56,621 research outputs found
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
Bayesian Decision Theory and Stochastic Independence
Stochastic independence has a complex status in probability theory. It is not part of the definition of a probability measure, but it is nonetheless an essential property for the mathematical development of this theory. Bayesian decision theorists such as Savage can be criticized for being silent about stochastic independence. From their current preference axioms, they can derive no more than the definitional properties of a probability measure. In a new framework of twofold uncertainty, we introduce preference axioms that entail not only these definitional properties, but also the stochastic independence of the two sources of uncertainty. This goes some way towards filling a curious lacuna in Bayesian decision theory
Probabilistic Default Reasoning with Conditional Constraints
We propose a combination of probabilistic reasoning from conditional
constraints with approaches to default reasoning from conditional knowledge
bases. In detail, we generalize the notions of Pearl's entailment in system Z,
Lehmann's lexicographic entailment, and Geffner's conditional entailment to
conditional constraints. We give some examples that show that the new notions
of z-, lexicographic, and conditional entailment have similar properties like
their classical counterparts. Moreover, we show that the new notions of z-,
lexicographic, and conditional entailment are proper generalizations of both
their classical counterparts and the classical notion of logical entailment for
conditional constraints.Comment: 8 pages; to appear in Proceedings of the Eighth International
Workshop on Nonmonotonic Reasoning, Special Session on Uncertainty Frameworks
in Nonmonotonic Reasoning, Breckenridge, Colorado, USA, 9-11 April 200
To Preference via Entrenchment
We introduce a simple generalization of Gardenfors and Makinson's epistemic
entrenchment called partial entrenchment. We show that preferential inference
can be generated as the sceptical counterpart of an inference mechanism defined
directly on partial entrenchment.Comment: 16 page
Expected utility theory, Jeffrey’s decision theory, and the paradoxes
In Richard Bradley’s book, Decision Theory with a Human Face, we have selected two themes for discussion. The first is the Bolker-Jeffrey theory of decision, which the book uses throughout as a tool to reorganize the whole field of decision theory, and in particular to evaluate the extent to which expected utility theories may be normatively too demanding. The second theme is the redefinition strategy that can be used to defend EU theories against the Allais and Ellsberg paradoxes, a strategy that the book by and large endorses, and even develops in an original way concerning the Ellsberg paradox. We argue that the BJ theory is too specific to fulfil Bradley’s foundational project and that the redefinition strategy fails in both the Allais and Ellsberg cases. Although we share Bradley’s conclusion that EU theories do not state universal rationality requirements, we reach it not by a comparison with BJ theory, but by a comparison with the non-EU theories that the paradoxes have heuristically suggested
Intransitivity in Theory and in the Real World
This work considers reasons for and implications of discarding the assumption
of transitivity, which (transitivity) is the fundamental postulate in the
utility theory of Von Neumann and Morgenstern, the adiabatic accessibility
principle of Caratheodory and most other theories related to preferences or
competition. The examples of intransitivity are drawn from different fields,
such as law, biology, game theory, economics and competitive evolutionary
dynamic. This work is intended as a common platform that allows us to discuss
intransitivity in the context of different disciplines. The basic concepts and
terms that are needed for consistent treatment of intransitivity in various
applications are presented and analysed in a unified manner. The analysis
points out conditions that necessitate appearance of intransitivity, such as
multiplicity of preference criteria and imperfect (i.e. approximate)
discrimination of different cases. The present work observes that with
increasing presence and strength of intransitivity, thermodynamics gradually
fades away leaving space for more general kinetic considerations.
Intransitivity in competitive systems is linked to complex phenomena that would
be difficult or impossible to explain on the basis of transitive assumptions.
Human preferences that seem irrational from the perspective of the conventional
utility theory, become perfectly logical in the intransitive and relativistic
framework suggested here. The example of competitive simulations for the
risk/benefit dilemma demonstrates the significance of intransitivity in cyclic
behaviour and abrupt changes in the system. The evolutionary intransitivity
parameter, which is introduced in the Appendix, is a general measure of
intransitivity, which is particularly useful in evolving competitive systems.
Quantum preferences are also considered in the Appendix.Comment: 44 pages, 14 figures, 47 references, 6 appendice
Bayesian Decision Theory and Stochastic Independence
As stochastic independence is essential to the mathematical development of probability theory, it seems that any foundational work on probability should be able to account for this property. Bayesian decision theory appears to be wanting in this respect. Savage’s postulates on preferences under uncertainty entail a subjective expected utility representation, and this asserts only the existence and uniqueness of a subjective probability measure, regardless of its properties. What is missing is a preference condition corresponding to stochastic independence. To fill this significant gap, the article axiomatizes Bayesian decision theory afresh and proves several representation theorems in this novel framework
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