Systematic cloud/cloud-shadow detection in multi-source single-date Earth observation (EO) imagery is an open problem yet to be solved in operating mode at the ground segment (upstream) by the remote sensing community. To accomplish e.g. systematic European Space Agency (ESA) EO Level 2 product generation at the ground segment, encompassing cloud and cloud-shadow quality layer detection, a multi-source single-date hybrid (combined top-down/physical and bottom-up/statistical) spatial context-sensitive cloud/cloud-shadow detector is proposed, in compliance with an object-based image analysis (OBIA) paradigm. First, cloud-objects and cloud-shadow candidate image-objects are detected in the image-domain by two target class-specific hybrid spatial context-sensitive multi-source single-date detectors. Next, cloud/cloud-shadow image-object pair spatial matching in shape is coped with by a bidirectional physical knowledge-based data model, accounting for the sun position. In the cloud-to-cloud-shadow unidirectional relationship, candidate cloud-shadows are searched for in the (2D) image-domain to be matched in shape by each individual cloud-object. This spatial search moves from the cloud-object of interest, in the direction opposite to the sun azimuth angle (usually known from the image metadata), for a spatial length estimated as dependent variable of the cloud height, which is the sole unknown independent physical variable to cope with. Candidate cloud/cloud-shadow image-object pairs are matched in shape according to a set of planar shape indicators. A similar spatial quest for object-pair matching in shape deals with the dual cloud-shadow-to-cloud unidirectional relationship. In general, to make inherently ill-posed inductive inference better posed for numerical solution, hybrid inference initializes inductive learning-from-data algorithms with physical model-based a priori knowledge. Hybrid inference accomplishes full automation (absence of human-machine interaction) and high robustness/transferability/interoperability across sensors and scenes acquired in space-time. In practice, the proposed hybrid cloud/cloud-shadow detector requires no system's free-parameter to be user-defined. This is in contrast with a traditional first-stage semi-automatic inductive image region-growing algorithm, typical for most OBIA applications, which requires many heuristic free-parameters to be user-defined based on empirical application- and site-specific criteria. The proposed hybrid cloud/cloud-shadow detector comprises: (1) radiometric calibration of multi-spectral (MS) digital numbers into top-of-atmosphere reflectance or surface reflectance values. (2) Self-organizing statistical color constancy, capable of uncalibrated image enhancement via histogram stretching. (3) Deductive (prior knowledge-based) Satellite Image Automatic Mapper (SIAM) for MS reflectance space hyperpolyhedralization into a finite and discrete vocabulary of MS color names. (4) RGB Image Automatic Mapper (RGBIAM) for RGB data cube polyhedralization into RGB color names. (5) Cloud-specific OBIA detector, based on a convergence of spatial evidence with SIAM and RGBIAM color names. (5) Cloud-shadow-specific OBIA detector of candidate cloud-shadow areas based on a convergence of spatial evidence with SIAM and RGBIAM color names. (6) Bidirectional physical knowledge-based data modeler for spatial reasoning, suitable for cloud/cloud-shadow image-object pair spatial matching in shape. The AutoCloud+ software prototype was tested starting from a 10 m resolution Sentinel-2 MS imagery, in comparison with alternative cloud/cloud-shadow detectors in operating mode, specifically, the single-date ESA Sentinel-2 (atmospheric) Correction Prototype Processor (Sen2Cor) and the multi-date CNES/CESBIO/DLR MACCS-ATCOR Joint Algorithm (MAJA). In this difficult test case affected by several error-prone situations, AutoCloud+ ran automatically with high accuracy, qualitatively affected by few false positives and few false negatives.