¹ School of Science, Xi’an Polytechnic University, Xi’an, Shaanxi, 710048, China
² School of Electronics and information, Northwestern Polytechnical University, Xi’an, Shaanxi, 710048, China
³ School of Computer Science, Northwestern Polytechnical University, Xi’an, Shaanxi, 710048, China

---

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 ULh (0 1] − ∈ , are introduced. Secondly, a predicate calculus formal deductive system ULh (0 1] − ∀ ∈ , based on 1-level universal AND operator is built. Thirdly, the soundness theorem and deduction theorem of system ULh (0 1] − ∀ ∈ , are given, which ensure that the theorems are tautologies and the reasoning rules are valid in system ULh (0 1] − ∀ ∈ , .

Index Terms—universal logic, predicate calculus formal system, universal AND operator

[PDF]

Cite: Yingcang Ma and Huacan He, " Predicate Formal System based on 1-level Universal AND Operator and its Soundness," Journal of Computers vol. 8, no. 6, pp. 1433-1440, 2013.