It is shown that the proof system using odd-superpositions Ⅱ is not complete.The reason leading to this incompleteness is that the use of idempotency rule is neglected.By defining the superpositions of first-order po...It is shown that the proof system using odd-superpositions Ⅱ is not complete.The reason leading to this incompleteness is that the use of idempotency rule is neglected.By defining the superpositions of first-order polynomials and zero,the concept of odd-superpositions Ⅱ is extended,and a complete proof system using the extended odd-superpositions Ⅱ is developed.In addition,this proof system is an improvement on remainder method;its completeness demonstrates actually that the remainder method using semantic strategy is still complete.展开更多
基金Project supported by the Chinese Climbing Project Foundation and China Postdoctoral Science Foundation.
文摘It is shown that the proof system using odd-superpositions Ⅱ is not complete.The reason leading to this incompleteness is that the use of idempotency rule is neglected.By defining the superpositions of first-order polynomials and zero,the concept of odd-superpositions Ⅱ is extended,and a complete proof system using the extended odd-superpositions Ⅱ is developed.In addition,this proof system is an improvement on remainder method;its completeness demonstrates actually that the remainder method using semantic strategy is still complete.
