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25 February 2023
Article (Scientific journals)
Detachment in Normative Systems: Examples, Inference Patterns, Properties
van der Torre, Leon; Parent, Xavier
2022In IfCoLog Journal of Logics and Their Applications, 9 (4), p. 1019-1062
Peer reviewed


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Keywords :
Algebra; Computer circuits; Formal logic; Formal methods; Algebraic method; Alternative Semantics; Deontic Logic; Inference patterns; Nonmonotonic logic; Normative reasoning; Normative system; Possible world semantics; Property; Reasoning methods; Semantics
Abstract :
[en] 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, Prakken and Sergot’s cottage regulations, Jeffrey’s disarmament example, Chisholm’s 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. Second, inference patterns can be used to compare different ways to reason with normative 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.
Disciplines :
Computer science
Identifiers :
Author, co-author :
van der Torre, Leon ;  University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Computer Science (DCS)
Parent, Xavier 
External co-authors :
Language :
Title :
Detachment in Normative Systems: Examples, Inference Patterns, Properties
Publication date :
Journal title :
IfCoLog Journal of Logics and Their Applications
Publisher :
College Publications
Volume :
Issue :
Pages :
Peer reviewed :
Peer reviewed
Funders :
Austrian Science Fund, FWF: M-3240-N


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