Deduction Modulo中理论的子句范式化
Clausal Presentation of Theories in Deduction Modulo
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摘要: Resolution Modulo通过添加重写规则将一阶Resolution扩展。在搜索证明的过程中,这些重写规则用来重写子句。在Resolution Modulo的第一个版本中,子句被重写成一般形式的命题。这些命题需要动态地转换成子句。如果重写系统是子句范式的,也就是,把子句重写成子句,那么就可以避免这些令人不愉快的动态转换。本文的工作是将任意一个重写系统转换成一个子句范式的重写系统,且保持了任意相继式无切证明的存在性。Abstract: Resolution modulo is an extension of first-order resolution in which rewrite rules are used to rewrite clauses during the search. In the first version of this method, clauses are rewritten to arbitrary propositions. These propositions are needed to be dynamically transformed into clauses. This unpleasant feature can be eliminated when the rewrite system is clausal, i.e., when it rewrites clauses to clauses. We show in this paper how to transform any rewrite system into a clausal one, preserving the existence of cut free proofs of any sequent.