This paper considers the case where a dispute occurs between a verifier and a signer about the validity of a digital signature. In non-repudiation services such dispute may occur long after the signature creation and approval. We present a security model for digital signature validation with the notion of dispute. The first contribution of this paper is the definition of the semantics of a Resolution of Dispute Rule (RDR ) in the scope of this model. The second contribution is a calculus for reasoning about the validation of digital signatures at a particular date which may be in the past (so-called long-term signature validation). This calculus is then used to implement the RDR. The usefulness of the calculus is demonstrated through modeling Evidence Record Syntax (ERS), one of the main protocols used in practice for long-term signature validation.