Deontic Logic Research Articles

Formal Ethical Obligations in Reinforcement Learning Agents: Verification and Policy Updates

When designing agents for operation in uncertain environments, designers need tools to automatically reason about what agents ought to do, how that conflicts with what is actually happening, and how a policy might be modified to remove the conflict. These obligations include ethical and social obligations, permissions and prohibitions, which constrain how the agent achieves its mission and executes its policy. We propose a new deontic logic, Expected Act Utilitarian deontic logic, for enabling this reasoning at design time: for specifying and verifying the agent's strategic obligations, then modifying its policy from a reference policy to meet those obligations. Unlike approaches that work at the reward level, working at the logical level increases the transparency of the trade-offs. We introduce two algorithms: one for model-checking whether an RL agent has the right strategic obligations, and one for modifying a reference decision policy to make it meet obligations expressed in our logic. We illustrate our algorithms on DAC-MDPs which accurately abstract neural decision policies, and on toy gridworld environments.

The Goal after Tomorrow: Offline Goal Reasoning with Norms

Recent studies have focused on autonomous agents that select their own goals and then select actions to achieve these goals, using online Goal Reasoning (GR). GR agents can revise goals and plans at execution time if unexpected outcomes occur. However, for ethical or legal agent design, even the partial execution of an online plan may result in foreseeable norm violations. To prevent these violations, it is crucial to incorporate GR already at the planning phase. To this end, we design an offline GR system that can harbour normative systems or deontic logics for goal generation. Our main results include a characterization and comparison of the completeness classes for a variety of offline GR planners, and a discussion of the irreducibility of offline GR to pure planning methods.

A Temporal Epistemic Deontic Logic

A Temporal Epistemic Deontic Logic

An ASP Implementation of Defeasible Deontic Logic

We present a novel implementation of Defeasible Deontic Logic as an Answer Set Programming meta-program, and we evaluate the performance of the implementation against a recent set of benchmarks.

Declarative Logic-Based Pareto-Optimal Agent Decision Making.

There are many applications where an autonomous agent can perform many sets of actions. It must choose one set of actions based on some behavioral constraints on the agent. Past work has used deontic logic to declaratively express such constraints in logic, and developed the concept of a feasible status set (FSS), a set of actions that satisfy these constraints. However, multiple FSSs may exist and an agent needs to choose one in order to act. As there may be many different objective functions to evaluate status sets, we propose the novel concept of Pareto-optimal FSSs or . We show that checking if a status set is a is co-NP-hard. We develop an algorithm to find a and in special cases when the objective functions are monotonic (or anti-monotonic), we further develop more efficient algorithms. Finally, we conduct experiments to show the efficacy of our approach and we discuss possible ways to handle multiple Pareto-optimal Status Sets.

Resolving the Judiciary Tensions between the Constitutional Court and the Supreme Court of Indonesia

This paper addresses a critical issue undermining the legal coherence and judicial stability in Indonesia: the discord between the Constitutional Court and the Supreme Court in the realm of judicial review. This paper uncovers the root cause as a weak chain of validity in law formation, aggravated by divergent legal frameworks governing each court through utilizing doctrinal research methods. Drawing on Bullygin's deontic logic theory, the paper reveals a lack of explicit cross-sectoral policy synchronization. To immediately alleviate these tensions, this paper proposes the establishment of a Memorandum of Understanding (MOU) between the two courts, aiming to solidify the chain of legal norms and restore systemic stability. For a long-term resolution, a comprehensive revision of the judiciary law is advocated. This research serves as an urgent call for coordinated reforms to bolster the integrity and efficiency of Indonesia's judicial system.

Learning Normative Behaviour Through Automated Theorem Proving

Reinforcement learning (RL) is a powerful tool for teaching agents goal-directed behaviour in stochastic environments, and many proposed applications involve adopting societal roles which have ethical, legal, or social norms attached to them. Though multiple approaches exist for teaching RL agents norm-compliant behaviour, there are limitations on what normative systems they can accommodate. In this paper we analyse and improve the techniques proposed for use with the Normative Supervisor (Neufeld, et al., 2021)—a module which uses conclusions gleaned from a defeasible deontic logic theorem prover to restrict the behaviour of RL agents. First, we propose a supplementary technique we call violation counting to broaden the range of normative systems we can learn from, thus covering normative conflicts and contrary-to-duty norms. Additionally, we propose an algorithm for constructing a “normative filter”, a function that can be used to implement the addressed techniques without requiring the theorem prover to be run at each step during training or operation, significantly decreasing the overall computational overhead of using the normative supervisor. In order to demonstrate these contributions, we use a computer game-based case study, and thereafter discuss remaining problems to be solved in the conclusion.

Overcoming von Wright's anxiety

AbstractThis article examines the anxiety expressed by von Wright over the status of the deontic permission, P, as an independent normative category, given the interdefinability between P and O at the foundation of deontic logic. Two concerns are noted: the reducibility of P to O, and the inadequacy of P to convey a full permission in a social setting. Drawing on resources from the Hohfeldian analytical framework, the relational and aggregate features of permission are explored, and an aggregate conception of permission, P, is recognized. With the assistance of insights from Demey and Smessaert on duals, Hansson on formalization, and Soames on interdefinability, it is concluded that the interdefinability thesis can be defended without threatening the independent status of P. Additional grounds for reaching this conclusion are provided from a detailed analysis of the relationship between P and P. Some implications of the more expansive notion of permission, P, are considered with regard to the resources of deontic logic and their application.

