Predicate temporal logics

Abstract The move from the propositional to the predicate version of a logic is simple in principle, though one has several options to consider. Temporal logic is a language for talking about several databases and the connections between them. Predicate logic talks about domains of individuals. Put together we have to deal with several domains of individuals and the question is what are the individuals of the combined domains? This is the source of our options. Technically, the move to predicate logic is undertaken by adding individual variables to the language and possibly individual constants, and adding atomic predicates and quantifiers ∀ and ∃.Thus predicate temporal logic is syntactically like classical predicate logic with the addition of the temporal connectives. The problem is what do the variables range over? Let us be more specific.