Depending on the considered refinement, minimal or maximal cardinality sets which satisfy approximations are chosen (minimal sets for query restrictions and maximal sets for query relaxations).
Finally, we consider refinements of this question for row contractions that are annihilated by a given ideal.
We consider refinements of this semantics to respect modularity in the rules, based on splitting sets, the major tool for modularity in modeling and evaluating answer set programs.
Higher order weak deformations Since our definition of weak deformations was motivated by semiclassical considerations one could perhaps consider refinements of this method using the asymptotic expansions of Hagedorn [31,32] and his followers; this could then lead to "higher order" weak deformations, depending on the number of terms that are retained.
These questions suggest there is a need to consider refinement of how we currently classify the quality of evidence according to study design.
In addition, for the smooth problems considered, p-refinement outperforms h-refinement in terms of the time required to reach a desired high accuracy level.
As an example of context refinement, consider the refinement of C4 context related to Collect timetables by email task in Fig. 1.
In the second round, core concepts were extracted and synthesised by the authors and used to create working definitions which were then considered for refinement by the advisory group in order to create the final definitions: The term theory was defined as: 'a set of concepts and/or statements with specification of how phenomena relate to each other.
The BMD0.05 of 0.362 mg BaP/kg/day we used is considered a refinement of the 0.815 mg BaP/kg/day BMD0.05 determined in previous work, employing the MLE method with quantal Weibull and polynomial regression modeling of earlier bioassays (Fitzgerald 1998; Neal and Rigdon 1967).
Two types of refinements are considered, namely, a predicate refinement and a refinement based on selected sets of parameterized inputs as is illustrated in details in Section 5. A high-level overview of the algorithm is provided below and the detailed algorithm is given in the following subsection.
Next we consider cyclic refinements of discrete and classical Jensen's inequalities (see [9]).
