  The property calculus is essentially a variation of Prior’s 1954 \(l\)-calculus described above. In the \(l\)-calculus, tense-modal propositions are treated as predicates expressing properties of dates, and quantification theory is supplemented with various special axioms for a binary relation ‘\(l\)’ taking dates as arguments. In the modal version of the calculus, sentences of modal logic are treated as if they express properties of certain objects \(a, b, c\), etc. Objects are related by a binary relation \(U\). In their 1956 paper Prior and Meredith supplied no account of what a formula of form ‘\(Uab\)’ might express. They gave the following definitions of necessity \(\Box\) and possibility \(\Diamond\), where ‘\(pa\)’ indicates that object \(a\) has the property expressed by the sentence \(p\).