## New Implementation Framework for Saturation-Based Reasoning (2006)

### BibTeX

@MISC{Riazanov06newimplementation,

author = {Alexandre Riazanov},

title = {New Implementation Framework for Saturation-Based Reasoning},

year = {2006}

}

### OpenURL

### Abstract

Abstract. The saturation-based reasoning methods are among the most theoretically developed ones and are used by most of the state-of-the-art first-order logic reasoners. In the last decade there was a sharp increase in performance of such systems, which I attribute to the use of advanced calculi and the intensified research in implementation techniques. However, nowadays we are witnessing a slowdown in performance progress, which may be considered as a sign that the saturation-based technology is reaching its inherent limits. The position I am trying to put forward in this paper is that such scepticism is premature and a sharp improvement in performance may potentially be reached by adopting new architectural principles for saturation. The top-level algorithms and corresponding designs used in the state-of-the-art saturation-based theorem provers have (at least) two inherent drawbacks: the insufficient flexibility of the used inference selection mechanisms and the lack of means for intelligent prioritising of search directions. In this position paper I analyse these drawbacks and present two ideas on how they could be overcome. In particular, I propose a flexible low-cost high-precision mechanism for inference selection, intended to overcome problems associated with the currently used instances of clause selection-based procedures. I also outline a method for intelligent prioritising of search directions, based on probing the search space by exploring generalised search directions. I discuss some technical issues related to implementation of the proposed architectural principles and outline possible solutions. 1

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Citation Context ...prover tries to refine a refutation from the previous step into a refutation which uses no generalisation. Octopus approach. The Octopus system [25] runs a large number of sessions of the prover Theo =-=[24]-=- distributed over a cluster of computers. Each Theo session first runs on a weakening of the original problem, obtained by replacing one of the clauses with one of its generalisations. If one of the s... |

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Citation Context ...implementation techniques, such as term indexing (see [12] and more recent survey [35]), heuristic methods for guiding proof search (see, e. g., [34]) and top-level saturation algorithms (see, e. g., =-=[13]-=- and [33]). Unfortunately, the initial momentum created by such work seems to have diminished, and nowadays we are witnessing a slowdown in performance progress 4 . Some researchers consider this to b... |

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Citation Context .... This is done by discarding some non-redundant but heuristically bad clauses and inferences. Waldmeister implements a sophisticated scheme to reduce the memory requirements by the DISCOUNT algorithm =-=[13,8]-=-. In both cases, the adjustments of the top level algorithms led to a great improvement in the effectiveness of the systems. This gives me hope that a radically different approach to inference selecti... |

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Citation Context ...h is technically unrelated to the one proposed here, but which also provides an alternative to local syntactic relevancy estimation. The semantic guidance approach, developed within the SCOTT project =-=[15]-=-, is roughly as follows. The prover tries to establish satisfiability of several sets of stored clauses (in SCOTT this is done with the help of an external model builder). Ideally, these sets must app... |

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Citation Context ... language of FOL are implied by some theory. The expressiveness of FOL and its relative mechanisability make automated theorem proving in FOL a useful instrument for such applications as verification =-=[5,4,1,6]-=- and synthesis [19] of hardware and software, knowledge representation [18], Semantic Web [16], assisting human mathematicians [21,3], background reasoning in interactive theorem provers [23], and oth... |

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2 |
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Citation Context ...efinement is performed repeatedly and at some point the prover tries to refine a refutation from the previous step into a refutation which uses no generalisation. Octopus approach. The Octopus system =-=[25]-=- runs a large number of sessions of the prover Theo [24] distributed over a cluster of computers. Each Theo session first runs on a weakening of the original problem, obtained by replacing one of the ... |

1 |
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Citation Context ...tracted clause set, and throwing away the input clauses whose abstractions do not participate in any of the obtained proofs with the abstracted set. Iterative generalisation-refinement. Some time ago =-=[29]-=- drew my attention to the simplest kind of clause abstractions – generalisations, which seems convenient for our purposes. The method works roughly as follows. A resolution prover is parameterised by ... |

1 |
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(Show Context)
Citation Context ...nted in the clausal form or require only minor transformation.and is implemented in a significant number of modern provers, e. g., E [34], E-SETHEO (the E component), Gandalf [38], Otter [22], SNARK =-=[36]-=-, Spass [39], Vampire [32,30], and Waldmeister [14]. In the last decade there has been a sharp increase in performance of such systems 3 , which I attribute to the use of advanced calculi and inferenc... |