Sequent calculus proof theory of intuitionistic apartness and order relations
Sequent calculus proof theory of intuitionistic apartness and order relations
复制标题
直觉相异性和序关系的序贯微积分证明理论
DOI：
--
复制
发表时间：
1999
影响因子：
0.3
通讯作者：
Sara Negri
中科院分区：
文献类型：
--
作者：
Sara Negri
抽象。给出了直觉主义的分离论和序论的无压缩演算，并证明了该演算的割消。结果的后果之一是这些理论的析取性质。通过证明分析和规则置换的方法，我们建立了对于所有原子公式都被否定的序列，分离论相对于定义为分离的否定的等式论的保守性。证明扩展到保守性结果的理论建设秩序的一般理论秩序。
Abstract. Contraction-free sequent calculi for intuitionistic theories of apartness and order are given and cut-elimination for the calculi proved. Among the consequences of the result is the disjunction property for these theories. Through methods of proof analysis and permutation of rules, we establish conservativity of the theory of apartness over the theory of equality defined as the negation of apartness, for sequents in which all atomic formulas appear negated. The proof extends to conservativity results for the theories of constructive order over the usual theories of order.