Deontic Logic Research Articles

Logik beim dogmatischen Setzen mit schwach inferenziellem Anspruch. Nicht-Monotonie und Geltungsränge in der juristischen Ordnungsbildung

How logic can cope with the law, and vice versa, strongly depends on how one imagines the structure of legal reasoning. Of course, one can analyze relationships between (supposed) statements of legal code in the conditional, prescriptive form deontic logic is acquainted with; they will behave as standard deontic sentences do. But that captures neither the set of sentences that actually guides legal decisions nor the way lawyers actually deal with it. Especially in the German doctrinal tradition, the actually decisive set contains further sentences that establish integrity and order; the work of lawyers is mainly to construct, compatibilize and apply such sentences. The big question is then, how well these sentences and their relationships can be digested in logical terms. The paper connects findings from the debate about the construction of legal systems with Wolfgang Spohn’s decision theory based on defeasible normative reasoning. Indeterminacy and overcomplexity will always rule out full formalizations of legal reasoning. But since doctrinal thinking strives for consistency and rule-based, deductive rationality, jurisprudence can draw on formal theory to reflect on its own standards of analysis.

Who is Right, Who is Wrong? Interpreting 14 Points of Wilson – A Case Study of Deontic Modals and their Meanings

Abstract The document titled “14 points of Wilson” was announced by the President of the United States Woodrow Wilson in his speech addressed to the United States Congress on 8th January 1918. The speech is one of the most well known documents of the First World War as it touched upon several world issues. The text has been interpreted ever since in respect to the importance and real meaning of points formulated by Wilson. One of the points referred to Poland. The aim of the paper is to focus on the exponents of deontic modality used in that text of historical value and to find the answer to the question concerning the deontic value of each point. The analysis will encompass the principles of deontic logic as well as the meaning of deontic modals in legal discourse at the time of speech delivery as those 14 points should be classified as a text belonging to legal genres. The aim of the paper is to present the historical background and the linguistic analysis in order to find out whether historical facts, interpretations and language used correspond with one another.

Formalizing commitments using the event calculus and RuleML

Smart Contracts enable the automated execution of exchanges on the blockchain. From an ontological perspective, smart contracts create and automate the fulfillment of social commitments between actors. Whereas traditional deontic logic is used to make a legal determination in contractual multi-actor interactions, this paper focuses on the consequences of these actions resulting from that determination, thereby shifting the focus from monitoring to execution. The interactions between actors and the consequences in terms of commitments have not yet been formalized for smart contracts. The perspective of smart contracts is interesting, since they are considered to be autonomous agents, able to generate automated actions. We use the Event Calculus as a formal logic to represent and reason about the effects of these automated actions and the resulting commitments. Since the Event Calculus deals with local events and the consideration of time, this approach enables the uniform representation of commitments, including their operations and reasoning rules.

MODAL LOGIC BETWEEN TRADITIONNAL (ARISTOTLE, IBN SINA) AND CONTEMPORARY APPROACH

Aristotle founded the science of logic in order to control language source of fallacies and sophistry. He built his syllogistic on two basic principles: non-contradiction and the excluded middle. He distinguished between different types of statements: declarative and non-declarative, only the first type was used in syllogism’s theory, because it is a tool of demonstrative science. He divided them, declarative statement, into two categories: Assertorics, and modals (necessary, possible, contingent, impossible) which he encountered difficulties in his logical analysis, because it is out of frame two valued according to the two principles, such as propositions that occur in the future whose cannot be determined now. This kind of statement was also treated by the Muslims logicians, especially Ibn Sīnā who expanded the modal concept to other field like Temporal modalities (always, sometimes, never), but he could not get out the Aristotelian context. The concept expended in contemporary logic system to include other sort of modality like: epistemological, deontic, tense … This resulted the emergence of contemporary logical systems, (epistemic logic, deontic logic, tense logic), whose approach differs from the traditional one. The propose of the article is to show the difference between the approaches Keywords: Logic; Modality; Epistemological; Deontic, Temporal; Truth; False.

