Deontic Action Logics via Algebra

P. Castro, V. Cassano, R. Fervari, and C. Areces. Deontic Action Logics via Algebra. In F. Liu, A. Marra, P. Portner, and F. Van De Putte, editors, Deontic Logic and Normative Systems - 15th International Conference, DEON 2020/21, Munich, Germany [virtual], July 21-24, 2021, pp. 77–93, College publications, 2021.

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Abstract

Deontic logics are dubbed the logics of normative or prescriptive reasoning. These logics can roughly be categorized into ought-to-be, dealing with the prescription of state of affairs, or ought-to-do, dealing with the prescription of actions. An important family of ought-to-do deontic logics have their origin in Segerberg's Deontic Action Logic (DAL, see [23]). In this work, we provide an algebraic characterization of DAL and some known variants. In brief, we capture actions and formulas as elements of dif- ferent base algebras, and deontic operators as algebraic operations; different algebras capture the different variants. This algebraization enables us to obtain complete- ness results via standard algebraic means. Moreover, we argue that this algebraic framework offers a natural way of (re-)thinking many deontic logical issues at large.

BibTeX

@InCollection{CastroCFA21,
  author =       "P. Castro and V. Cassano and R. Fervari and C.
                 Areces",
  booktitle =    "Deontic Logic and Normative Systems - 15th
                 International Conference, {DEON} 2020/21, Munich,
                 Germany [virtual], July 21-24, 2021",
  title =        "Deontic Action Logics via Algebra",
  abstract =     "Deontic logics are dubbed the logics of normative or
                 prescriptive reasoning. These logics can roughly be
                 categorized into ought-to-be, dealing with the
                 prescription of state of affairs, or ought-to-do,
                 dealing with the prescription of actions. An important
                 family of ought-to-do deontic logics have their origin
                 in Segerberg's Deontic Action Logic (DAL, see [23]). In
                 this work, we provide an algebraic characterization of
                 DAL and some known variants. In brief, we capture
                 actions and formulas as elements of dif- ferent base
                 algebras, and deontic operators as algebraic
                 operations; different algebras capture the different
                 variants. This algebraization enables us to obtain
                 complete- ness results via standard algebraic means.
                 Moreover, we argue that this algebraic framework offers
                 a natural way of (re-)thinking many deontic logical
                 issues at large.",
  year =         "2021",
  editor =       "F. Liu and A. Marra and P. Portner and F. Van De
                 Putte",
  pages =        "77--93",
  publisher =    "College publications",
  bibsource =    "dblp computer science bibliography, https://dblp.org",
  biburl =       "https://dblp.org/rec/conf/deon/CastroCFA21.bib",
  timestamp =    "Wed, 02 Mar 2022 10:36:37 +0100",
  ISBN =         "978-1-84890-352-4",
}