66 research outputs found
A Dyadic Deontic Logic in HOL
A shallow semantical embedding of a dyadic deontic logic by Carmo
and Jones in classical higher-order logic is presented. This
embedding is proven sound and complete, that is, faithful.
The work presented here provides the theoretical foundation for the
implementation and automation of dyadic deontic logic within
off-the-shelf higher-order theorem provers and proof assistants
Implementation of Dyadic Deontic Logic E in Isabelle/HOL
We have devised a shallow semantical embedding of a dyadic deontic logic (by B.Hansson and \AA{}qvist) in classical higher-order logic. This embedding has been encoded in Isabelle/HOL, which turns this system into a proof assistant for deontic logic reasoning. The experiments with this environment provide evidence that this logic \textit{implementation} fruitfully enables interactive and automated reasoning at the meta-level and the object-level
Faithful Semantical Embedding of a Dyadic Deontic Logic in HOL
A shallow semantical embedding of a dyadic deontic logic by Carmo and Jones
in classical higher-order logic is presented. This embedding is proven sound
and complete, that is, faithful.
The work presented here provides the theoretical foundation for the
implementation and automation of dyadic deontic logic within off-the-shelf
higher-order theorem provers and proof assistants.Comment: 23 pages, 3 figure
Designing Normative Theories for Ethical and Legal Reasoning: LogiKEy Framework, Methodology, and Tool Support
A framework and methodology---termed LogiKEy---for the design and engineering
of ethical reasoners, normative theories and deontic logics is presented. The
overall motivation is the development of suitable means for the control and
governance of intelligent autonomous systems. LogiKEy's unifying formal
framework is based on semantical embeddings of deontic logics, logic
combinations and ethico-legal domain theories in expressive classic
higher-order logic (HOL). This meta-logical approach enables the provision of
powerful tool support in LogiKEy: off-the-shelf theorem provers and model
finders for HOL are assisting the LogiKEy designer of ethical intelligent
agents to flexibly experiment with underlying logics and their combinations,
with ethico-legal domain theories, and with concrete examples---all at the same
time. Continuous improvements of these off-the-shelf provers, without further
ado, leverage the reasoning performance in LogiKEy. Case studies, in which the
LogiKEy framework and methodology has been applied and tested, give evidence
that HOL's undecidability often does not hinder efficient experimentation.Comment: 50 pages; 10 figure
Harnessing Higher-Order (Meta-)Logic to Represent and Reason with Complex Ethical Theories
The computer-mechanization of an ambitious explicit ethical theory, Gewirth's
Principle of Generic Consistency, is used to showcase an approach for
representing and reasoning with ethical theories exhibiting complex logical
features like alethic and deontic modalities, indexicals, higher-order
quantification, among others. Harnessing the high expressive power of Church's
type theory as a meta-logic to semantically embed a combination of quantified
non-classical logics, our work pushes existing boundaries in knowledge
representation and reasoning. We demonstrate that intuitive encodings of
complex ethical theories and their automation on the computer are no longer
antipodes.Comment: 14 page
Computer Science and Metaphysics: A Cross-Fertilization
Computational philosophy is the use of mechanized computational techniques to
unearth philosophical insights that are either difficult or impossible to find
using traditional philosophical methods. Computational metaphysics is
computational philosophy with a focus on metaphysics. In this paper, we (a)
develop results in modal metaphysics whose discovery was computer assisted, and
(b) conclude that these results work not only to the obvious benefit of
philosophy but also, less obviously, to the benefit of computer science, since
the new computational techniques that led to these results may be more broadly
applicable within computer science. The paper includes a description of our
background methodology and how it evolved, and a discussion of our new results.Comment: 39 pages, 3 figure
First Experiments with a Flexible Infrastructure for Normative Reasoning
A flexible infrastructure for normative reasoning is outlined. A small-scale
demonstrator version of the envisioned system has been implemented in the proof
assistant Isabelle/HOL by utilising the first authors universal logical
reasoning approach based on shallow semantical embeddings in meta-logic HOL.
The need for such a flexible reasoning infrastructure is motivated and
illustrated with a contrary-to-duty example scenario selected from the General
Data Protection Regulation.Comment: 9 pages, 4 figure
Faithful Semantical Embedding of a Dyadic Deontic Logic in HOL
A shallow semantical embedding of a dyadic deontic logic by Carmo
and Jones in classical higher-order logic is presented. This
embedding is proven sound and complete, that is, faithful.
The work presented here provides the theoretical foundation for the
implementation and automation of dyadic deontic logic within
off-the-shelf higher-order theorem provers and proof assistants
Normative Conditional Reasoning as a Fragment of HOL
We report some results regarding the mechanization of normative
(preference-based) conditional reasoning. Our focus is on Aqvist's system E for
conditional obligation (and its extensions). Our mechanization is achieved via
a shallow semantical embedding in Isabelle/HOL. We consider two possible uses
of the framework. The first one is as a tool for meta-reasoning about the
considered logic. We employ it for the automated verification of deontic
correspondences (broadly conceived) and related matters, analogous to what has
been previously achieved for the modal logic cube. The second use is as a tool
for assessing ethical arguments. We provide a computer encoding of a well-known
paradox in population ethics, Parfit's repugnant conclusion. Whether the
presented encoding increases or decreases the attractiveness and persuasiveness
of the repugnant conclusion is a question we would like to pass on to
philosophy and ethics.Comment: 22 pages, 28 figures, 3 table
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