Article (Scientific journals)
Probabilistic Deontic Logics for Reasoning about Uncertain Norms
de Wit, Vincent; Doder, Dragan; Meyer, John Jules
2023In IfCoLog Journal of Logics and Their Applications
Peer reviewed
 

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Keywords :
Monadic Deontic Logic; Normative Reasoning; Probabilistic Logic; Completeness; Decidability
Abstract :
[en] In this article, we present a proof-theoretical and model-theoretical approach to probabilistic logic for reasoning about uncertainty about normative state- ments. We introduce two logics with languages that extend both the language of monadic deontic logic and the language of probabilistic logic. The first logic allows statements like “the probability that one is obliged to be quiet is at least 0.9”. The second logic allows iteration of probabilities in the language. We axiomatize both logics, provide the corresponding semantics and prove that the axiomatizations are sound and complete. We also prove that both logics are decidable. In addition, we show that the problem of deciding satisfiability for the simpler of our two logics is in PSPACE, no worse than that of deontic logic.
Disciplines :
Computer science
Author, co-author :
de Wit, Vincent  ;  University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Computer Science (DCS)
Doder, Dragan;  Utrecht University > Department of Information and Computing Sciences
Meyer, John Jules;  Utrecht University > Department of Information and Computing Sciences
External co-authors :
yes
Language :
English
Title :
Probabilistic Deontic Logics for Reasoning about Uncertain Norms
Publication date :
2023
Journal title :
IfCoLog Journal of Logics and Their Applications
ISSN :
2055-3714
Publisher :
College Publishing, Londres, United Kingdom
Special issue title :
Formal and Cognitive Reasoning
Peer reviewed :
Peer reviewed
Focus Area :
Computational Sciences
Available on ORBilu :
since 23 January 2023

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