Functional Completeness in Tense Logic

Consider a partially ordered set(T <,=), where T is non-empty,< is an irreflexive and transitive relation on T and = is equality. We can regard T as a set of moments of time and < as the earlier later relation. We refer to any fixed (T,<,=) as a flow of time. Consider now a propositional language with atomic propositions p, q, r, . . . the usual classical connectives ∼,∧,∨ → and some additional connectives denoted by various symbols such as |=, , etc. We can form wffs using all the above connectives and regard them as propositions having truth values depending on time. That is, we talk about the wff A being true or false at a moment of time t. We denote this situation by