PKIs are complex distributed systems that are responsible for giving users enough information to make reasonable trust judgments about one another. Since the currencies of PKI are trust and certificates, users who make trust decisions (often called relying parties) must do so using only some initial trust beliefs about the PKI and some pile of certificates (and other assertions) they received from the PKI. Given a certificate, a relying party needs to conclude that the keyholder described by the certificate actually possesses the properties described by the certificate. In this paper, we present a calculus that allows relying parties to make such trust judgements. Our calculus extends Maurer’s deterministic model, and is focused on real world issues such as time, revocation, delegation, and heterogeneous certificate formats. We then demonstrate how our calculus can be used to reason about numerous situations that arise in practice.