47,313 research outputs found
Martingale characterizations of coherent acceptability measures
The coherent risk framework is linked to martingale valuation by adding hedgeinvariance as a fifth axiom, motivated by the concept of consistent hedging. The resulting subclass, called coherent pre-hedge (CoPr) measures, is characterized by a martingale condition on the test set that underlies a coherent measure. It is also made explicit how consistent hedging, optimal as well as non-optimal, transforms the test set of a given coherent measure into a martingale test set. These results are put in perspective of the fundamental theorems of asset pricing and the concept of valuation bounds
Free will, robots, and the axiom of choice
There are quite a number of similarities between the moral concept of choice and the mathematical axiom of choice. These similarities shed light on how to adapt law to solve cases that arise with the increasing “autonomy” of robots
Repairing Ontologies via Axiom Weakening.
Ontology engineering is a hard and error-prone task, in which
small changes may lead to errors, or even produce an inconsistent
ontology. As ontologies grow in size, the need for automated
methods for repairing inconsistencies while preserving
as much of the original knowledge as possible increases.
Most previous approaches to this task are based on removing
a few axioms from the ontology to regain consistency.
We propose a new method based on weakening these axioms
to make them less restrictive, employing the use of refinement
operators. We introduce the theoretical framework for
weakening DL ontologies, propose algorithms to repair ontologies
based on the framework, and provide an analysis of
the computational complexity. Through an empirical analysis
made over real-life ontologies, we show that our approach
preserves significantly more of the original knowledge of the
ontology than removing axioms
A consistent multidimensional Pigou-Dalton transfer principle
The Pigou-Dalton principle demands that a regressive transfer decreases social welfare. In the unidimensional setting this principle is consistent, because regressivity in terms of attribute amounts and regressivity in terms of individual well-being coincide in the case of a single attribute. In the multidimensional setting, however, the relationship between the various attributes and well-being is complex. To formulate a multidimensional Pigou-Dalton transfer principle, a concept of wellbeing must therefore first be defined. We propose a version of the Pigou-Dalton principle that defines regressivity in terms of the individual well-being ranking that underlies the social ranking on which the principle is imposed. This well-being ranking (of attribute bundles) is induced from the social ranking over distributions in which all individuals have the same attribute bundle. It is shown that this new principle—the consistent Pigou-Dalton principle—imposes a quasi-linear structure on the well-being ranking. We discuss the implications of this result within the literature on multidimensional inequality measurement and within the literature on needs.Pigou-Dalton principle, Multidimensional inequality measurement, Majorization, Budget dominance, Needs, Weak equity axiom
Two Approaches to Ontology Aggregation Based on Axiom Weakening
Axiom weakening is a novel technique that allows
for fine-grained repair of inconsistent ontologies.
In a multi-agent setting, integrating ontologies corresponding
to multiple agents may lead to inconsistencies.
Such inconsistencies can be resolved after
the integrated ontology has been built, or their
generation can be prevented during ontology generation.
We implement and compare these two approaches.
First, we study how to repair an inconsistent
ontology resulting from a voting-based aggregation
of views of heterogeneous agents. Second,
we prevent the generation of inconsistencies by letting
the agents engage in a turn-based rational protocol
about the axioms to be added to the integrated
ontology. We instantiate the two approaches using
real-world ontologies and compare them by measuring
the levels of satisfaction of the agents w.r.t.
the ontology obtained by the two procedures
A consistent multidimensional Pigou-Dalton transfer principle.
The Pigou-Dalton principle demands that a regressive transfer decreases social welfare. In the unidimensional setting this principle is consistent, because regressivity in terms of attribute amounts and regressivity in terms of individual well-being coincide in the case of a single attribute. In the multidimensional setting, however, the relationship between the various attributes and well-being is complex. To formulate a multidimensional Pigou-Dalton transfer principle, a concept of wellbeing must therefore first be defined. We propose a version of the Pigou-Dalton principle that defines regressivity in terms of the individual well-being ranking that underlies the social ranking on which the principle is imposed. This well-being ranking (of attribute bundles) is induced from the social ranking over distributions in which all individuals have the same attribute bundle. It is shown that this new principle—the consistent Pigou-Dalton principle—imposes a quasi-linear structure on the well-being ranking. We discuss the implications of this result within the literature on multidimensional inequality measurement and within the literature on needs.Pigou-Dalton principle; Multidimensional inequality measurement; Majorization; Budget dominance; Needs; Weak equity axiom;
The Complexity of Satisfiability for Sub-Boolean Fragments of ALC
The standard reasoning problem, concept satisfiability, in the basic
description logic ALC is PSPACE-complete, and it is EXPTIME-complete in the
presence of unrestricted axioms. Several fragments of ALC, notably logics in
the FL, EL, and DL-Lite family, have an easier satisfiability problem;
sometimes it is even tractable. All these fragments restrict the use of Boolean
operators in one way or another. We look at systematic and more general
restrictions of the Boolean operators and establish the complexity of the
concept satisfiability problem in the presence of axioms. We separate tractable
from intractable cases.Comment: 17 pages, accepted (in short version) to Description Logic Workshop
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