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1432 JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013 Figure 7: Query efficiency on thread number and tuple number query. Although Paillier and Elgamal encryption scheme is not so efficient comparing to symmetric encryption schemes like DES and SHA. But it is good enough for some cases that users pay more attention on information security than computation performance. Future work includes improving efficiency of the system and extending system functionality, such as extended query on range, aggregation, and join. REFERENCES [1] The legion of the bouncy castle. http://www. bouncycastle.org/, 2013. [Online; accessed 10-Jan- 2013]. [2] Non - relational universe. http://nosql-database. org/, 2013. [Online; accessed 10-Jan-2013]. [3] Nosql, a relational database management system. http://www.strozzi.it/cgi-bin/CSA/tw7/ I/en US/nosql/Home\%20Page, 2013. [Online; accessed 10-Jan-2013]. [4] Nosql data modeling techniques. http: //highlyscalable.wordpress.com/2012/ 03/01/nosql-data-modeling-techniques/, 2013. [Online; accessed 10-Jan-2013]. [5] Rakesh Agrawal, Jerry Kiernan, Ramakrishnan Srikant, and Yirong Xu. Order preserving encryption for numeric data. In Proceedings of the 2004 ACM SIGMOD international conference on Management of data, SIGMOD ’04, pages 563–574, New York, NY, USA, 2004. ACM. [6] Haipeng Chen, Xuanjing Shen, and Yingda Lv. An implicit elgamal digital signature scheme. JSW, 6(7):1329–1336, 2011. [7] Taher El Gamal. A public key cryptosystem and a signature scheme based on discrete logarithms. In CRYPTO, pages 10–18, 1984. [8] Tingjian Ge, Stanley B. Zdonik, and Stanley B. Zdonik. Answering aggregation queries in a secure system model. In VLDB, pages 519–530, 2007. [9] Hakan Hacgm, Bala Iyer, and Sharad Mehrotra. Efficient execution of aggregation queries over encrypted relational databases. In YoonJoon Lee, Jianzhong Li, Kyu-Young Whang, and Doheon Lee, editors, Database Systems for Advanced Applications, volume 2973 of Lecture Notes in Computer Science, pages 125–136. Springer Berlin Heidelberg, 2004. [10] Haibo Hu and Jianliang Xu. Non-exposure location anonymity. In Yannis E. Ioannidis, Dik Lun Lee, and Raymond T. Ng, editors, ICDE, pages 1120–1131. IEEE, 2009. [11] Haibo Hu, Jianliang Xu, Chushi Ren, Byron Choi, and Byron Choi. Processing private queries over untrusted data cloud through privacy homomorphism. In ICDE, pages 601–612, 2011. [12] Yong Hu, Xizhu Mo, Xiangzhou Zhang, Yuran Zeng, Jianfeng Du, and Kang Xie. Intelligent analysis model for outsourced software project risk using constraint-based bayesian network. JSW, 7(2):440–449, 2012. [13] Daniele Micciancio. A first glimpse of cryptography’s holy grail. page 96, 2010. [14] Ayman Mousa, Elsayed Nigm, El-Sayed El-Rabaie, Osama S. Faragallah, and Osama S. Faragallah. Query processing performance on encrypted databases by using the rea algorithm. pages 280–288, 2012. [15] Einar Mykletun and Gene Tsudik. Aggregation queries in the database-as-a-service model. In Ernesto Damiani and Peng Liu, editors, Data and Applications Security XX, volume 4127 of Lecture Notes in Computer Science, pages 89–103. Springer Berlin / Heidelberg, 2006. [16] Pascal Paillier. Public-key cryptosystems based on composite degree residuosity classes. In EUROCRYPT, pages 223–238, 1999. [17] R. Rivest, L. Adleman, and M. Dertouzos. On data banks and privacy homomorphisms. pages 169–177. Academic Press, 1978. [18] Yonghong Yu and Wenyang Bai. Enforcing data privacy and user privacy over outsourced database service. JSW, 6(3):404–412, 2011. GuoYubin Received Ph. D. from South China University of Technology in 2007. She is now lecturer in South China Agricultural University. Her research interests include Database theory and technology, cryptography and network computing. Zhang Liankuan Received Ph. D. from South China Agricultural University in 2012. He is now lecturer in South China Agricultural University. His research interests include Database theory, technology and network computing. Lin Fengren He is now Bachelor student in South China Agricultural University. His research interests include Database theory and technology. Li Ximing Received Ph.D. degree from College of Informatics, South China Agricultural University, Guangzhou, Guangdong, China, in 2011. His current research interests include computer theory and cryptography. © 2013 ACADEMY PUBLISHER
JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013 1433 Predicate Formal System based on 1-level Universal AND Operator and its Soundness Yingcang Ma School of Science, Xi’an Polytechnic University, Xi’an, Shaanxi, 710048, China School of Electronics and information, Northwestern Polytechnical University, Xi’an, Shaanxi, 710048, China Email: mayingcang@126.com Huacan He School of Computer Science, Northwestern Polytechnical University, Xi’an, Shaanxi, 710048, China Email: hehuac@nwpu.edu.cn Abstract—The aim of this paper is solving the predicate calculus formal system based on 1-level universal AND operator. Firstly, universal logic and propositional calculus formal deductive system UL − h∈ (0, 1] are introduced. Secondly, a predicate calculus formal deductive system ∀ UL − h∈ (0, 1] based on 1-level universal AND operator is built. Thirdly, the soundness theorem and deduction theorem of system ∀ UL − h∈ (0, 1] are given, which ensure that the theorems are tautologies and the reasoning rules are valid in system ∀ h (0 1] . UL − ∈ , Index Terms—universal logic, predicate calculus formal system, universal AND operator I. INTRODUCTION How to deal with various uncertainties and evolution problems have been critical issues for further development of artificial intelligence [1,2]. Mathematical logic is too rigid and it can only solve certainty problems, therefore, non-classical logic and modern logic develop rapidly, for example, fuzzy logic and universal logic. Considerable progresses have been made in logical foundations of fuzzy logic in recent years, especially for logic system based on t-norm and its residua [3]. Some well-known logic systems have been built up, such as, the basic logic (BL) [4, 5] introduced by Hajek; the monoidal t-norm based logic [6, 7] introduced by Esteva and Godo; a formal deductive system L* introduced by Wang [8-10], Universal logic proposed by He [11], and so on. Universal logic is a new continuous-valued logic system in studying flexible world’s logical rule, which uses generalized correlation and generalized autocorrelation to describe the relationship between propositions, more studies can be found in [12-14]. For a logic system, the formalization’s studies are very important, which include propositional calculus and predicate calculus. The propositional calculus formal systems are studied in [15-18]. But the studies of predicate calculus formal systems of universal logic are relatively rare, so we will mainly study the predicate calculus formal system in this paper, which can enrich the formalization’s studies of universal logic. Some predicate calculus formal deductive systems are built for fuzzy logic systems, for example, the predicate calculus formal deductive systems of Schweizer-Sklar t- norm in [19, 20]. The predicate calculus formal deductive systems of universal logic have been studies in [21-24], which mainly focus on the 0-level universal AND operator. In this paper, we focus on the formal system of universal logic based on 1-level universal AND operator. We will build predicate formal system ∀UL − h∈ (0, 1] for 1- level universal AND operator, and its soundness and deduction theorem are given. The paper is organized as follows. After this introduction, Section II contains necessary background knowledge about BL and UL. Section III we will build the predicate calculus formal deductive system ∀ UL − h∈ (0, 1] for 1-level universal AND operator. In Section IV the soundness and deduction theorem of system ∀ UL − h∈ (0, 1] will be given. The final section offers the conclusion. II. PRELIMINARIES A. The Basic Fuzzy Logic BL and BL-algebra The languages of BL [3] include two basic connectives → and & , one truth constant 0 . Further connectives are defined as follows: ϕ ∧ ψ is ϕ & ( ϕ → ψ) , ϕ ∨ ψ is (( ϕ →ψ) →ψ) ∧( ψ →ϕ) → ϕ) , ¬ ϕ is ϕ → 0 , ϕ ≡ ψ is ( ϕ →ψ) & ( ψ → ϕ) . The following formulas are the axioms of BL: (i) ( ϕ →ψ) →(( ψ → χ)( ϕ → χ)) (ii) ( ϕ & ψ) → ϕ (iii) ( ϕ & ψ) → ( ψ & ϕ) (iv) ϕ &( ϕ →ψ) →( ψ &( ψ → ϕ)) (v) ( ϕ →( ψ → χ)) →(( ϕ& ψ) → χ) (vi) (( ϕ & ψ) → χ) →( ϕ →( ψ → χ)) © 2013 ACADEMY PUBLISHER doi:10.4304/jcp.8.6.1433-1440
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Journal of Computers ISSN 1796-203X
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Corn Moisture Measurement using a C
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Call for Papers and Special Issues
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(Contents Continued from Back Cover
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