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Alethic-Deontic Logic: Some Theorems
Stockholm University, Faculty of Humanities, Department of Philosophy.
2015 (English)In: Filosofiska notiser, ISSN 2002-0198, Vol. 2, no 1, 61-77 p.Article in journal (Other academic) Published
Abstract [en]

The purpose of this paper is to prove some theorems in alethic-deontic logic. Alethic-deontic logic is a kind of bimodal logic that combines ordinary alethic (modal) logic and deontic logic. Ordinary alethic logic is a branch of logic that deals with modal concepts, such as necessity and possibility, modal sentences, arguments and systems. Deontic logic is the logic of norms. It is about normative words, such as “ought”, “right” and “wrong”, normative sentences, arguments and systems. Alethic-deontic logic contains both modal and normative concepts and can be used to study how these interact. This paper contains some interesting theorems that can be proved in alethic-deontic logic. I will show that all primitive deontic operators are redundant when prefixed to the alethic operators in some systems. I will prove that necessarily equivalent sentences have the same deontic status in many systems. I will establish that the set of sentences in some alethic-deontic systems can be partitioned into five, mutually exclusive, exhaustive subsets. Finally, I will show that there are exactly ten distinct modalities in some alethic-deontic systems.

Place, publisher, year, edition, pages
2015. Vol. 2, no 1, 61-77 p.
National Category
Philosophy
Research subject
Philosophy
Identifiers
URN: urn:nbn:se:su:diva-114514OAI: oai:DiVA.org:su-114514DiVA: diva2:792861
Available from: 2015-03-05 Created: 2015-03-05 Last updated: 2015-12-30Bibliographically approved

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