Deontic Logic

Making decisions despite conflicting norms and incomplete or unreliable information is a fundamental challenge for autonomous systems. We introduce a simple doxastic deontic logic for this setting: a classically reducible fragment of Chellas' Minimal Deontic Logic, extended with explicit conditional norms and combined with multi-agent KD45, so that norms can depend on agents' beliefs about both facts and norms. On this logic we define the Doxastic Norm Compliance Optimization Problem, where an agent chooses a decision minimizing weighted norm violations. We distinguish subjective optimization (relative to the agent's beliefs) from objective optimization (relative to the actual facts). We give conditions under which (i) the two coincide and (ii) optimal decision-making can be reduced to weighted partial MaxSAT in polynomial time.

As robotic systems grow more general, legal norms are needed to integrate them into society. This paper extends the isomorphism problem of aligning legal source texts with their encodings, and measures two key challenges to robot normative control: (1) the grounding isomorphism gap, where perception error grounds false atoms for legal reasoning, and (2) the ontological isomorphism gap, where one legal conclusion admits many faithful translations into planning constraints. The paper introduces a legal planning stack that employs Defeasible Deontic Logic (DDL) to constrain a motion planner. The stack leverages learned world models to plan and to provide legal context, enabling ex ante governance that intervenes before an illegal action is executed. It was deployed on a simulated robot arm pushing a cube across a 3x3 grid. The findings were (1) the legislated agent abided substantially more often than the non-legislated one, and modeling perception uncertainty lifted abidance even further, (2) the legal reasoning ran efficiently at runtime and its verdicts were auditable, and (3) the stack adapted to exogenous signals and endogenous rule changes. Both gaps were measured: (4) world model and probe error corrupted the factual input for the DDL reasoner, and (5) a single law admitted several faithful metric interpretations yielding drastically different abidance. Thus, ex ante legislation functions as intended, and closing these gaps with a standardized mapping from the law to runtime constraints and improved fact grounding from perception will yield robust laws that align robot behavior with society's norms. Project page: https://dylanwaldner-cail.github.io/Legislated-Planner/.

Institutional policies stay in natural language while the systems that check compliance demand machine-readable constraints. Bridging that gap is still done by hand. PolicyKG closes the loop. It is an LLM pipeline that reads a policy PDF, classifies each sentence as an obligation, permission, or prohibition, lifts the label into first-order deontic logic, and emits SHACL constraints. Four stages run on a LangGraph state machine with per-stage validators. The piece that matters most is the Corpus Adapter: a YAML vocabulary registry that grounds LLM predicates in a target ontology. Retargeting to a new domain means swapping the registry, not retraining a model. On the Asian Institute of Technology Policies and Procedures corpus (1,663 sentences, 443 rules), PolicyKG reaches 86.9% deontic classification accuracy (Cohen's kappa = .709). Three annotators independently re-label a 50-item sample and agree at Fleiss' kappa = .844. SHACL shape correctness on a 69-shape subset is F1 = .866. The FOL path handles 79.2% of rules; the rest go through a direct NL-to-SHACL fallback. We audited every one of the 443 rules for second- or higher-order constructs. An automated regex checklist flagged none, and a first-author pass on the 92 FOL-fallback cases confirmed the same. The exact upper 95% Clopper-Pearson bound on the true HOL rate is 0.67%. This is an audit finding for one corpus, not a proof of FOL sufficiency for institutional policy. Swapping the AIT registry for a GDPR registry raises exact property alignment from 1/15 to 11/15 (Fisher's exact p < .001; Cohen's h = 1.53). On the LexDeMod lease-contract benchmark (N = 200), Macro F1 drops to .370 because lease English uses "shall be entitled" for permission -- exactly the vocabulary mismatch registry swap is meant to fix. Repeated runs produce hash-identical SHACL outputs.

ODRL policy evaluators produce verdicts, but say nothing about the normative positions a policy brings into existence, the authority structures those positions presuppose, or who holds the power to declare a norm violated. We formulate the Cross-Level Design Principle: any normative language with violable, consequential norms requires both conduct-level positions (Permission, Duty, Right, No right) and competence-level positions (Power, Subjection, Immunity, Disability). Applying this to ODRL, we establish that prohibition is sanctioned (violation possible and consequential), that permission is underspecified across its behaviour parameter (open vs. closed world), and that the formal semantics covers achievement obligations only. We ground ODRL in UFO-L, mapping each activated rule to a simple legal relator and extending coverage from two to eight legal positions; violation-declaration authority, implicit in every existing evaluator, becomes an explicit Power-Subjection pair. All axioms are mechanically verified in Isabelle/HOL and across a 39-problem benchmark under Vampire, E, and Z3.

