An Ordinal View of Independence with Application to Plausible Reasoning

An ordinal view of independence is studied in the framework of possibility theory. We investigate three possible definitions of dependence, of increasing strength. One of them is the counterpart to the multiplication law in probability theory, and the two others are based on the notion of conditional possibility. These two have enough expressive power to support the whole possibility theory, and a complete axiomatization is provided for the strongest one. Moreover we show that weak independence is well-suited to the problems of belief change and plausible reasoning, especially to address the problem of blocking of property inheritance in exception-tolerant taxonomic reasoning.Comment: Appears in Proceedings of the Tenth Conference on Uncertainty in Artificial Intelligence (UAI1994

Background-Independence

Intuitively speaking, a classical field theory is background-independent if the structure required to make sense of its equations is itself subject to dynamical evolution, rather than being imposed ab initio. The aim of this paper is to provide an explication of this intuitive notion. Background-independence is not a not formal property of theories: the question whether a theory is background-independent depends upon how the theory is interpreted. Under the approach proposed here, a theory is fully background-independent relative to an interpretation if each physical possibility corresponds to a distinct spacetime geometry; and it falls short of full background-independence to the extent that this condition fails.Comment: Forthcoming in General Relativity and Gravitatio

Coping with the Limitations of Rational Inference in the Framework of Possibility Theory

Possibility theory offers a framework where both Lehmann's "preferential inference" and the more productive (but less cautious) "rational closure inference" can be represented. However, there are situations where the second inference does not provide expected results either because it cannot produce them, or even provide counter-intuitive conclusions. This state of facts is not due to the principle of selecting a unique ordering of interpretations (which can be encoded by one possibility distribution), but rather to the absence of constraints expressing pieces of knowledge we have implicitly in mind. It is advocated in this paper that constraints induced by independence information can help finding the right ordering of interpretations. In particular, independence constraints can be systematically assumed with respect to formulas composed of literals which do not appear in the conditional knowledge base, or for default rules with respect to situations which are "normal" according to the other default rules in the base. The notion of independence which is used can be easily expressed in the qualitative setting of possibility theory. Moreover, when a counter-intuitive plausible conclusion of a set of defaults, is in its rational closure, but not in its preferential closure, it is always possible to repair the set of defaults so as to produce the desired conclusion.Comment: Appears in Proceedings of the Twelfth Conference on Uncertainty in Artificial Intelligence (UAI1996

Choice-Consistent Resolutions of the Efficiency-Equity Trade-Off

In a standard framework of choice theory, we formulate two contrasting principles for social choice under the efficiency-equity trade-off. The equity-first principle states that we should select from equitable allocations if any, but if the equity criterion is not at all effective for selection either because all the available allocations are equitable or because no allocation is equitable, we should select from Pareto efficient allocations. The efficiency-first principle switches the roles of the equity criterion and the efficiency criterion above. We examine the choice-consistency properties, known as Path Independence (Arrow, 1963) and Contraction Consistency (Chernoff, 1954), of the social choice correspondences satisfying the equity-first or the efficiency-first principle. Several possibility and impossibility theorems are obtained, which indicate that possibility of consistent social decisions depends crucially on which principle we take as well as what is the precise notion of equity.equity, efficiency, lexicographic composition, choice-consistency, path-independence

Neutrino Oscillations from String Theory

We derive the character of neutrino oscillations that results from a model of equivalence principle violation suggested recently by Damour and Polyakov as a plausible consequence of string theory. In this model neutrino oscillations will take place through interaction with a long range scalar field of gravitational origin even if the neutrinos are degenerate in mass. The energy dependence of the oscillation length is identical to that in the conventional mass mixing mechanism. This possibility further highlghts the independence of and need for more exacting direct neutrino mass measurements together with a next generation of neutrinoless double beta decay experiments.Comment: 7 pages LaTE

Categorial subsystem independence as morphism co-possibility

This paper formulates a notion of independence of subobjects of an object in a general (i.e. not necessarily concrete) category. Subobject independence is the categorial generalization of what is known as subsystem independence in the context of algebraic relativistic quantum field theory. The content of subobject independence formulated in this paper is morphism co-possibility: two subobjects of an object will be defined to be independent if any two morphisms on the two subobjects of an object are jointly implementable by a single morphism on the larger object. The paper investigates features of subobject independence in general, and subobject independence in the category of C∗ - algebras with respect to operations (completely positive unit preserving linear maps on C∗ - algebras)as morphisms is suggested as a natural subsystem independence axiom to express relativistic locality of the covariant functor in the categorial approach to quantum field theory