rules that lead you to begin
a reductio argument

rules for completing reductio arguments
(either in fact completing one
or planning how to do so)

││φ
│├─
││
│├─
││⊥
├─
RAA │¬ φ

if ¬ φ is your goal, use RAA to plan how to derive it

if you have ¬ φ among the re­sources of a reductio, then ...







if you also have φ, use Nc to close gap

│¬ φ
│φ
││●
│├─
Nc ││⊥


││¬ φ
│├─
││
│├─
││⊥
├─
IP │φ

[φ is atomic]

if φ is your goal, you may use IP to plan how to derive it—but do this only when φ is atomic

if don’t also have φ, use CR to plan how to derive it—but do this only when φ is not atomic

│¬ φ
│││
││├─
│││φ
│├─
CR ││⊥

[φ is not atomic]