Automated Theorem Proving by Translation to Description Logic

Abstract

Many Automated Theorem Proving (ATP) systems for different logics, and translators for translating different logics from one to another, have been developed and are now available. Some logics are more expressive than others, and it is easier to express problems in those logics. However, their ATP systems are relatively newer, and need more development and testing in order to solve more problems in a reasonable time. To benefit from the available tools to solve more problems in more expressive logics, different ATP systems and translators can be combined. Problems in logics more expressive than CNF can be translated directly to CNF, or indirectly by translation via intermediate logics. Description Logic (DL) sits between CNF and propositional logic. Saffron a CNF to DL translator, has been developed, which fills the gap between CNF and DL. ATP by translation to DL is now an alternative way of solving problems expressed in logics more expressive than DL, by combining necessary translators from those logics to CNF, Saffron, and a DL ATP system.