Effect algebras with a full set of states (Q2836170)

A numerical algebra is a partial algebra of the form \((A,+,',0)\) where \(S\) is a non-empty set, \(A\subseteq [0,1]^S\), \(f+g\) is defined for \(f,g\in A\) if and only if \(f+g\leq 1\), \(f':=1-f\) for all \(f\in A\) and \(0\) denotes the constant function on \(S\) with value \(0\). If one additionally requires \(f+g+h\leq 1\) whenever \(f,g,h\in A\) and \(f+g\), \(g+h\), \(h+f\leq 1\) then one obtains a so-called space of numerical events. These spaces are (up to isomorphism) exactly the orthomodular posets having a full, i.e., order-determining set of states. In the paper under review, numerical algebras are considered in connection with so-called tense operators and time frames in order to model dependence of events on time.