S0 (Halldén)

Notes

This system is known to be weaker than S10 [Feys, 1965, p139]

The following are known to *NOT* be provable in S0:

[Feys, 1965, p139] (Quoting Halldén's paper)

S0 can be inbedded in the Relevant Logic R[] (R box), making it one of the earliest Relevant logics. [Priest, 2007 (email)]

In a later email, Dr. Priest Clairified: "... if one maps the strict conditional of S0 to the arrow a relevant logic, the result is a subsystem of R[].

S0 appears to be a paraconsistent logic, pubilshed the same year as Jaśkowski's paper giving system D2, which is normally credited as being the first paraconsistent logic. [Priest, 2007 (email)]

Jaskowski's paper is alleged to be: [But I've not seen it personally -JH] S. Jaśkowski. "Propositional calculus for contradictory deductive systems" (in Polish). Studia Societatis Scientiarum Torunensis, section A-I:57-77, 1948. Translated into English: Studia Logica, 24:143-157, 1967. (Note that Jaśkowski's paper should probably retain that credit, since it was specificly intending to treat something like paraconsistency. -JH)

Basis

S0 is Lewis' basis for S1 without the definition p => q =def ~M(p&~q) [Feys, 1965, p139] (Quoting Halldén's paper)

Or in other words, it is:

Basis for

System S1 = S0 + definition p => q =def ~M(p&~q)


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