The Correspondence between Propositional Modal Logic with Axiom and the Propositional Logic

摘要：

　　The propositional modal logic is obtained by adding the necessity operator □ to the propositional logic.Each formula in the propositional logic is equivalent to a formula in the disjunctive normal form.In order to obtain the correspondence between the propositional modal logic and the propositional logic, we add the axiom □(ψ)←→◇(ψ) to K and get a new system K+.Each formula in such a logic is equivalent to a formula in the disjunctive normal form, where □k(k ≥ 0) only occurs before an atomic formula p, and (~) only occurs before a pseudo-atomic formula of form □kp.Maximally consistent sets of K+ have a property holding in the propositional logic: a set of pseudo-atom-complete formulas uniquely determines a maximally consistent set.When a pseudo-atomic formula □kpi(k, i ≥ 0) is corresponding to a propositional variable qki, each formula in K+ then can be corresponding to a formula in the propositional logic P+.We can also get the correspondence of models between K+ and P+.Then we get correspondences of theorems and valid formulas between them.So, the soundness theorem and the completeness theorem of K+ follow directly from those of P+.

关键词： propositional modal logic propositional logic disjunctive normal form pseudo-atomic formula pseudo-atom-complete completeness

作者: Meiying Sun Shaobo Deng Yuefei Sui

作者单位: Key Laboratory of Intelligent Information Processing,Institute of Computing Technology, Chinese Acad Key Laboratory of Intelligent Information Processing,Institute of Computing Technology, Chinese Acad

会议类型: 国际会议

会议名称: 8th International Conference on Intelligent Information Processing(2014年IFIP智能信息处理国际会议)

会议地点: 杭州

会议语种:英文

页码: 141-151

在线出版日期: 2014-10-01（万方平台首次上网日期，不代表论文的发表时间）