A Logic for Contracts

We investigate the logical foundations of contracts in distributed applications. A contract is an agreement stipulated between two or more parties, which speci es the duties and the rights of the parties involved therein. We model contracts as formulae in an intuitionistic logic extended with a contractual form of implication . This supports for a variant of Modus Ponens, where from a promise a b to deduce b, one does not need to know a; yet, it su ces to have a dual promise b a. We study the proof theory for our logic. In particular, we provide it with a Hilbertstyle axiomatisation, which is shown consistent, and with a Gentzen-style sequent calculus, shown equivalent to the axiomatization. We prove our logic decidable, via a cut elimination property. The rights and the duties deriving from any set of contracts can therefore be mechanically inferred.