We introduce a logic for reasoning about contextual trust for web addresses, provide a Kripke semantics for it, and prove its soundness under reasonable assumptions about principals' policies. Self-Authenticating Traditional Addresses (SATAs) are valid DNS addresses or URLs that are generally meaningful -- to both humans and web infrastructure -- and contain a commitment to a public key in the address itself. Trust in web addresses is currently established via domain name registration, TLS certificates, and other hierarchical elements of the internet infrastructure. SATAs support such structural roots of trust but also complementary contextual roots associated with descriptive properties. The existing structural roots leave web connections open to a variety of well-documented and significant hijack vulnerabilities. Contextual trust roots provide, among other things, stronger resistance to such vulnerabilities. We also consider labeled SATAs, which include descriptive properties such as that a SATA is an address for a news organization, a site belonging to a particular government or company, a site with information about a certain topic, etc. Our logic addresses both trust in the bound together identity of the address and trust in the binding of labels to it. Our logic allows reasoning about delegation of trust with respect to specified labels, relationships between labels that provide more or less specific information, and the interaction between these two aspects. In addition to soundness, we prove that if a principal trusts a particular identity (possibly with label), then either this trust is initially assumed, or there is a trust chain of delegations to this from initial trust assumptions. We also present an algorithm that effectively derives all possible trust statements from the set of initial trust assumptions and show it to be sound, complete, and terminating.