Algorithmic Ethics: Formalization and Verification of Autonomous Vehicle Obligations

In this article, we develop a formal framework for automatic reasoning about the obligations of autonomous cyber-physical systems, including their social and ethical obligations. Obligations, permissions, and prohibitions are distinct from a system's mission, and are a necessary part of specifying advanced, adaptive AI-equipped systems. They need a dedicated deontic logic of obligations to formalize them. Most existing deontic logics lack corresponding algorithms and system models that permit automatic verification. We demonstrate how a particular deontic logic, Dominance Act Utilitarianism (DAU) [23], is a suitable starting point for formalizing the obligations of autonomous systems like self-driving cars. We demonstrate its usefulness by formalizing a subset of Responsibility-Sensitive Safety (RSS) in DAU; RSS is an industrial proposal for how self-driving cars should and should not behave in traffic. We show that certain logical consequences of RSS are undesirable, indicating a need to further refine the proposal. We also demonstrate how obligations can change over time, which is necessary for long-term autonomy. We then demonstrate a model-checking algorithm for DAU formulas on weighted transition systems and illustrate it by model-checking obligations of a self-driving car controller from the literature.

On Blass Translation for Leśniewski’s Propositional Ontology and Modal Logics

In this paper, we shall give another proof of the faithfulness of Blass translation (for short, B-translation) of the propositional fragment $$\mathbf{L}_1$$ of Leśniewski’s ontology in the modal logic $$\mathbf{K}$$ by means of Hintikka formula. And we extend the result to von Wright-type deontic logics, i.e., ten Smiley-Hanson systems of monadic deontic logic. As a result of observing the proofs we shall give general theorems on the faithfulness of B-translation with respect to normal modal logics complete to certain sets of well-known accessibility relations with a restriction that transitivity and symmetry are not set at the same time. As an application of the theorems, for example, B-translation is faithful for the provability logic $$\mathbf{PrL}$$ (= $$\mathbf{GL}$$ ), that is, $$\mathbf{K}$$ $$+$$ $$\Box (\Box \phi \supset \phi ) \supset \Box \phi $$ . The faithfulness also holds for normal modal logics, e.g., $$\mathbf{KD}$$ , $$\mathbf{K4}$$ , $$\mathbf{KD4}$$ , $$\mathbf{KB}$$ . We shall conclude this paper with the section of some open problems and conjectures.

Stit semantics for epistemic notions based on information disclosure in interactive settings

We characterize four types of agentive knowledge using a stit semantics over branching discrete-time structures. These are ex ante knowledge, ex interim knowledge, ex post knowledge, and know-how. The first three are notions that arose from game-theoretical analyses on the stages of information disclosure across the decision making process, and the fourth has gained prominence both in logics of action and in deontic logic as a means to formalize ability. In recent years, logicians in AI have argued that any comprehensive study of responsibility attribution and blameworthiness should include proper treatment of these kinds of knowledge. This paper intends to clarify previous attempts to formalize them in stit logic and to propose alternative interpretations that in our opinion are more akin to the study of responsibility in the stit tradition. The logic we present uses an extension with knowledge operators of the Xstit language, and formulas are evaluated with respect to branching discrete-time models. We also present an axiomatic system for this logic, and address its soundness and completeness.

A Deontic Stit Logic Based on Beliefs and Expected Utility

The formalization of action and obligation using logic languages is a topic of increasing relevance in the field of ethics for AI. Having an expressive syntactic and semantic framework to reason about agents' decisions in moral situations allows for unequivocal representations of components of behavior that are relevant when assigning blame (or praise) of outcomes to said agents. Two very important components of behavior in this respect are belief and belief-based action. In this work we present a logic of doxastic oughts by extending epistemic deontic stit theory with beliefs. On one hand, the semantics for formulas involving belief operators is based on probability measures. On the other, the semantics for doxastic oughts relies on a notion of optimality, and the underlying choice rule is maximization of expected utility. We introduce an axiom system for the resulting logic, and we address its soundness, completeness, and decidability results. These results are significant in the line of research that intends to use proof systems of epistemic, doxastic, and deontic logics to help in the testing of ethical behavior of AI through theorem-proving and model-checking.