Autonomous agentic AI systems driven by Large Language Models (LLMs) introduce a new class of security, privacy, and compliance challenges: an agent that can invoke tools, manipulate data, install software, and coordinate with peer agents across organizational boundaries must be constrained not just by authentication and access control, but by the full structure of enterprise governance. This includes specifying what agents are permitted and prohibited from doing, what they areobliged to do after certain actions (e.g., notify the CISO), under what conditions a standing obligation may be waived, and which rules take precedence when policies conflict. This governance problem exceeds what current policy engines provide. Systems such as XACML, Rego, and Cedar address only the permit/prohibit subset of this governance structure. They do not provide obligation lifecycle management, meta-policy conflict resolution, dispensations that waive obligations in specific circumstances, and ontological reasoning over domain class hierarchies commonly found in applications such as healthcare, cybersecurity, or data privacy. We propose AgenticRei, which realizes key governance requirements such as obligations, dispensations, policy conflict resolutions, and reasoning over policies, as well as the basic permit/prohibit constraints. We use a deontic policy language built on the Rei framework, expressed as OWL (Web Ontology Language) and evaluated at runtime by a high-performance logic engine entirely outside the LLM. The same pipeline governs both tool invocations by the agent and agent-to-agent messages. We show through examples that deontic policies capture governance constraints around security and privacy that mostly cannot be expressed in current production engines. Our approach composes naturally with industry-standard frameworks like A2AS.

This paper proposes a Situation Calculus solution to the frame problem for obligation-producing actions, which are actions that create obligations on the part of the agent that performs them. As an example of such actions, we have an opening door action performed by an agent, which has the subsequent obligation of getting the door closed. Demolombe and others extend Raymond Reiter's solution to the frame problem for ordinary actions to accommodate obligation-producing actions. Obligation-producing actions do affect the truth value of a newly introduced fluent that captures the accessibility relation used in semantics of obligation modalities in the Situation Calculus. Our work simplifies Demolombe's characterization of the accessibility relation by eliminating the notion of ideality of situations, thereby remaining close to Kripke-style possible-world semantics for deontic logic, in the spirit of Governatori's approach. Furthermore, we spell out details of a complete solution by extending basic action theories of Reiter to the new setting. Finally, we extend Reiter's regression operator for reasoning about actions back to the initial situation to this new setting. Our solution yields intuitive properties that one would expect from obligations: for example, if a sentence is obligatory to an agent in a given situation, it remains so in subsequent situations unless the obligation is explicitly stopped.

Rule-following agents tasked with executing policies and regulations often fail via Silent Scope Omission (SSO): a model applies a general rule but silently drops nested exceptions or counter-exceptions, producing outputs that appear compliant yet break on important edge cases. Although such failures are often framed as an agentic-systems problem, the underlying bottleneck is statutory and policy understanding, a capability typically studied in legal NLP. However, most existing legal NLP benchmarks emphasize end-task outcomes, which can overlook the structural omissions that cause SSO. To diagnose and mitigate SSO, we introduce NormBench, a benchmark of 2,290 provisions spanning Chinese (laws and local policies), English (U.S. tax law, GDPR, and corporate policies), and cross-lingual settings, designed for defeasible scope parsing: identifying precisely which clause overrides which. NormBench uses Span-Grounded Deontic Trees (SG-DT), a compiler-style intermediate representation that anchors every logical branch to source spans and requires explicit exclusion guards, enabling deterministic compilation and audit. Evaluations of frontier LLMs reveal two recurring pathologies: (1) Recursion Decay, where performance drops sharply as defeater depth increases, and (2) an Auditability Trap, where models retrieve relevant spans but fail to assemble correct control flow. Using SG-DT as a constrained intermediate output improves whole-tree fidelity and defeater recovery, and downstream experiments show that its utility is mechanism-specific: gains concentrate on exception-active, SSO-prone cases, while aggregate accuracy can be mixed when the added structure is unnecessary or parser fidelity is low.

Technical-standard compliance reasoning may involve incomplete evidence, inconsistent observations, exceptions, and derived normative outputs. This paper presents \textsc{Monir}, a four-valued normative intermediate representation for ASP-oriented compliance workflows. \textsc{Monir} separates factual support from normative outputs: facts are represented by positive and negative support bits, while deontic labels are rule-generated output constructors interpreted by aggregation policies. Its core semantics is a staged transition system over support configurations. We define the language, rule-state interface, diagnostics, and policy-parametric reporting; characterize admissible staged evaluation by a dependency graph; prove deterministic polynomial-time evaluation for fixed evidence; and give NP/coNP upper bounds, with matching hardness for representative completion-based verdict queries.

In response to a concern raised by Horty, this paper develops a two-tiered, preference-based semantic framework for modeling defeasible conditional obligations. The paper extends a Hansson-Lewis style preference semantics for dyadic deontic logic by incorporating a nonmonotonic reasoning mechanism that enables previously derived obligations to be withdrawn when new, potentially conflicting information comes in. The account is bi-preferential: two orderings--ideality and normality--on worlds are employed to address shortcomings in earlier approaches, with a separate ranking method for each. At the nonmonotonic layer, a number of postulates are considered, including antecedent strengthening, inclusion and no-drowning. A connection is established with so-called constrained input/output (I/O) logic--an existing standard for normative reasoning based on a different methodology.