Abstract
In this paper we introduce several new improvements to the bottom-up model generation (BUMG) paradigm. Our techniques are based on non-trivial transformations of first-order problems into a certain implicational form, namely range-restricted clauses. These refine existing transformations to range-restricted form by extending the domain of interpretation with new Skolem terms in a more careful and deliberate way. Our transformations also extend BUMG with a blocking technique for detecting recurrence in models. Blocking is based on a conceptually rather simple encoding together with standard equality theorem proving and redundancy elimination techniques. This provides a general-purpose method for finding small models. The presented techniques are implemented and have been successfully tested with existing theorem provers on the satisfiable problems from the TPTP library.
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Baumgartner, P., Schmidt, R.A. (2006). Blocking and Other Enhancements for Bottom-Up Model Generation Methods. In: Furbach, U., Shankar, N. (eds) Automated Reasoning. IJCAR 2006. Lecture Notes in Computer Science(), vol 4130. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11814771_11
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DOI: https://doi.org/10.1007/11814771_11
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