Complementary Sentential Logics
Achille C. Varzi · PhilPapers (PhilPapers Foundation) · 1990
We describe a simple axiomatic system by means of which exactly those sentences can be derived that are rated non-tautologous in classical sentential logic. Since the set of all tautologies is also specifiable by means of syntactic systems, the resulting picture would appear to give a fairly good account of that logic, let alone semantic considerations. The picture can then be completed by developing related systems adequate to specify the set of all contradictions, the set of all non-contradictions, the set of all contingencies and the set of all non-contingencies respectively: systems of this kind, which provide additional examples of paraconsistent calculi with a classical background, are also presented.