Strong Equivalence in Argumentation

Abstract

The problem of equivalence has received substantial attention in the knowledge-representation (KR) community in the past several years. This is due to the fact that the replacement theorem from classical logic does not necessarily hold in typical (non-monotonic) KR formalisms. In fact, the problem is as follows: Consider a theory S is replaced by another theory S within a larger knowledge base T. Naturally, one wants to ensure that the resulting knowledge base (T \ S) ∪ S has the same meaning as T. But this is not guaranteed by standard equivalence between S and S under nonmonotonic semantics, and therefore, stronger notions of equivalence are required. In particular, the following definition of equivalence guarantees that a replacement as discussed above is faithful: two theories S and S are called strongly equivalent, if and only if S ∪ T and S ∪ T have the same same meaning for each theory T.