Caching and lemmaizing in model elimination theorem provers

Astrachan, Owen; Stickel, Mark E.

doi:10.1007/3-540-55602-8_168

Cited by 49 publications

(20 citation statements)

References 19 publications

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“…De nition6. For an arbitrary set of chains CH in ST 0 , w e de ne a binary relation CH on the nodes of ST 0 : n 1 CH n 2 i n 1 and n 2 are sibling nodes or belong to the same chain in CHand n 2 is a successor of n 1 G(CH ST) n 2 2 ST 0 we h a ve that n 1 CH n 2 implies n 2 …”

Section: Refutation Graphsmentioning

confidence: 99%

“…Set CH=K 1 K 2 . A l l chains inK 1 have their end nodes in the subtree rooted in n 1 and neither n 1 nor n 2 is in G(CH ST). Hence, by the induction hypothesis, for all nodes of G(CH ST), with the exception of n 0 , also its sibling is in G(CH ST).…”

Section: G(ch St) a Graph G(ch St) I S A Semi Refutation Graph I It mentioning

confidence: 99%

“…seq is repetition free), all n i n i+1 are siblings for odd i, and all n i n i+1 are members of the same chain in CHfor even i. W e s a y that n m is connected to n 1 . I f n m is connected to n 1 , then obviously there is a chain that contains n m and all of whose nodes are also connected to n 1 . W e c a l l t h e s e t cc(CH n 1 ) of chains in G(CH ST) all of whose nodes are connected to n 1 the connected component of n 1 .…”

Section: Refutation Graphs For Tableauxmentioning

confidence: 99%

“…Observe that node n 5 is connected to every chain in CHnffn 4 n 5 gg. Hence, CH (1) := cc(CHnffn 4 n 5 gg n 5 ) = CHnffn 4 n 5 gg is the next connected component. We c hoose fn 2 n 3 g and extend the tableau with the corresponding labels in Figure 7(c).…”

Section: Refutation Graphs For Tableauxmentioning

confidence: 99%

“…We c hoose fn 2 n 3 g and extend the tableau with the corresponding labels in Figure 7(c). ;C (2) B A (3) ;C (4) (c) T ;A C A (1) ;C (2) B A ;A (3) ;B (4) ;C (5) ;C (6) (d) T ;A C A (1) ;C (2) B A ;A (3) ;B (4) ;C C (5) ;C C (6) (e) Fig. 7.…”

Section: Refutation Graphs For Tableauxmentioning

confidence: 99%

See 4 more Smart Citations

Semantic tableaux with ordering restrictions

Klingenbeck

Hähnle

1994

Automated Deduction — CADE-12

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Abstract. The aim of this paper is to make restriction strategies based on orderings of the Herbrand universe available for semantic tableau-like calculi as well. A marriage of tableaux and ordering restriction strategies seems to be most promising in applications where generation of counter examples is required. In this paper, starting out from semantic trees, we develop a formal tool called refutation graphs, w h i c h (i) serves as a basis for completeness proofs of both resolution and tableaux, and (ii) is compatible with so-called A-ordering restrictions. The main result is a rst-order ground tableau procedure complete for A-ordering restrictions.

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Section: Refutation Graphsmentioning

confidence: 99%

Section: G(ch St) a Graph G(ch St) I S A Semi Refutation Graph I It mentioning

confidence: 99%

Section: Refutation Graphs For Tableauxmentioning

confidence: 99%

Section: Refutation Graphs For Tableauxmentioning

confidence: 99%

Section: Refutation Graphs For Tableauxmentioning

confidence: 99%

See 3 more Smart Citations

Semantic tableaux with ordering restrictions

Klingenbeck

Hähnle

1994

Automated Deduction — CADE-12

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On the Modelling of Search in Theorem Proving— Towards a Theory of Strategy Analysis

Bonacina

Hsiang

1998

Information and Computation

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We present a model for representing search in theorem proving. This model captures the notion of contraction, which has been central in some of the recent developments in theorem proving. We outline an approach to measuring the complexity of search which can be applied to analyze and evaluate the behaviour of theorem-proving strategies. Using our framework, we compare contraction-based strategies of different contraction power and show how they affect the evolution of the respective search spaces during the derivation. * This paper is a significantly extended version of "On the representation of dynamic search spaces in theorem proving," C.-S. Yang, ed.,

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Controlled Use of Clausal Lemmas in Connection Tableau Calculi

Fuchs

2000

Journal of Symbolic Computation

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Proof procedures based on model elimination or the connection tableau calculus have become more and more successful. But these procedures still suffer from long proof lengths as well as from a rather high degree of redundant search effort in comparison with resolution-style search procedures. In order to overcome these problems we investigate the use of clausal lemmas. We develop a method to augment a given set of clauses by a lemma set in a preprocessing phase and discuss the ability of this technique to reduce proof lengths and depths and to provide an appropriate reordering of the search space. We deal with the basic connection tableau calculus as well as with several calculus refinements and extensions. In order to control the use of lemmas we develop techniques for selecting relevant lemmas based on partial evaluation techniques. Experiments with the prover Setheo performed in several domains demonstrate the high potential of our approach.

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Caching and lemmaizing in model elimination theorem provers

Cited by 49 publications

References 19 publications

Semantic tableaux with ordering restrictions

Semantic tableaux with ordering restrictions

On the Modelling of Search in Theorem Proving— Towards a Theory of Strategy Analysis

Controlled Use of Clausal Lemmas in Connection Tableau Calculi

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