An impossibility result on methodological individualism

Methodological individualists often claim that any social phenomenon can ultimately be explained in terms of the actions and interactions of individuals. Any Nagelian version of methodological individualism requires that there be bridge laws that translate social statements into individualistic ones. We show that Nagelian individualism can be put to logical scrutiny by making the relevant social and individualistic languages fully explicit and mathematically precise. In particular, we prove that the social statement that a group of (at least two) agents performs a deontically admissible group action cannot be expressed in a well-established deontic logic of agency that models every combination of actions, omissions, abilities, and obligations of finitely many individual agents.

Logic of defeasible permission and its dynamics

Abstract This paper develops a deontic logic for defeasible permission and studies norm change in various updated semantics. When one grants that $\varphi $ or $\psi $ is permitted, normally, it goes together with the conjunction of a permission of $\varphi $ and that of $\psi $. In the monotonic reasoning on this permission, a permission of $\varphi $ leads to a permission of $\varphi $ and $\psi $; however, if a prohibition of $\psi $ is introduced, we get into trouble. We face a paradox of free choice permission. Many solutions have been proposed, but a systematic account of handling norm change is still needed. This paper first introduces the notion of normality to develop a sound and complete deontic logic for defeasible permission, which can be used to analyse several notions in natural language and in game theory. Further, following Lewis’ idea of norm change, a systematic way to capture various dynamics for updating permission and obligation is proposed.

Towards an efficient rule-based framework for legal reasoning

A rule based knowledge system consists of three main components: a set of rules, facts to be fed to the reasoning corresponding to the data of a case, and an inference engine. In general, facts are stored in (relational) databases that represent knowledge in a first-order based formalism. However, legal knowledge uses defeasible deontic logic for knowledge representation due to its particular features that cannot be supported by first-order logic. In this work, we present a unified framework that supports efficient legal reasoning. In the framework, a novel inference engine is proposed in which the Semantic Rule Index can identify candidate rules with their corresponding semantic rules if any, and an inference controller is able to guide the executions of queries and reasoning. It can eliminate rules that cannot be fired to avoid unnecessary computations in early stages. The experiments demonstrated the effectiveness and efficiency of the proposed framework.

Ontology and rule-based natural language processing approach for interpreting textual regulations on underground utility infrastructure

The nation’s massive underground utility infrastructure must comply with a multitude of regulations. The regulatory compliance checking of underground utilities requires an objective and consistent interpretation of the regulations. However, utility regulations contain a variety of domain-specific terms and numerous spatial constraints regarding the location and clearance of underground utilities. It is challenging for the interpreters to understand both the domain and spatial semantics in utility regulations. To address the challenge, this paper adopts an ontology and rule-based Natural Language Processing (NLP) framework to automate the interpretation of utility regulations – the extraction of regulatory information and the subsequent transformation into logic clauses. Two new ontologies have been developed. The urban product ontology (UPO) is domain-specific to model domain concepts and capture domain semantics on top of heterogeneous terminologies in utility regulations. The spatial ontology (SO) consists of two layers of semantics – linguistic spatial expressions and formal spatial relations – for better understanding the spatial language in utility regulations. Pattern-matching rules defined on syntactic features (captured using common NLP techniques) and semantic features (captured using ontologies) were encoded for information extraction. The extracted information elements were then mapped to their semantic correspondences via ontologies and finally transformed into deontic logic (DL) clauses to achieve the semantic and logical formalization. The approach was tested on the spatial configuration-related requirements in utility accommodation policies. Results show it achieves a 98.2% precision and a 94.7% recall in information extraction, a 94.4% precision and a 90.1% recall in semantic formalization, and an 83% accuracy in logical formalization.

