deal only with the future (or past). For example, = FP = GP or, = P and/or FP = P and GP The operators F and G may seem initially foreign, but they create normal modal systems. Note that FP is the same as ¬G¬P. We can combine the above operators to form complex statements. For example, PP → □PP says (effectively), Everything that is past and true is necessary. It seems reasonable to say that possibly it will rain tomorrow, and possibly it won't; on the other hand, since we can't change the past, if it is true that it rained yesterday, it cannot be true that it may not have rained yesterday. It seems the past is "fixed", or necessary, in a way the future is not. This is sometimes referred to as accidental necessity. But if the past is "fixed", and everything that is in the future will eventually be in the past, then it seems plausible to say that future events are necessary too. Similarly, the problem of future contingents considers the semantics of assertions about the future: is either of the propositions 'There will be a sea battle tomorrow', or 'There will not be a sea battle tomorrow' now true? Considering this thesis led Aristotle to reject the principle of bivalence for assertions concerning the future. Additional binary operators are also relevant to temporal logics (see Linear temporal logic). Versions of temporal logic can be used in computer science to model computer operations and prove theorems about them. In one version, ◇P means "at a future time in the computation it is possible that the computer state will be such that P is true"; □P means "at all future times in the computation P will be true". In another version, ◇P means "at the immediate next state of the computation, P might be true"; □P means "at the immediate next state of the computation, P will be true". These differ in the choice of Accessibility relation. (P always means "P is true at the current computer state".) These two examples involve nondeterministic or not-fully-understood computations; there are many other modal logics specialized to different types of program analysis. Each one naturally leads to slightly different axioms. Deontic logic Likewise talk of morality, or of obligation and norms generally, seems to have a modal structure. The difference between "You must do this" and "You may do