In fact, as (Heifetz 1999) shows, the hierarchical and fixed-point accounts are equivalent for all finite levels of iteration, while fixed-point common knowledge implies the conjunction of mutual knowledge up to any transfinite order, but it is never implied by any such conjunction.
For instance the principle that knowledge of a statement entails its truth is rendered as \(K_i \phi \rightarrow \phi\) and the principle that knowledge of a conjunction entails knowledge of its conjuncts is rendered as \(K_i(\phi \wedge \psi) \rightarrow (K_i \phi \wedge K_i \psi)\).
But although these techniques can be used to circumvent particular cases of (i) and (ii), they also typically complicate the task of explaining why the set of sentences known by an agent may exhibit some potentially desirable closure properties (e.g. that knowledge of a conjunction entails knowledge of its conjuncts).
Due to the relatively recent licensure of the HPV vaccine in males in conjunction with the lack of knowledge about HPV vaccine decision-making in this population, we conducted a qualitative study of parent-son dyads immediately after they have been offered and made the decision to receive/refuse the HPV vaccine.
As we gain a better understanding of this relationship, it should be possible to use these HSAB descriptors, in conjunction with knowledge of physicochemical features, to accurately predict the potential toxicity of a given chemical structure.
In conjunction with knowledge of recipe, this information is used to determine the optimal number of time points.
This model builds on the conjunction of the digital commons of knowledge and design with desktop and benchtop manufacturing technologies (from three-dimensional printers and laser cutters to low-tech tools and crafts).
This is especially problematic in conjunction with the overall lack of knowledge about schizophrenia found in this population.
The design principles of this library emerged from the application of molecular modeling calculations in conjunction with our knowledge of previously obtained ELDKWA-displaying chimeras, including knowledge of a chimera with one of the best 2F5-binding characteristics obtained to date.
After all, the conjunction of CP1 and CP2 precludes knowledge in both circumstances.
