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.
Deontic Dynamic Logic: a Retrospective
In this paper a retrospective is given on the development of deontic
dynamic logic. It first reviews the basic system PDeL as introduced
in 1988, with emphasis on conceptual issues and technical choices
and properties. It then continues with later developments and
applications by ourselves and related work by others. Thus we
will see how contrary-to-duties and free choice permissions are
treated, and how violations can be handled more expressively,
including a way of dealing with red/green states and transitions.
Joining conceptual systems - three remarks on TJS
The Theory of Joining Systems, abbreviated TJS, is a general theory
of representing for example legal and other normative systems
as formal structures. It uses algebraic tools and a fundamental
idea in this algebraic approach is the representation of a conditional
norm as an ordered pair of concepts. Another fundamental idea
is that the components in such a pair are concepts of different
sorts. Conditional norms are thus links from for example descriptive
to normative concepts and the result is the joining of two conceptual
systems. However, there are often at least three kinds of concepts
involved in many normative systems, viz. descriptive, normative
and intermediate concepts. Intermediate concepts such as ‘being
the owner’ and ‘being a citizen’ have descriptive grounds and
normative consequences and can be said to be located intermediately
between the system of grounds and the system of consequences.
Intermediate concepts function as bridges (links, joinings) between
concepts of different sorts. The aim of this paper is to further
develop TJS and widen the range of application of the theory.
It will be shown that the idea of norms as ordered pairs is flexible
enough to handle nested implications and hypothetical consequences.
Minimal joinings, which are important in TJS, are shown to be
closely related to formal concepts in Formal Concept Analysis.
TJS was developed for concepts of a special kind, namely conditions.
In this paper a new model of TJS is developed, where the concepts
are attributes and aspects, and the role of intermediate concepts
in this model is discussed.