Temporal Propositional Logic

The focus of the present chapter as well as the rest of the present work is Temporal Logic. The focus will be on the fundamental level of temporal logic - the system is named minimal temporal logic. It is equivalent to the system 142#142 in figure 2.1 om page . It will be shown in the course of the following chapter that at this level there are no restrictions on the topology of time, and that in order for us to describe formally some situations we need to impose a certain topology on time. In the traditional view of temporal logic there are two operators in temporal logic:

Definition 27   Weak Temporal Operators 55#55 83#83: to be read ``it will be the case that 16#16''. (Weak Future tense) 55#55 84#84: to be read ``it was the case that 16#16''. (Weak Past tense)

Usually the following two operators are defined :

Definition 28   Strong Temporal Operators 55#55 85#85: to be read ``it is always going to be the case that 16#16''.(Strong Future tense) 55#55 86#86: to be read ``it was always the case that 16#16''.(Strong Past tense) ²²

It can be shown that the following are equivalent: 87#87 and 88#88.