The literature on conditionals is rife with alternate formulations of the abstract semantics of conditional logic. Each formulation has its own advantages in terms of applications and generalizations; nevertheless, they are for the most part equivalent, in the sense that they underwrite the same range of logical systems. The purpose of the present note is to bring under this umbrella the partition semantics introduced by Brian Skyrms in (Skyrms, 1984).

A system of modal logic with the operator is proposed, and proved complete. In contrast with a previous one by Stalnaker and Thomason, this system does not require two categories of singular terms.