# Deontic Logics based on Boolean Algebra

In Robert Trypuz (ed.), Krister Segerberg on Logic of Actions. Springer (forthcoming)

# Abstract

Deontic logic is devoted to the study of logical properties of normative predicates such as permission, obligation and prohibition. Since it is usual to apply these predicates to actions, many deontic logicians have proposed formalisms where actions and action combinators are present. Some standard action combinators are action conjunction, choice between actions and not doing a given action. These combinators resemble boolean operators, and therefore the theory of boolean algebra offers a well-known athematical framework to study the properties of the classic deontic operators when applied to actions. In his seminal work, Segerberg uses constructions coming from boolean algebras to formalize the usual deontic notions. Segerberg’s work provided the initial step to understand logical properties of deontic operators when they are applied to actions. In the last years, other authors have proposed related logics. In this chapter we introduce Segerberg’s work, study related formalisms and investigate further challenges in this area.

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# Author's Profile

Piotr Kulicki
John Paul II Catholic University of Lublin

# Citations of this work

Basic Action Deontic Logic.Alessandro Giordani & Ilaria Canavotto - 2016 - In O. Roy, T. Allard & W. Malte (eds.), Deontic Logic and Normative Systems. College Publications. pp. 80-92.
Enriching Deontic Logic.Ilaria Canavotto & Alessandro Giordani - 2018 - Journal of Logic and Computation 1:1-23.
Deontic logic as a study of conditions of rationality in norm-related activities.Berislav Žarnić - 2016 - In Olivier Roy, Allard Tamminga & Malte Willer (eds.), Deontic Logic and Normative Systems. College Publications. pp. 272-287.
Deontic Logic and Normative Systems.Olivier Roy, Allard Tamminga & Malte Willer (eds.) - 2016 - London, UK: College Publications.

# References found in this work

New foundations for ethical theory.Stig Kanger - 1981 - In Risto Hilpinen (ed.), Deontic Logic: Introductory and Systematic Readings. Sold and Distributed in the U.S.A. And Canada by Kluwer Boston. pp. 36--58.
A deontic logic of action.Krister Segerberg - 1982 - Studia Logica 41 (2-3):269 - 282.