Towards a Proof Theory for Basic Logic

Abstract

Proof systems based on rules with the property that all formulas contained in the assumptions are contained as subformulas in the conclusion as well, are particularly suitable for automated proof search. Systems of this kind were found for several well-known fuzzy logics. However, for BL (Basic Logic), the logic of continuous t-norms and their residua, the situation is less satisfactory. We consider two proof systems for BL which fulfill the desired property in quite contrasting ways.