Xavier Parent

FLAP Journal 2025 Journal Article

Extensionality vs Intensionality: A Perspectival Account of Conditional Ought with Definite Descriptions

• Xavier Parent
• Dominik Pichler

The theme of extensionality in first-order deontic logic has been thoroughly studied in the past, but not in the context of a combination of different types of modalities. An operator is extensional if it allows substitution salva veritate of co-referential terms within its scope and intensional if it does not. It can be argued that one distinctive feature of “ought” (as opposed to the other modal- ities) is that it is extensional. The question naturally arises as to whether it is possible to combine extensionality and intensionality of different modal opera- tors in the same semantics without creating the deontic collapse. We answer this question within a particular framework, Åqvist’s system F for conditional obligation. We develop in full detail a perspectival account of obligation (and related notions), as was done for Standard Deontic Logic (SDL) by Goble. It is called “perspectival”, because one always evaluates the content of an obligation in one world from the perspective of another one. This requires using some form of cross-world evaluation to handle non-rigid terms like definite descrip- tions. The proposed framework allows for a more nuanced way of approaching first-order deontic principles.

FLAP Journal 2022 Journal Article

Detachment in Normative Systems: Examples, Inference Patterns, Properties.

• Leendert van der Torre
• Xavier Parent

FLAP Journal 2021 Journal Article

A Modal Characterisation of an Intuitionistic I/O Operation.

• Xavier Parent

It is known that Makinson and van der Torre’s basic I/O operation out2 can faithfully be “embedded” into (or “encoded” in) classical modal logic. It is shown that an analogous result holds for the intuitionistic variant of out2. The target of the embedding is the constructive modal logic CK that evolved through work of Wijesekera, Mendler, de Paiva and Ritter. The very same translation that embeds out2 into classical modal logic is used.

AIJ Journal 2020 Journal Article

Designing normative theories for ethical and legal reasoning: LogiKEy framework, methodology, and tool support

• Christoph Benzmüller
• Xavier Parent
• Leendert van der Torre

A framework and methodology—termed LogiKEy—for the design and engineering of ethical reasoners, normative theories and deontic logics is presented. The overall motivation is the development of suitable means for the control and governance of intelligent autonomous systems. LogiKEy's unifying formal framework is based on semantical embeddings of deontic logics, logic combinations and ethico-legal domain theories in expressive classic higher-order logic (HOL). This meta-logical approach enables the provision of powerful tool support in LogiKEy: off-the-shelf theorem provers and model finders for HOL are assisting the LogiKEy designer of ethical intelligent agents to flexibly experiment with underlying logics and their combinations, with ethico-legal domain theories, and with concrete examples—all at the same time. Continuous improvements of these off-the-shelf provers, without further ado, leverage the reasoning performance in LogiKEy. Case studies, in which the LogiKEy framework and methodology has been applied and tested, give evidence that HOL's undecidability often does not hinder efficient experimentation.

FLAP Journal 2019 Journal Article

I/O Logic in HOL.

• Christoph Benzmüller
• Ali Farjami
• Paul Meder
• Xavier Parent

A shallow semantical embedding of Input/output logic in classical higherorder logic is presented, and shown to be faithful (sound and complete). This embedding has been implemented in Isabelle/HOL, a proof assistant tool. It is applied to a well-known example in moral philosophy, the example of moral luck.

FLAP Journal 2019 Journal Article

åqvist's Dyadic Deontic Logic E in HOL.

• Christoph Benzmüller
• Ali Farjami
• Xavier Parent

We devise a shallow semantical embedding of Åqvist’s dyadic deontic logic E in classical higher-order logic. This embedding is shown to be faithful, viz. sound and complete. This embedding is also encoded in Isabelle/HOL, which turns this system into a proof assistant for deontic logic reasoning. The experiments with this environment provide evidence that this logic implementation fruitfully enables interactive and automated reasoning at the meta-level and the object-level.

FLAP Journal 2017 Journal Article

Detachment in Normative Systems: Examples, Inference Patterns, Properties.

• Xavier Parent
• Leendert W. N. van der Torre

There is a variety of ways to reason with normative systems. This partly reflects a variety of semantics developed for deontic logic, such as traditional semantics based on possible worlds, or alternative semantics based on algebraic methods, explicit norms or techniques from non-monotonic logic. This diversity raises the question how these reasoning methods are related, and which reasoning method should be chosen for a particular application. In this paper we discuss the use of examples, inference patterns, and more abstract properties. First, benchmark examples can be used to compare ways to reason with normative systems. We give an overview of several benchmark examples of normative reasoning and deontic logic: van Fraassen’s paradox, Forrester’s paradox, paradox, Makinson’s Möbius strip, and Horty’s priority examples. Moreover, we distinguish various interpretations that can be given to these benchmark examples, such as consistent interpretations, dilemma interpretations, and violability interpretations. mative systems. Instead of analysing the benchmark examples semantically, as it is usually done, in this paper we use inference patterns to analyse them at a higher level of abstraction. We discuss inference patterns reflecting typical logical properties such as strengthening of the antecedent or weakening of the consequent. Third, more abstract properties can be defined to compare different ways to reason with normative systems. To define these more abstract properties, we first present a formal framework around the notion of detachment. Some of the ten properties we introduce are derived from the inference patterns, but others are more abstract: factual detachment, violation detection, substitution, replacements of equivalents, implication, para-consistency, conjunction, factual monotony, norm monotony, and norm induction. We consider these ten properties as desirable for a reasoning method for normative systems, and thus they can be used also as requirements for the further development of formal methods for normative systems and deontic logic.

KR Conference 2014 Short Paper

System O: New Foundations for Deontic Logic

• Xavier Parent
• Leon van der Torre

AILAW Journal 2011 Journal Article

Moral particularism in the light of deontic logic

• Xavier Parent

Abstract The aim of this paper is to strengthen the point made by Horty about the relationship between reason holism and moral particularism. In the literature prima facie obligations have been considered as the only source of reason holism. I strengthen Horty’s point in two ways. First, I show that contrary-to-duties provide another independent support for reason holism. Next I outline a formal theory that is able to capture these two sources of holism. While in simple settings the proposed account coincides with Horty’s one, this is not true in more complicated or “realistic” settings in which more than two norms collide. My chosen formalism is so-called input/output logic. A bottom-line example is introduced. It raises the issue of whether the conventional wisdom is right in assuming that normative reasons run parallel to epistemic ones.

AILAW Journal 2007 Journal Article

Normative-informational positions: a modal-logical approach

• Andrew J. I. Jones
• Xavier Parent

Abstract This paper is a preliminary investigation into the application of the formal-logical theory of normative positions to the characterisation of normative-informational positions, pertaining to rules that are meant to regulate the supply of information. First, we present the proposed framework. Next, we identify the kinds of nuances and distinctions that can be articulated in such a logical framework. Finally, we show how such nuances can arise in specific regulations. Reference is made to Data Protection Law and Contract Law, among others. The proposed approach is articulated around two essential steps. The first involves identifying the set of possible interpretations that can be given to a particular norm. This is done by using formal methods. The second involves picking out one of these interpretations as the most likely one. This second step can be resolved only by using further information (e. g. , the context or other parts of the regulation).