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”.KeywordsTemporal LogicBasic SystemTemporal HomogeneityLogical TheoryPropositional VariableThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.