| ¡¡ | Chinese Journal of Computers Full Text |
| Title | Logical Properties on Translations between Logics |
| Authors | SHEN Yu-Ming1),2) MA Yue1),2) CAO Cun-Gen1) SUI Yue-Fei1) WANG Ju3) |
| Address | 1)(Key Laboratory of Intelligent Information Processing,Institute of Computing Technology,Chinese Academy of Sciences,Beijing£º100190) 2)(Graduate University of Chinese Academy of Sciences, Beijing 100039) 3)(School of Computer Science and Information Engineering, Guangxi Normal University, Guilin, Guangxi 541004) |
| Year | 2009 |
| Issue | No.10(2091¡ª2098) |
| Abstract & Background | Abstract Translating one logic into another logic in a satisfiability-preserving way does not immediately lead to the preservation of the unsatisfiability, if the models translation is taken into account and the class of models of the first logic is translated to a proper subclass of the class of models of the second logic. In this paper, two logical properties: the faithfulness and the fullness are defined to ensure the preservations of the satisfiability and the unsatisfiability. As an example, the translation from second-order logic into first-order logic is given. It is shown that under standard semantics, the translation is faithful but not full, whereas it is faithful and full under Henkin semantics. Keywords translation; faithful translation; full translation; second-order logic; first-order logic |