A Formal Treatment of Contract Signature

The paper develops a logical understanding of processes for signature of legal contracts, motivated by applications to legal recognition of smart contracts on blockchain platforms. A number of axioms and rules of inference are developed that can be used to justify a ``meeting of the minds'' precondition for contract formation from the fact that certain content has been signed. In addition to an ``offer and acceptance'' process, the paper considers ``signature in counterparts'', a legal process that permits a contract between two or more parties to be brought into force by having the parties independently (possibly, remotely) sign different copies of the contract, rather than placing their signatures on a common copy at a physical meeting. It is argued that a satisfactory account of signature in counterparts benefits from a logic with syntactic self-reference. The axioms used are supported by a formal semantics, and a number of further properties of the logic are investigated. In particular, it is shown that the logic implies that when a contract has been signed, the parties do not just agree, but are in mutual agreement (a common-knowledge-like notion) about the terms of the contract.