Refutational theorem proving for hierarchic first-order theories
Refutational theorem proving for hierarchic first-order theories
复制标题
证明层次一阶理论的反驳定理
DOI：
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发表时间：
1994
期刊：
影响因子：
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通讯作者：
Uwe Waldmann
中科院分区：
文献类型：
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作者：
L. Bachmair;H. Ganzinger;Uwe Waldmann
我们扩展以前的结果，定理证明一阶条款的平等层次的一阶理论。从语义上讲，这些理论局限于基本模型的保守扩展。结果表明，叠加与变量抽象和约束反驳是反驳完全的理论是足够完整的简单的情况下。为了证明，我们引入了定理证明系统之间的近似的概念，这使得有可能将问题减少到已知的（平坦的）一阶理论的情况。这些结果允许模块化组合的叠加为基础的定理证明与任意反驳证明的原始基础理论，其公理表示在某些逻辑可能仍然隐藏。此外，它们可以用来消除某些二阶公式中的存在量化谓词符号。
We extend previous results on theorem proving for first-order clauses with equality to hierarchic first-order theories. Semantically such theories are confined to conservative extensions of the base models. It is shown that superposition together with variable abstraction and constraint refutation is refutationally complete for theories that are sufficiently complete with respect to simple instances. For the proof we introduce a concept of approximation between theorem proving systems, which makes it possible to reduce the problem to the known case of (flat) first-order theories. These results allow the modular combination of a superposition-based theorem prover with an arbitrary refutational prover for the primitive base theory, whose axiomatic representation in some logic may remain hidden. Furthermore they can be used to eliminate existentially quantified predicate symbols from certain second-order formulae.