Propositional Calculus(PC) Logic System can be defined in four different ways: Principia, Hilbert, Lukasiewicz and Rosser.
The following table are the proofs of equivalence between these PC based systems by using SystemOnTPTP.PCDefns.ax are the definitions of PC systems.
| To From | PCHilbert | PCPrincipia | PCLukasiewicz | PCRosser |
|---|---|---|---|---|
| PCHilbert | X | 4 out of 4 proved | 3 out of 3 proved | 3 out of 3 proved |
| PCPrincipia | 2 out of 12 proved | X | 0 out of 3 proved | 1 out of 3 proved |
| PCLukasiewicz | 7 out of 12 proved | 3 out of 4 proved | X | 0 out of 3 proved |
| PCRosser | 9 out of 12 proved | 3 out of 4 proved | 2 out of 3 proved | X |
Succeeded on -- By Weina Shen w.shen@umiami.edu
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