Extensional Higher-Order Paramodulation in Leo-III

Leo-III is an automated theorem prover for extensional type theory with Henkin semantics and choice. Reasoning with primitive equality is enabled by adapting paramodulation-based proof search to higher-order logic. The prover may cooperate with multiple external specialist reasoning systems such as first-order provers and SMT solvers. Leo-III is compatible with the TPTP/TSTP framework for input formats, reporting results and proofs, and standardized communication between reasoning systems, enabling e.g. proof reconstruction from within proof assistants such as Isabelle/HOL. Leo-III supports reasoning in polymorphic first-order and higher-order logic, in all normal quantified modal logics, as well as in different deontic logics. Its development had initiated the ongoing extension of the TPTP infrastructure to reasoning within non-classical logics.

Deontic Concepts and Their Clash in Mīmāṃsā: Towards an Interpretation

AbstractThe article offers an overview of the deontic theory developed by the philosophical school of Mīmāṃsā, which is, and has been since the last centuries BCE, the main source of normative concepts in Sanskrit thought. Thus, the Mīmāṃsā deontics is interesting for any historian of philosophy and constitutes a thought‐provoking occasion to rethink deontic concepts, taking advantage of centuries of systematic reflections on these topics. Some comparison with notions currently used in Euro‐American normative theories and metaethical principles is offered in order to show possible points of contact and deep divergences. In more detail, after an introduction explaining the methodology and aims of our work, we discuss how Mīmāṃsā authors distinguished and defined some fundamental deontic concepts, such as different types of prescriptions and prohibitions. We then discuss how Mīmāṃsā authors approached the problem of conflicts among commands without jeopardising the validity of the normative text issuing them. In the second part of the article we introduce our formal apparatus, which is construed around the main taxonomic and conceptual distinctions used in the first part. Our formal rendering captures the most important features of the Mīmāṃsā theory and can thus serve as a concise and rigorous presentation of it for scholars working in deontic logic.

Killing Gently by Means of the śyena: The Navya-Nyāya Analysis of Vedic and Secular Injunctions (vidhi) and Prohibitions (niṣedha) from the Perspective of Dynamic Deontic Logic

In the present paper we model the Navya-Nyāya analysis of Vedic and secular injunctions and prohibitions by means of Giordani’s and Canavotto’s system ADL (“Action Deontic Logic”) of dynamic deontic logic. Navya-Naiyāyikas analyze the meaning of injunctions and prohibitions by reducing them to plain indicative statements about certain properties whose presence or absence in the enjoined or prohibited action serves as a criterion for the truth or falsity of the “inducing” or “restraining knowledge”, a kind of qualificative cognition instilled in the recipient of an injunction or prohibition. Thus, Navya-Naiyāyikas have found their own way to solve Jorgensen’s Puzzle concerning the very idea of a deontic logic as a tool to analyze arguments based on sentences which do not seem to be truth-apt. The teleological aspect of the Navya-Nyāya characterization of an enjoined or prohibited action can also give a clue to solutions of other puzzles and paradoxes which have beset the development of deontic logic in the West. A specific contrary-to-duty puzzle from the Indian tradition is related to the śyena, a malefic sacrifice meant for harming one’s enemy. The Vedic injunction to perform such a sacrifice runs counter to a religious practitioner’s duty not to harm a living being. In the present paper we examine the cogency of the very different solutions to this dilemma suggested by the Mīmāṃsaka Prabhākara on the one hand and the Navya-Naiyāyika Gaṅgeśa on the other hand.

Why formal objections to the error theory fail

Abstract Many philosophers argue that the error theory should be rejected because it is incompatible with standard deontic logic and semantics. We argue that such formal objections to the theory fail. Our discussion has two upshots. First, it increases the dialectical weight that must be borne by objections to the error theory that target its content rather than its form. Second, it shows that standard deontic logic and semantics should be revised.