The Logical Possibility of Moral Dilemmas in Expressivist Semantics

In this paper, using Mark Schroeder’s (2008a) expressivist semantic framework for normative language as a case study, I will identify difficulties that even an expressivist semantic theory capable of addressing the Frege-Geach problem will encounter in handling the logical possibility of moral dilemmas. To this end, I will draw on a classical puzzle formulated by McConnell (1978) that the logical possibility of moral dilemmas conflicts with some of the prima facie plausible axioms of the standard deontic logic, which include obligation implies permission. On the tentative assumption that proponents of ethical expressivism should be generally committed to securing the logical possibility of moral dilemmas in their semantic theories, I will explore whether and how expressivists can successfully invalidate obligation implies permission within the framework developed by Schroeder. The case study eventually reveals that this can indeed be a hard task for expressivists. Generalizing from the case study, I will suggest that the source of the difficulty ultimately lies in the mentalist assumption of the expressivist semantic project that the logico-semantic relations exhibited by normative sentences should be modeled in terms of the psychological attitudes that speakers express by uttering them. My final goal will be to show that the difficulty expressivists face in dealing with the logical possibility of moral dilemmas is a reflection of the more general problem that their commitment to the mentalist assumption prevents them from flexibly adopting or dropping axioms in their semantic theories to get the right technical results.

Digital Health Consent - for Better Interoperability and Consumer Control.

We present a framework for digital health consent in support of computable expression of medico-legal policies to govern consumer data sharing across providers. The approach is aligned with HL7 FHIR© standard, and is based on generic formalism for policy modelling, grounded in normative systems and deontic logic. We show the use of the framework for a clinical research scenario.

Language, culture and society: Modality, face and societal logic

It is common to distinguish between individualistic cultures typically associated with Western countries and collectivistic cultures normally linked to Asian countries. Some countries are not easily characterized, because they are placed right in the middle of the continuum. This concerns, for instance, Russia. In this paper, I will attempt to demonstrate on the basis of the theory of communicative supertypes that the notion of individualism is intimately connected to the notion of alethic modality – concerned with laws of nature, i.e. what is possible, impossible, necessary and unnecessary – whereas the notion of collectivism is tied up with the notion of deontic modality having to do with laws of society, i.e. permission, prohibition, obligation and non-obligation. Specifically, the British-English speaking speech community is based on the alethic notion of possibility and guided by the hearer's face, i.e. second person, in contrast to the Mandarin-Chinese-speaking community which is based on the deontic notion of obligation and guided by the speaker’s face, i.e. first person. Compared to this, the Russian-speaking community stands out as a third unnoticed variant that seems to differentiate nature and society by making a sharp distinction within their aspectually defined modality system, between alethic and deontic logic expressed by the perfective and the imperfective aspect, respectively. That Russian culture must be a third variant is confirmed by their understanding of face as being defined in relation to the situation itself, i.e. third person.

Using n-ary multi-modal logics in argumentation frameworks to reason about ethics

Autonomous behaviors may raise ethical issues that agents must consider in their reasoning. Some approaches use deontic logics, while others consider a value-based argumentation framework. However, no work combines both modal logic and argumentation to reason about ethics. Hence, we propose a new argumentation framework where arguments are built from a n-ary multi-modal logic. It allows to express different kinds of operators, e.g. nullary choice or moral worth operators, dyadic deontic operators or mental states. However the standard attacks based on logical contradictions are no longer sufficient to catch an intuitive meaning for attacks. Hence, we enrich standard attacks by characterizing how oppositions between modal operators arise. Furthermore we show the standard logic-based attacks have a quasi-symmetry property, i.e. when an argument attacks another, this argument is necessarily attacked by another one. Our modal attacks do not have this property, which is highly relevant to decide a dilemma.

The Simplest Solution to the Deepest Paradox of Deontic Logic

The Simplest Solution to the Deepest Paradox of Deontic Logic

Deontic meta-rules

Abstract The use of meta-rules in logic, i.e., rules whose content includes other rules, has recently gained attention in the setting of non-monotonic reasoning: a first logical formalisation and efficient algorithms to compute the (meta)-extensions of such theories were proposed in Olivieri et al. (2021, Computing defeasible meta-logic. In JELIA 2021, LNCS, vol. 12678, pp. 69–84. Springer.). This work extends such a logical framework by considering the deontic aspect. The resulting logic will not just be able to model policies but also tackle well-known aspects that occur in numerous legal systems. The use of Defeasible Logic to model meta-rules in the application area we just alluded to has been investigated. Within this line of research, the study mentioned above was not focusing on the general computational properties of meta-rules. This study fills this gap with two major contributions. First, we introduce and formalise two variants of Defeasible Deontic Logic (DDL) with meta-rules to represent (i) defeasible meta-theories with deontic modalities and (ii) two different types of conflicts among rules: Simple Conflict DDL and Cautious Conflict DDL. Second, we advance efficient algorithms to compute the extensions for both variants.

