The 5-dimensional spin-0 form of the Kemmer-Duffin-Petiau (KDP) equation is used to calculate scattering observables [elastic differential cross sections ($dsigma/dOmega$), total cross sections ($sigma_{Tot}$), and reaction cross sections ($sigma_{Reac}$})] and to deduce $sigma_{Tot}$ and $sigma_{Reac}$ from transmission data for $K^+ + $ $^{6}$Li, $^{12}$C, $^{28}$Si, and $^{40}$Ca at several momenta in the range $488 - 714 MeV/c$. Realistic uncertainties are generated for the theoretical predictions. These errors, mainly due to uncertainties associated with the elementary $K^+ +$ nucleon amplitudes, are large, so that the disagreement that has been noted between experimental and theoretical $sigma_{Tot}$ and $sigma_{Reac}$ is not surprising. The results suggest that the $K^+ +$ nucleon amplitudes need to be much better determined before unconventional medium effects are invoked to explain the data.
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