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”.