Solving Schubert's Steamroller by Guarded Resolution

Abstract

The clause form is very popular knowledge representation method for logic based reasoning systems. Recently, most working systems adapt Horn clause form. In fact, Horn clause set covers a great part of our knowledge. It will be true, however, that there exist problems which cannot be formalized by only Horn clausis problem can be solved, ordinary mechanical provers cannot reach the solution because of physical restrictions. Namely, slmple resolution ends in combinatorial explosion of search space. Some solution methods have been reported for this problem. At present, many-sorted resolution is the best solution method among them. In this paper, we propose an extended clause form and its resolution method. They are called guarded clause form (GCF) and guarded linear resolution (GL-resolution) respectively. GCF reflects meta-level knowledge about roles of predicatees. Schubert's steamroller is one of such problems. Although it is clear that ths in a clause. GL-resolution makes use of this feature of GCF to gain high search efficiency. We demonstrate the advantage of guarded resolution by proving Schubert's steamroller in comparison with many-sorted resolution.