Let \(T=(T,<)\) be a partially ordered set, and LT be the set of all ideals of T (including \(\emptyset)\). An algebra \(A=(A,+,\circ,\to,\neg,(d_ t)_{t\in T},(e_ s)_{s\in LT})\) is said to be a plain semi-Post algebra (psP-algebra) of type T if (p0) \((A,+,\circ,\to,\neg)\) is a Heyting (pseudo Boolean) algebra with unit \(e_ T\) and zero \(e_{\emptyset}\), and \(e_ T=\neg e_{\emptyset},\) (p1) \(d_ t(a+b)=d_ ta+d_ tb,\) (p2) \(d_ t(a\circ b)=d_ ta\circ d_ tb,\) (p3) \(d_ wd_ ta=d_ td_ wa,\) (p4) \(d_ te_ s=e_ T\) if \(t