Dyadic Deontic Logic in HOL : Faithful Embedding and Meta-Theoretical Experiments

Faculty/Professorship: AI Systems Engineering 
Author(s): Benzmüller, Christoph  ; Farjami, Ali; Parent, Xavier
Title of the compilation: New developments in legal reasoning and logic : from ancient law to modern legal systems
Editors: Rahman, Shahid; Armgardt, Matthias; Nordtveit Kvernenes, Hans Christian
Publisher Information: Cham : Springer
Year of publication: 2022
Pages: 353-377
ISBN: 978-3-030-70084-3
Language(s): English
DOI: 10.1007/978-3-030-70084-3_14
A shallow semantical embedding of a dyadic deontic logic by Carmo and Jones in classical higher-order logic is presented. The embedding is proven sound and complete, that is, faithful. This result provides the theoretical foundation for the implementation and automation of dyadic deontic logic within off-the-shelf higher-order theorem provers and proof assistants. To demonstrate the practical relevance of our contribution, the embedding has been encoded in the Isabelle/HOL proof assistant. As a result a sound and complete (interactive and automated) theorem prover for the dyadic deontic logic of Carmo and Jones has been obtained. Experiments have been conducted which illustrate how the exploration and assessment of meta-theoretical properties of the embedded logic can be supported with automated reasoning tools integrated with Isabelle/HOL.
GND Keywords: Deontische Logik; HOL; Semantik; Treue <Motiv>
Keywords: Dyadic deontic logic, Classical higher-order logic, Semantic embedding, Faithfulness
DDC Classification: 004 Computer science  
510 Mathematics  
RVK Classification: SK 130   
Peer Reviewed: Ja
International Distribution: Ja
Type: Contribution to an Articlecollection
URI: https://fis.uni-bamberg.de/handle/uniba/54432
Release Date: 11. July 2022