Temporal Logic pp 31-49 | Cite as

# The Basic System **R** of Temporal Logic

## Abstract

Let *A* be some temporally indefinite statement. Then we can in general form another statement asserting that *A* holds (obtains) at the particular time *t*. Correspondingly, we introduce the statement-forming operation *R*, the operation of *temporal realization*. We shall write “*R* _{ t } (*A*)” to be read “*A* is realized at the time *t*”, which is to represent the explicit statement that *A* holds (obtains) specifically at the time *t*. Thus if *t* _{1} is 3 *p. m. Greenwich time on January 1, 2000*, and *p* _{1} is the (temporally indefinite) statement, “All men are (i. e., are *now*) playing chess”, then “*R* _{ t } (*p* _{1})” is the statement “It is the case at 3 p. m. Greenwich time on January 1, 2000 that all men are (now) playing chess”, or equivalently simply, “All men are playing chess at 3 p. m. Greenwich time on January 1, 2000”. Again, if *p* _{2} is the statement “All men will play chess tomorrow”, then “*R* _{ t } _{1} (*p* _{2})” is the statement “It is the case at 3 p. m. Greenwich time on January 1, 2000 that all men will be playing chess tomorrow”.

## Keywords

Temporal Logic Basic System Temporal Homogeneity Logical Theory Propositional Variable## Preview

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## References

- 1.A. N. Prior, Now, Nous, vo1. 2 (1968), pp. 101–119 (see especially pp. 102–103).CrossRefGoogle Scholar
- 2.See Alfred Tarski, Logic, Semantics, Metamathematics (Oxford, 1956 ), pp. 385–386.Google Scholar
- 6.For a proof, see Alonzo Church, Introduction to Mathematical Logic (Princeton, 1956), pp. 284–285.Google Scholar