A systematics of deontic action logics based on Boolean algebra

Robert Trypuz, Piotr Kulicki

DOI: http://dx.doi.org/10.12775/LLP.2009.012

Abstract


Within the scope of interest of deontic logic, systems in which names of actions are arguments of deontic operators (deontic action logic) have attracted less interest than purely propositional systems. However, in our opinion, they are even more interesting from both theoretical and practical point of view. The fundament for contemporary research was established by K. Segerberg, who introduced his systems of basic deontic logic of urn model actions in early 1980s. Nowadays such logics are considered mainly within propositional dynamic logic (PDL). Two approaches can be distinguished: in one of them deontic operators are introduced using dynamic operators and the notion of violation, in the other at least some of them are taken as primitive. The second approach may be further divided into the systems based on Boolean algebra of actions and the systems built on the top of standard PDL.

In the present paper we are interested in the systems of deontic action logic based on Boolean algebra. We present axiomatizations of six systems and set theoretical models for them. We also show the relations among them and the position of some existing theories on the resulting picture. Such a presentation allows the reader to see the spectrum of possibilities of formalization of the subject.

Keywords


deontic action logic; algebra of actions; Segerberg; Castro and Maibaum

Full Text:

PDF

References


Castro, Pablo F., and T.S.E. Maibaum, Deontic action logic, atomic boolean algebras and fault-tolerance, Journal of Applied Logic 7, 4 (2009): 441–466. doi: 10.1016/j.jal.2009.02.001. URL http://dx.doi.org/10.1016/j.jal.2009.02.001.

Dignum, F., J.-J.Ch. Meyer, and R.J. Wieringa, Free choice and contextually permitted actions, Studia Logica 57, 1 (1996): 193–220.

Hughes, J., and L.M.M. Royakkers, Don’t ever do that! Long-term duties in PD e L, Studia Logica 89, 1 (2008): 59–79.

Kalinowski, J., Theorie des propositions normatives, Studia Logica 1 (1953): 147–182.

[Lockhorst, 1996] Lockhorst, C. G.-J., Reasoning about actions and obligations in first-order logic, Studia Logica 57, 1 (1996): 221–237.

McCarty, L.T., Permissions and obligations, pp. 287–294 in: Proccedings of IJCAI-83, 1983.

Van Der Meyden, R., The dynamic logic of permission, Journal of Logic and Computation 6 (1996): 465–479.

Meyer, J.J.Ch., A different approach to deontic logic: Deontic logic viewed as a variant of dynamic logic, Notre Dame Journal of Formal Logic 1 (1988): 109–136.

Segerberg, K., Action-games, Acta Philosophica Fennica 32 (1981): 220–231.

Segerberg, K., A deontic logic of action, Studia Logica 41 (1982): 269–282.

Trypuz, R., Formal Ontology of Action: a unifying approach, PhD thesis, Università degli Studi di Trento, ICT International Doctorate School, 2007.

Trypuz, R., Setna – prosta teoria norm i działań, Filozofia Nauki 3–4, 63–64 (2008): 155–175.

von Wright, G.H., Deontic logic, Mind LX, 237 (1951): 1–15.








ISSN: 1425-3305 (print version)

ISSN: 2300-9802 (electronic version)

Partnerzy platformy czasopism