Various model-independent aspects of theKN → K reaction are investigated, starting from the determination of the most general structure of the reaction amplitude for baryons with J P = 1 2 ± and 3 2 ± and the observables that allow a complete determination of these amplitudes. Polarization observables are constructed in terms of spin-density matrix elements. Reflection symmetry about the reaction plane is exploited, in particular, to determine the parity of the produced in a model-independent way. In addition, extending the work of Biagi et al. [Z. Phys. C 34, 175 (1987)], a way of determining simultaneously the spin and parity of the ground state of baryons as well as those of the excited states is presented.