22,798 research outputs found
Qualitative Evaluation of Associations by the Transitivity of the Association Signs
We say that the signs of association measures among three variables {X, Y, Z}
are transitive if a positive association measure between the variable X and the
intermediate variable Y and further a positive association measure between Y
and the endpoint variable Z imply a positive association measure between X and
Z. We introduce four association measures with different stringencies, and
discuss conditions for the transitivity of the signs of these association
measures. When the variables follow exponential family distributions, the
conditions become simpler and more interpretable. Applying our results to two
data sets from an observational study and a randomized experiment, we
demonstrate that the results can help us to draw conclusions about the signs of
the association measures between X and Z based only on two separate studies
about {X, Y} and {Y, Z}.Comment: Statistica Sinica 201
Proving Craig and Lyndon Interpolation Using Labelled Sequent Calculi
We have recently presented a general method of proving the fundamental
logical properties of Craig and Lyndon Interpolation (IPs) by induction on
derivations in a wide class of internal sequent calculi, including sequents,
hypersequents, and nested sequents. Here we adapt the method to a more general
external formalism of labelled sequents and provide sufficient criteria on the
Kripke-frame characterization of a logic that guarantee the IPs. In particular,
we show that classes of frames definable by quantifier-free Horn formulas
correspond to logics with the IPs. These criteria capture the modal cube and
the infinite family of transitive Geach logics
On aggregation operators of transitive similarity and dissimilarity relations
Similarity and dissimilarity are widely used concepts. One of the most studied matters is their combination or aggregation. However, transitivity property is often ignored when aggregating despite being a highly important property, studied by many authors but from different points of view. We collect here some results in preserving transitivity when aggregating, intending to clarify the relationship between aggregation and transitivity and making it useful to design aggregation operators that keep transitivity property. Some examples of the utility of the results are also shown.Peer ReviewedPostprint (published version
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