Driving Decision Making of Autonomous Vehicle According to Queensland Overtaking Traffic Rules

Improving the safety of autonomous vehicles (AVs) by making driving decisions in accordance with traffic rules is a complex task. Traffic rules are often expressed in a way that allows for interpretation and exceptions, making it difficult for AVs to follow them. This paper proposes a novel methodology for driving decision making in AVs based on defeasible deontic logic (DDL). We use DDL to formalize traffic rules and facilitate automated reasoning, allowing for the effective handling of rule exceptions and the resolution of vague terms in rules. To supplement the information provided by traffic rules, we incorporate an ontology for AV driving behaviour and environment information. By applying automated reasoning to formalized traffic rules and ontology-based AV driving information, our methodology enables AVs to make driving decisions in accordance with traffic rules. We present a case study focussing on the overtaking traffic rule to illustrate the usefulness of our methodology. Our evaluation demonstrates the effectiveness of the proposed driving decision-making methodology, highlighting its potential to improve the safety of AVs on the road.

Fractional-Valued Modal Logic and Soft Bilateralism

In a recent paper, under the auspices of an unorthodox variety of bilateralism, we introduced a new kind of proof-theoretic semantics for the base modal logic \(\mathbf{K}\), whose values lie in the closed interval \([0,1]\) of rational numbers [14]. In this paper, after clarifying our conception of bilateralism – dubbed “soft bilateralism” – we generalize the fractional method to encompass extensions and weakenings of \(\mathbf{K}\). Specifically, we introduce well-behaved hypersequent calculi for the deontic logic \(\mathbf{D}\) and the non-normal modal logics \(\mathbf{E}\) and \(\mathbf{M}\) and thoroughly investigate their structural properties.

Mitigating Adversarial Norm Training with Moral Axioms

This paper addresses the issue of adversarial attacks on ethical AI systems. We investigate using moral axioms and rules of deontic logic in a norm learning framework to mitigate adversarial norm training. This model of moral intuition and construction provides AI systems with moral guard rails yet still allows for learning conventions. We evaluate our approach by drawing inspiration from a study commonly used in moral development research. This questionnaire aims to test an agent's ability to reason to moral conclusions despite opposed testimony. Our findings suggest that our model can still correctly evaluate moral situations and learn conventions in an adversarial training environment. We conclude that adding axiomatic moral prohibitions and deontic inference rules to a norm learning model makes it less vulnerable to adversarial attacks.

Do de re necessities express semantic rules?

ABSTRACT Amie Thomasson's Norms and Necessity offers a non-factualist theory of the language of metaphysical necessity, centering on the idea that statements of necessity express semantic norms. This article identifies a potential problem for the view by distinguishing two kinds of conditional necessity, investigates a solution derived from a well-known parallel pair of conditional necessities in deontic logic, but finds it is not up to the job. The last part of the paper suggests a different route, largely in keeping with the underlying ideas behind Thomasson's approach.

Permissive and regulative norms in deontic logic

Abstract This article provides a systematic analysis of the well-known notions of weak and strong permission in input/output (I/O) logic. We extend the account of permission initially put forward by Makinson and Van der Torre to the whole family of I/O systems developed during the last two decades. The main contribution is a series of characterization results for strong permission, based on establishing the so-called non-repetition property. We also study an input/output logic not yet covered in the literature. It supports reasoning by cases—a natural feature of human reasoning. The output is not closed under logical entailment. At the same time, it avoids excess output using a consistency check—a technique familiar from non-monotonic logic. This makes it well suited for contrary-to-duty reasoning. The axiomatic characterization is in terms of a generalized OR rule. We discuss the implications of all this for our understanding of the notion of the coherence of a normative system. Topics for future research are identified.1

A BERT-based deontic logic learner

In recent years, large-scale Pre-trained Language Models (PLMs) like BERT have achieved state-of-the-art results on many NLP tasks. We explore whether BERT understands deontic logic which is important for the fields of legal AI and digital government. We measure BERT's understanding of deontic logic through the Deontic Modality Classification (DMC) task. Experiments show that without fine-tuning or fine-tuning with only a small amount of data, BERT cannot achieve good performance on the DMC task. Therefore, we propose a new method for BERT fine-tuning and prediction, called DeonticBERT. The method incorporates heuristic knowledge from deontic logic theory as an inductive bias into BERT through a template function and a mapping between category labels and predicted words, to steer BERT understand the DMC task. This can also stimulate BERT to recall the deontic logic knowledge learned in pre-training. We use an English dataset widely used as well as a Chinese dataset we constructed to conduct experiments. Experimental results show that on the DMC task, DeonticBERT can achieve 66.9% and 91% accuracy under zero-shot and few-shot conditions, respectively, far exceeding other baselines. This demonstrates that DeonticBERT does enable BERT to understand deontic logic and can handle related tasks without using much fine-tuning data. Our research helps facilitate applying large-scale PLMs like BERT into legal AI and digital government.