Context : We performed a uniform and detailed analysis of 1112 high-resolution spectra of FGK dwarfs obtained with the HARPS spectrograph at the ESO 3.6 m telescope ( La Silla , Chile ) . Most stars have effective temperatures 4700 K \leq T { } _ { \mathrm { eff } } \leq 6300 K and lie in the metallicity range of -1.39 \leq [ Fe/H ] \leq 0.55 . Our main goal is to investigate whether there are any differences between the elemental abundance trends ( especially [ \alpha /Fe ] ratio ) for stars of different subpopulations . The equivalent widths of spectral lines are automatically measured from HARPS spectra with the ARES code . The abundances of three \alpha elements are determined using a differential LTE analysis relative to the Sun , with the 2010 revised version of the spectral synthesis code MOOG and a grid of Kurucz ATLAS9 atmospheres.The stars of our sample fall into two populations , clearly separated in terms of [ \alpha /Fe ] up to super-solar metallicities . In turn , high- \alpha stars are also separated into two families with a gap in both [ \alpha /Fe ] ( [ \alpha /Fe ] \approx 0.17 ) and metallicity ( [ Fe/H ] \approx -0.2 ) distributions . The metal-poor high- \alpha stars ( thick disk ) and metal-rich high- \alpha stars are on average older than chemically defined thin disk stars ( low- \alpha stars ) . The two \alpha -enhanced families have different kinematics and orbital parameters . The metal-rich \alpha -enhanced stars , such as thin disk stars have nearly circular orbits , close to the Galactic plane . We put forward the idea that these stars may have been formed in the inner Galactic disk , but their exact nature still remains to be clarified . Aims : Methods : Results : Conclusions : stars : abundances – stars : kinematics and dynamics – Galaxy : disk