On handling distinct objects in the superposition calculus
On handling distinct objects in the superposition calculus
复制标题
关于叠加微积分中不同对象的处理
DOI：
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发表时间：
2005
期刊：
影响因子：
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通讯作者：
M. P. Bonacina
中科院分区：
文献类型：
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作者：
S. Stephan;M. P. Bonacina
许多推理领域都包含一组不同的对象。对于通用的自动定理证明器，这个属性必须明确指定，包括独特性公理。由于它们的数量与不同对象的数量成二次方增长，这会导致大而笨拙的规范，这可能会对性能产生不利影响。我们表明，对象的独特性可以直接处理的修改后的基于叠加的推理系统，包括额外的推理规则。新的微积分被证明是健全和完整的。一个初步的实施显示出可喜的成果，在理论的阵列。
Many domains of reasoning include a set of distinct objects. For general-purpose automated theorem provers, this property has to be specified explicitly, by including distinctness axioms. Since their number grows quadratically with the number of distinct objects, this results in large and clumsy specifications, that may affect performance adversely. We show that object distinctness can be handled directly by a modified superposition-based inference system, including additional inference rules. The new calculus is shown to be sound and complete. A preliminary implementation shows promising results in the theory of arrays.