We present SBTrust, a logical framework designed to formalize decision trust. Our logic integrates a doxastic modality with a novel non-monotonic conditional operator that establishes a positive support relation between statements and is closely related to a known dyadic deontic modality. For SBTrust, we provide semantics, proof theory and complexity results, as well as motivating examples. Compared to existing approaches, our framework seamlessly accommodates the integration of multiple factors in the emergence of trust.