In order to estimate the reactivity of a large number of potentially complex heterogeneous catalysts while searching for novel and more efficient materials, physical as well as data-centric models have been developed for a faster evaluation of adsorption energies compared to first-principles calculations. However, global models designed to describe as many materials as possible might overlook the very few compounds that have the appropriate adsorption properties to be suitable for a given catalytic process. Here, the subgroup-discovery (SGD) local artificial-intelligence approach is used to identify the key descriptive parameters and constrains on their values, the so-called SG rules, which particularly describe transition-metal surfaces with outstanding adsorption properties for the oxygen-reduction and -evolution reactions. We start from a data set of 95 oxygen adsorption-energy values evaluated by density-functional-theory calculations for several monometallic surfaces along with 16 atomic, bulk and surface properties as candidate descriptive parameters. From this data set, SGD identifies constraints on the most relevant parameters describing materials and adsorption sites that (i) result in O adsorption energies within the Sabatier-optimal range required for the oxygen-reduction reaction and (ii) present the largest deviations from the linear-scaling relations between O and OH adsorption energies, which limit the catalyst performance in the oxygen-evolution reaction. The SG rules not only reflect the local underlying physicochemical phenomena that result in the desired adsorption properties, but also guide the challenging design of alloy catalysts.