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The $\alpha$-particle light response of liquid scintillators based on linear alkylbenzene (LAB) has been measured with three different experimental approaches. In the first approach, $\alpha$-particles were produced in the scintillator via $^{12}$C($n$,$\alpha$)$^9$Be reactions. In the second approach, the scintillator was loaded with 2% of $^{\mathrm{nat}}$Sm providing an $\alpha$-emitter, $^{147}$Sm, as an internal source. In the third approach, a scintillator flask was deployed into the water-filled SNO+ detector and the radioactive contaminants $^{222}$Rn, $^{218}$Po and $^{214}$Po provided the $\alpha$-particle signal. The behavior of the observed $\alpha$-particle light outputs are in agreement with each case successfully described by Birks' law. The resulting Birks parameter $kB$ ranges from $(0.0066\pm0.0016)$ cm/MeV to $(0.0076\pm0.0003)$ cm/MeV. In the first approach, the $\alpha$-particle light response was measured simultaneously with the light response of recoil protons produced via neutron-proton elastic scattering. This enabled a first time a direct comparison of $kB$ describing the proton and the $\alpha$-particle response of LAB based scintillator. The observed $kB$ values describing the two light response functions deviate by more than $5\sigma$. The presented results are valuable for all current and future detectors, using LAB based scintillator as target, since they depend on an accurate knowledge of the scintillator response to different particles., Comment: 14 pages, 15 figures, 3 tables