A modal truth-tabular interpretation for necessary and sufficient conditons.
Peter A. Facione · Notre Dame Journal of Formal Logic · 1972
An event, D, is a necessary condition for an event, B, if and only if it is never the case that B occurs and D does not occur.1 On the other hand, D is a sufficient condition for B if and only if it is never the case that D occurs and B does not occur.These familiar definitions lend themselves readily to truth-tabular schematization.In the tables below we can interpret 'P' to mean that the event is present or did occur.The Ά 9 is then read , ( {D © BY, and (NS)£)' are to be read "Event D is a necessary condition for event B", "Event D is a sufficient condition for event B", and "Event D is a necessary and sufficient condition for events" respectively.(1) (D ®B)^(B © D).1.It would be better to use 'event-type, B,' or 'an event of type B\ 2. Skyrms, Brian, Choice and Chance, pp.47-51.