Model generation is a problem complementary to theorem proving and is important for fault analysis and debugging of formal specifications of security protocols, programs and terminological definitions, for example. This paper discusses several ways of enhancing the paradigm of bottom-up model generation, with the two main contributions being a new range-restriction transformation and generalized blocking techniques. The range-restriction transformation refines existing transformations to range-restricted clauses by carefully limiting the creation of domain terms. The blocking techniques are based on simple transformations of the input set together with standard equality reasoning and redundancy elimination techniques, and allow for finding small, finite models. All possible combinations of the introduced techniques and a classical range-restriction technique were tested on the clausal problems of the TPTP Version 6.0.0 with an implementation based on the SPASS theorem prover using a hyperresolution-like refinement. Unrestricted domain blocking gave best results for satisfiable problems, showing that it is an indispensable technique for bottom-up model generation methods, that yields good results in combination with both new and classical range-restricting transformations. Limiting the creation of terms during the inference process by using the new range-restricting transformation has paid off, especially when using it together with a shifting transformation. The experimental results also show that classical range restriction with unrestricted blocking provides a useful complementary method. Overall, the results show bottom-up model generation methods are good for disproving theorems and generating models for satisfiable problems, but less efficient for unsatisfiable problems.

中文翻译：

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自下而上模型生成方法的阻塞和其他增强功能

模型生成是定理证明的补充问题，对于安全协议、程序和术语定义的形式规范的故障分析和调试很重要。本文讨论了几种增强自底向上模型生成范式的方法，其中两个主要贡献是新的范围限制转换和广义阻塞技术。范围限制转换通过仔细限制域术语的创建，将现有转换细化为范围限制条款。分块技术基于输入集的简单转换以及标准的等式推理和冗余消除技术，并允许找到小的、有限的模型。引入的技术和经典范围限制技术的所有可能组合都在 TPTP 6.0.0 版的条款问题上进行了测试，并使用基于 SPASS 定理证明器的实现，使用了类似超分辨率的改进。无限制域阻塞对可满足的问题给出了最好的结果，表明它是自底向上模型生成方法不可或缺的技术，与新的和经典的范围限制变换相结合产生了良好的结果。通过使用新的范围限制变换在推理过程中限制项的创建已经得到了回报，尤其是在将其与移位变换一起使用时。实验结果还表明，具有无限制阻塞的经典范围限制提供了一种有用的补充方法。全面的，