New Generation Computing

, Volume 16, Issue 2, pp 163–200 | Cite as

On semantic resolution with lemmaizing and contraction and a formal treatment of caching

  • Maria Paola Bonacina
  • Jieh Hsiang
Regular Papers


Reducing redundancy in search has been a major concern for automated deduction. Subgoal-reduction strategies, such as those based on model elimination and implemented in Prolog technology theorem provers, prevent redundant search by usinglemmaizing andcaching, whereas contraction-based strategies prevent redundant search by usingcontraction rules, such assubsumption. In this work we show that lemmaizing and contraction can coexist in the framework ofsemantic resolution. On the lemmaizing side, we define two meta-level inference rules for lemmaizing in semantic resolution, one producing unit lemmas and one producing non-unit lemmas, and we prove their soundness. Rules for lemmaizing are meta-rules because they use global knowledge about the derivation, e.g. ancestry relations, in order to derive lemmas. Our meta-rules for lemmaizing generalize to semantic resolution the rules for lemmaizing in model elimination. On the contraction side, we give contraction rules for semantic strategies, and we define apurity deletion rule for first-order clauses that preserves completeness. While lemmaizing generalizes success caching of model elimination, purity deletion echoes failure caching. Thus, our approach integrates features of backward and forward reasoning. We also discuss the relevance of our work to logic programming.


Resolution Set-of-Support Lemmaizing Caching Forward and Backward Reasoning Theorem Proving Logic Programming 


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Copyright information

© Ohmsha, Ltd. and Springer 1998

Authors and Affiliations

  • Maria Paola Bonacina
    • 1
  • Jieh Hsiang
    • 2
  1. 1.Department of Computer ScienceUniversity of IowaIowa CityUSA
  2. 2.Department of Computer ScienceNational Taiwan UniversityTaipeiTaiwan

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