Deontic Logic in
2020-2030
Deontic logic investigates the logical relations among normative concepts such as obligation, permission, and prohibition. This branch of symbolic logic received more attention in recent years due to trustworthy and responsible AI applications. In this online event, some experts in this domain will discuss the future of deontic logic in 2020-2030. The Individual and Collective Reasoning Group (ICR) organizes the workshop at the University of Luxembourg on 2 October 2020. If you want to attend the workshop, please contact the organizer (ali.farjami@uni.lu).
Program
Deontic Logic as Nonmonotonic Logic
Abstract: Traditionally deontic logic was perceived as a branch of modal logic. However, research in the past thirty years have developed deontic logic as a generalization of nonmonotonic logic. In this talk I present an overview of this development, and the challenge of unifying preference-based and rule-based semantics in deontic logic as well as in non-monotonic logic.
How to make the BOID ethical
From (Deontic) Logic to (the Lawyer’s) Practice
Abstract: How can Deontic logic help non-logicians, such as lawyers, auditors and jurists in their work? In this talk, I describe a current effort to establish the whole process from the theoretical logic to the desktop of legal practitioners. I will explain the different stations in the process, what are the challenges for each one of them and some possible solutions.
Some Notes on Priorities, Defaults and Argumentation
Abstract: Default logic and formal argumentation are paradigmatic methods in the study of nonmonotonic inference. Defeasible information often comes in different strengths stemming from different degrees of reliability in epistemic applications or from varying strengths of authorities issuing norms in deontic applications. In both paradigms methods have been developed to deal with prioritized knowledge bases. Questions of comparability of these methods therefore naturally arise. Argumentation theory has been developed with a strong emphasis on unification. It is therefore a desideratum to obtain natural representations of various approaches to (prioritized) default logic within frameworks of structured argumentation, such as ASPIC. Important steps in this direction have been presented in Liao et al. [2016,2019]. In this talk I will present some new results and generalizations of earlier translations.
New Standard Linear Deontic Logic with Choice Connective
Legal Balancing — A Case Study in LogiKEy
Christoph Benzmüller, David Fuenmayor, Bertram Lomfeld
Abstract: Enabling machines to legal balancing is a non-trivial task challenged by a multitude of factors some of which are addressed and explored in this work. We propose a holistic approach to formal modeling at different abstraction layers supported by a pluralistic framework in which the encoding of an ethico-legal value and upper ontology is developed in combination with the exploration of a formalization logic, with legal domain knowledge and with exemplary use cases until a reflective equilibrium is reached. Our work is enabled by a meta-logical approach to universal logical reasoning and it applies the recently introduced \logikey\ methodology for designing normative theories for ethical and legal reasoning. The particular focus in this paper is on the formalization and encoding of a value ontology suitable e.g. for explaining and resolving legal conflicts in property law (wild animal cases).
Ibn Ḥazm on Heteronomous Imperatives
Remarks on The Emergence of Deontic Logic
Abstract: Ibn Ḥazm of Córdoba’s (994-1064) defence of logic has lasting consequences for the logic of norms. His book Facilitating the Understanding of the Rules of Logic and Introduction Thereto, with Common Expressions and Juristic Examples is a demonstration of how Aristotelian logic may be applied in the religious sciences, especially law. Among other things, he thoroughly investigates deontic notions and their modal counterparts, assuring him a place among the fathers of the logic of norms. The basic units of Islamic deontic logic qualify the performance of actions as subject to either reward, or sanction, or neither; and they might therefore be called, indulging in terminological anachronism, heteronomous imperatives. With remarkable insight, Ibn Ḥazm pairs these with the natural modalities of necessity, possibility, and impossibility. Employing Martin-Löf’s Constructive Type Theory (CTT) to shape the logic of heteronomous imperatives thus emerging from Ibn Ḥazm’s insights, the authors formulate a new approach to the logical analysis of deontic categories. The present talk is based on the papers: (1) S. Rahman, J. G. Granström and A. Farjami (2019). “Legal Reasoning and Some Logic After All. The Lessons of the Elders.” In D. Gabbay, L. Magnani, W. Park and A-V. Pietarinen (eds.), Natural Arguments. A Tribute to John Woods, pp. 743-780. (2) Rahman, F. Zidani & W. E. Young (2020). “Ibn Ḥazm on Heteronomous Imperatives. A Landmark in the History of the Logical Analysis of Legal Norms.” In P. McNamara, A. Jones, M. Brown (eds.), Agency, Normative Systems, Artifacts, and Beliefs: Essays in Honour of Risto Hilpinen. Dordrecht: Synthese Library-Springer. Forthcoming.
Discursive Input/Output Logic:
Deontic Modals, and Computation
Abstract: The thesis investigates logical and computational aspects of normative reasoning using deontic logic and theorem provers. This interdisciplinary study draws inspiration from logic-based knowledge representation in the field of artificial intelligence (AI), deontic modality in Linguistics and philosophical logic. The modal logic and norm-based paradigms in deontic logic investigate the logical relations among normative concepts such as obligation, permission, and prohibition. The thesis unifies these two paradigms by introducing an algebraic framework, called discursive input/output logic, in which deontic modals are evaluated with reference both to a set of possible worlds and a set of norms. The distinctive feature of the new framework is the non-adjunctive definition of input/output operations. Non-adjunctive logical systems are those where deriving the conjunctive formula φ∧ψ from the set {φ,ψ} fails. These systems are especially suited for modeling discursive reasoning. Moreover, the thesis presents a new compositional theory of conditional obligation and permission, which separates the contributions of ‘’if‘’ and ‘’ought‘’ (‘’may‘’). We propose to combine input/output logic as a logical theory about deontic modals with Hansson and Lewis’s conditional theory simultaneously. In addition, we provide a dataset of semantic embeddings of deontic logics in Isabelle/HOL. The dataset can be used for ethical and legal reasoning tasks.