No-Right and its Correlative

Abstract: This article aims to dispel the confusion over no-right by drawing attention to three straightforward points, and by examining a neglected source of complexity. The former embrace the practical significance of a no-right within Hohfeld’s scheme; the important difference between the practical significance of a normative position and the theoretical status of the concept representing it; and, the relationship between logical duals and contradictories when applied to normative positions. The complexity is associated with liberty as the correlative of no-right, and involves recognizing a connection with the operators of deontic logic. The conventional interdefinability of permission and obligation is challenged; “liberty” is regarded as an inadequate label for the normative position signifying the absence of duty, and, as a distinctive position, is not a true correlative of any other position. Implications are noted for the theoretical problem faced by deontic logic when confronting normative relations between individuals, and for the solution of practical problems within a (legal or moral) normative system.

Practical Sentences, Their Meaning and Their Validity

Following Richard M. Hare1 I think that we use practical sentences as decision criteria. We understand their meaning if we know what decision to take according to them. But it is not clear, how exactly decision criteria are related to decisions and how they function as criteria. To fully understand this role, we need a formal semantics of practical sentences. For this I have to introduce a formal language and give an interpretation of it. This language has to be constructed in such a way that a translation into ordinary language is always possible in principle. Thus, we make sure that our semantics and logic will have an impact on the solution of concrete practical problems. According to this program I will first introduce the formal language ‘LP1’. To give an interpretation of it I will then clarify what a decision is and show how practical sentences function as decision criteria. On this basis I give an interpretation of the primitive two-place operator ‘PT p,q’ and the one-place operator ‘VTp’. I further argue that we make meta-decisions concerning the application of first-order decision-criteria. This allows me to introduce a new concept of practical validity, which differs radically from the concept of truth. Using this concept, I then give an interpretation of the deontic operators ‘OTp’, ‘FTp’, ‘ATp’ and ‘ITp’. The concept of practical validity makes it also possible to introduce practical logical connectors and mixed logical connectors on the basis of practical or mixed value tables. These connectors are used – among others – in bridge-principles, which play an important role in ethical and juridical theories. Finally, I shortly explain the semantics of the main kinds of practical sentences, i.e. value judgments, imperatives, norms and intentions, and I argue that we need a deontic logic in order to use practical sentences in a correct way.

Towards a Metatheoretical Postmodern Approach to Legal Reasoning

This paper focuses on legal reasoning, arguing that although methodological theories are important, they are not enough to explain how to reason in law. In fact, because the different philosophical perspectives vary so significantly in their ability to resolve legal conflicts, when a less “adapted” perspective decides a legal question, the results can be disastrous. Thus, this paper inaugurates a new attitude, stating that a general philosophical perspective is the only way out. Relying on a metatheoretical postmodern approach, it argues that logic, analysis, argumentation and hermeneutics are complementary theories that offer a unique perception of law. It concludes that the approach proposed makes possible not only a comprehensive view of the way legal reasoning behaves, but more than this, a proportionate flexibility to both civil and common law systems. Keywords: Paraconsistent Logic; Metatheoretical Postmodern Approach; Metatheoretical Perspective; Paraconsistent Deontic Logic; Ontological Hermeneutics

Hypersequent calculi for non-normal modal and deontic logics: countermodels and optimal complexity

AbstractWe present some hypersequent calculi for all systems of the classical cube and their extensions with axioms ${T}$, ${P}$ and ${D}$ and for every $n \geq 1$, rule ${RD}_n^+$. The calculi are internal as they only employ the language of the logic, plus additional structural connectives. We show that the calculi are complete with respect to the corresponding axiomatization by a syntactic proof of cut elimination. Then, we define a terminating proof search strategy in the hypersequent calculi and show that it is optimal for coNP-complete logics. Moreover, we show that from every failed proof of a formula or hypersequent it is possible to directly extract a countermodel of it in the bi-neighbourhood semantics of polynomial size for coNP logics, and for regular logics also in the relational semantics. We finish the paper by giving a translation between hypersequent rule applications and derivations in a labelled system for the classical cube.