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Abstract
We discuss the axiomatic base of some of the most prominent theories of parthood (mereologies), in particular of General (Classical) Extensional Mereology (GEM). Parthood is axiomatized in GEM as a partial ordering to which a supplementation axiom and a general summing axiom are added. In this paper, we disprove the common assumption that it makes no difference for the strength of the resulting theory whether in the above framework the so-called Strong or the Weak Supplementation Principle is taken as supplementation axiom. We further show some more counterexamples to common assertions from literature concerning the interdependance of some of the axioms of the various mereological theories. It turns out that only the Strong Supplementation Principle is sufficient to fit the theories with a strong kind of extensionality.
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