# The Basic System R of Temporal Logic

• Nicholas Rescher
• Alasdair Urquhart
Part of the LEP Library of Exact Philosophy book series (LEP, volume 3)

## 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

## References

1. 1.
A. N. Prior, Now, Nous, vo1. 2 (1968), pp. 101–119 (see especially pp. 102–103).
2. 2.
See Alfred Tarski, Logic, Semantics, Metamathematics (Oxford, 1956 ), pp. 385–386.Google Scholar
3. 6.
For a proof, see Alonzo Church, Introduction to Mathematical Logic (Princeton, 1956), pp. 284–285.Google Scholar