Notiser Årgång 6, Nr 1, 2019
This is a special issue
on deontic logic.
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.
Federico L. G. Faroldi
Deontic Modality, Generically
This position paper aims to explore some preliminary suggestions
to develop a theory of deontic modalities under a generic understanding.
I suggest, for instance, that a sentence such as ‘Everyone ought
to pay taxes’ is true just in case the generic (deontically relevant)
individual pays taxes. Different degrees of genericity are explored,
without assuming too much about a specific theory of genericity.
I argue that such an analysis captures our intuitions about exceptions
and the general character of deontic claims better than classical
approaches based on possibleworld semantics and than defeasibility-based
approaches, while remaining within a broadly deductive framework.
Toward a Systematization of Logics for Monadic and Dyadic Agency
& Ability, Revisited
I specify a very large class of logics with monadic and dyadic
modal operators, primarily (but not exclusively) intended to represent
monadic and dyadic agency in the tradition of Kanger, Pörn, Elgesem,
etc. I explore logics both for pure monadic agency, pure dyadic
agency, and mixed monadic-dyadic agency. Employing neighborhood
semantic frames, but with an extra parameter governed by a modest
algebraic structure, I prove determination theorems for all the
consistent logics of those specified. I briefly present some motivation
and rationales for some of the principles, but the main focus
is on the framework and key meta-theorems.
Xavier Parent and Leendert
van der Torre
Input/output logics without weakening
Makinson and van der Torre introduced a number of input/output
(I/O) logics to reason about conditional norms. The key idea is
to make obligations relative to a given set of conditional norms.
The meaning of the normative concepts is, then, given in terms
of a set of procedures yielding outputs for inputs. Using the
same methodology, Stolpe has developed some more I/O logics to
include systems in which the rule of weakening of the output (or
principle of inheritance) is replaced by a rule of closure under
logical equivalence. We extend Stolpe’s account in two directions.
First, we show how to make it support reasoning by cases–a common
form of reasoning. Second, we show how to inject a new (as we
call it, aggregative) form of cumulative transitivity, which we
think is more suitable for normative reasoning. The main outcomes
of the paper are soundness and completeness theorems for the proposed
systems with respect to their intended semantics.
Quantified Temporal Alethic Boulesic Deontic Logic
The purpose of this paper is to develop a set of quantified temporal
alethic boulesic deontic systems. Every system in this class consists
of five parts: a 'quantified' part, a temporal part, a modal part
(an alethic part), a boulesic part and a deontic part. Separately,
all these parts, except the boulesic part, have been studied extensively,
but there are no systems in the literature that combine them all.
So, all systems in this paper are new. The 'quantified part' consists
of relational predicate logic with identity, where the quantifiers
are, in effect, a kind of possibilist quantifiers that vary over
every object in the domain. The alethic part includes two types
of modal operators, for absolute and historical necessity and
possibility. By 'boulesic logic', I mean the logic of the will;
it treats 'willing' ('consenting', 'rejecting', 'indifference'
and 'non-indifference') as a kind of modal operator. Deontic logic
is the logic of norms; it deals with such concepts as ought, permitted
and forbidden. I will investigate some possible relationships
between these different parts, and consider various principles
that include more than one type of logical expression. Every system
is described both semantically and proof theoretically. I use
a kind of T x W semantics to describe the systems semantically,
and semantic tableaux to describe them proof theoretically. I
prove that every tableau system in the paper is sound and complete
with respect to its semantics. Finally, I consider some examples
of valid and invalid sentences and arguments, show how one can
use semantic tableaux to prove their validity or invalidity, and
try to illustrate the philosophical usefulness of the systems
developed in the paper.