Notiser Årgång 6, Nr 1, 2019
This is a special issue
on deontic logic. More papers will appear later.
Franz von Kutschera
Obligations are addressed to persons and require that they do something,
refrain from doing something, prevent something or see to it, that
a certain state of affairs is realized or preserved. Therefore a
theory of action is the appropriate frame for deontic logic. The
frame for such a theory is the logic of branching histories (T x
W logic), a combination of tense and modality, to which alternatives
for persons are added. In a paper on collective alternatives (2014)
I have shown that the alternatives for groups of agents do not always
derive from the alternatives of their members. In this paper I want
to examine the consequences for deontic logic. Its largest part,
however, is about the action-theoretic preliminaries. Readers familiar
with them may turn directly to the last paragraph.
Axioms for Hansson's Dyadic Deontic Logics
This paper presents axiomatic systems equivalent to Bengt Hansson's
semantically defined dyadic deontic logics, DSDL1, DSDL2 and DSDL3.
Each axiomatic system is demonstrated to be sound and complete
with respect to the particular classes of models Hansson defined,
and in that way to be equivalent to his logics. I also include
another similar member of the family I call DSDL2.5 and provide
an axiomatic system for it. These systems are further found to
be decidable, and, although DSDL3 is compact, the three weaker
ones are shown not to be.