Eradication

Eradication is a radical form of contraction that removes not only a sentence but also all of its non-tautological consequences from a belief set. Eradication of a single sentence that was included in the original belief set coincides with full meet contraction, but if the sentence is external to the belief set then the two operations differ. Multiple eradication, i.e. simultaneous eradication of several sentences, differs from full meet contraction even if the sentences to be contracted are all included in the original belief set. Eradication is axiomatically characterized and its properties investigated. It is shown to have close connections with the recovery postulate for multiple contraction. Based on these connections it is proposed that eradication rather than full meet contraction is the appropriate lower limiting case for multiple contraction operators.