Faithful Semantical Embedding of a Dyadic Deontic Logic in HOL

A shallow semantical embedding of a dyadic deontic logic by Carmo and Jones in classical higher-order logic is presented. This embedding is proven sound and complete, that is, faithful. The work presented here provides the theoretical foundation for the implementation and automation of dyadic deontic logic within off-the-shelf higher-order theorem provers and proof assistants.Comment: 23 pages, 3 figure

Faithful Semantical Embedding of a Dyadic Deontic Logic in HOL

A shallow semantical embedding of a dyadic deontic logic by Carmo and Jones in classical higher-order logic is presented. This embedding is proven sound and complete, that is, faithful. The work presented here provides the theoretical foundation for the implementation and automation of dyadic deontic logic within off-the-shelf higher-order theorem provers and proof assistants

Designing Normative Theories for Ethical and Legal Reasoning: LogiKEy Framework, Methodology, and Tool Support

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.Comment: 50 pages; 10 figure

First Experiments with a Flexible Infrastructure for Normative Reasoning

A flexible infrastructure for normative reasoning is outlined. A small-scale demonstrator version of the envisioned system has been implemented in the proof assistant Isabelle/HOL by utilising the first authors universal logical reasoning approach based on shallow semantical embeddings in meta-logic HOL. The need for such a flexible reasoning infrastructure is motivated and illustrated with a contrary-to-duty example scenario selected from the General Data Protection Regulation.Comment: 9 pages, 4 figure

A Dyadic Deontic Logic in HOL

A shallow semantical embedding of a dyadic deontic logic by Carmo and Jones in classical higher-order logic is presented. This embedding is proven sound and complete, that is, faithful. The work presented here provides the theoretical foundation for the implementation and automation of dyadic deontic logic within off-the-shelf higher-order theorem provers and proof assistants

Implementation of Dyadic Deontic Logic E in Isabelle/HOL

We have devised a shallow semantical embedding of a dyadic deontic logic (by B.Hansson and \AA{}qvist) in classical higher-order logic. This embedding has been 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 \textit{implementation} fruitfully enables interactive and automated reasoning at the meta-level and the object-level

Normative Conditional Reasoning as a Fragment of HOL

We report some results regarding the mechanization of normative (preference-based) conditional reasoning. Our focus is on Aqvist's system E for conditional obligation (and its extensions). Our mechanization is achieved via a shallow semantical embedding in Isabelle/HOL. We consider two possible uses of the framework. The first one is as a tool for meta-reasoning about the considered logic. We employ it for the automated verification of deontic correspondences (broadly conceived) and related matters, analogous to what has been previously achieved for the modal logic cube. The second use is as a tool for assessing ethical arguments. We provide a computer encoding of a well-known paradox in population ethics, Parfit's repugnant conclusion. Whether the presented encoding increases or decreases the attractiveness and persuasiveness of the repugnant conclusion is a question we would like to pass on to philosophy and ethics.Comment: 22 pages, 28 figures, 3 table

I/O Logic in HOL

A shallow semantical embedding of Input/Output logic in classical higher-order logic is presented, and shown to be faithful (sound an complete). This embedding has been implemented in the higher-order proof assistant Isabelle/HOL. We provide an empirical regulative framework for assessing General Data Protection Regulation