for analysing, explaining, and refining modal theories. Starting from a theory formalised in Isabelle/HOL and a conjecture under investigation, the system enumerates a bounded set of finite countermodels. Model-specific blocking axioms prevent previously found structures from being returned again without changing the underlying normative theory. ModalLens represents the resulting models as directed attributed graphs. Graphlet-based comparison and clustering group structurally similar models and identify patterns that recur within individual clusters. The models and characteristic patterns are presented through visualisations, including preference-layer diagrams for dyadic deontic models. Optional natural-language explanations summarise selected information from the analysis reports, and link their statements to the corresponding report entries. A user may select a characteristic pattern, which is then automatically compiled into a formalised refinement candidate for the theory. We validate the countermodel analysis and refinement workflow on preference-based dyadic deontic logic and epistemic deontic see-to-it-that semantics (EDS). Case studies in an EDS fragment illustrate how agent-indexed beliefs, choices, and obligations can be extracted and visualised in regulatory scenarios. The workflow thus complements the LogiKEy methodology with visual and analytical support for iterative assessment across its layers of logics and logic combinations, domain theories, and applications. |
Jan Broersen
| Can LLMs have introspection? |
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| I argue that LLM introspection, at least as construed by Cappelen and Dever, is not immune to error through misidentification, whereas paradigmatic human introspection is, as Shoemaker argued following Wittgenstein. On Cappelen and Dever's account an LLM may introspect by applying a general theory of mind to information about itself. But an LLM that is given all information that could possibly be relevant to such an inference can still fail to determine whether that information concerns itself or a qualitatively identical copy. The self-ascription therefore contains a separable identity premise, and wherever there is such a premise there is room for misidentification. No such premise occurs in first-person introspective judgements such as "I am in pain'': the human case leaves no room for the question "someone is in pain, but is it me?''. A second argument is that LLM introspection, so construed, is also not immune to what I call switch-off. If introspection is the result of self-observation combined with information about one's own states and general knowledge of the philosophy of mind, as Capellen and Dever propose, then an LLM could possibly switch off its introspection and continue to function as a non-introspective agent by cutting of the inferential route to its inner states. It could take, as it were, a moral holiday. I argue that this is not possible for human agents: we cannot switch off our first-personhood without switching off entirely. Both arguments point to the same underlying issue, the first-person individuation of the agent, and I close by connecting this to the conditions for genuine responsibility. |