Efficiency and Completeness of the Set of Support Strategy in Theorem Proving

Wos, Larry; Robinson, George; Carson, Daniel F.

doi:10.1145/321296.321302

Cited by 242 publications

(49 citation statements)

References 1 publication

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“…(A proof compatible with that program's strategy does exist; this must be stated since the strategy used in [4] is definitely not complete.) A question which naturally arises is whether or not it would be preferable to combine a treatment of partial ordering by rule with the set-of-support strategy [10], in order to take full advantage of the "working backward" which that would provide. The basic step in adapting the partial ordering rule for this purpose is to allow for each transitivity axiom (such as ~.~xCy V ~-~yC_z V xCz) an additional inference of the form ~-~x~z, yC_z I--~-~xCy (i.e.…”

Section: Discussionmentioning

confidence: 99%

Experiment with an automatic theorem-prover having partial ordering inference rules

Slagle

Norton

1973

Commun. ACM

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Step 2. Place a dot at coordinate X, Y.Step 3. If Y equals the y coordinate of the bottom end of the line, stop. Otherwise, go to Step 4. Step 4. lfD is negative, set D = D + 2 lAX [, and set Y = Y + 1.Go to Step 2. If Dis positive, set D = D + 2 [ AX ] --2 I AY I, setY = Y+ 1, andsetX = X+ l. GotoStep2.By careful initialization of constants it is possible to combine the procedures given here for slopes less than 45 degrees and slopes greater than 45 degrees into a single procedure for all cases. However, the procedures are so simple and compact to start with that the additional code required to combine them is difficult to justify. Experience has shown that a faster and more compact program is obtained if the two cases are treated separately.The precision with which the calculations in the procedures must be carried out depends on the resolution of the particular plotter to be used and the characteristics of the dot-generating algorithm. If there are k dots along the maximum dimension of the rectangular raster, the maximum value of AX or AY for any line in the drawing will he k units. Since the values of the variables in the Bresenham algorithm may range between -t-2 AX or -t-2 AY, the arithmetic of the procedure will encounter signed integers with a maximum range of -I-2k units. The number of bits required to represent these signed integers in 2's complement arithmetic is V-logs 4k-1 bits. The largest plotting area in general use is 1024 × 1024 units, which would require 12 bit calculations. Arithmetic of this magnitude is within the single precision integer arithmetic capability of most popular minicomputers.

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Section: Discussionmentioning

confidence: 99%

Experiment with an automatic theorem-prover having partial ordering inference rules

Slagle

Norton

1973

Commun. ACM

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“…I5 The analogue of this capturing lemma for resolution alone plays a basic role in proving the refutation-completeness of resolution (see J. Robinson, 1965 andSlagle, 1967) and of set-of-support (Wos et al, 1965). 16 Alternatively, one can view the difficulty as resulting from the fact that it is not always possible to satisfy the hypotheses of the restricted subterm form.…”

Section: Capturing Lemma}mentioning

confidence: 99%

Paramodulation and Theorem-proving in First-Order Theories with Equality

Robinson¹,

Wos²

The Collected Works of Larry Wos (In 2 Volumes) - Volume I: Exploring the Power of Automated Reasoning - Volume II: Applying Au

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“…The Set of Support strategy [22] is a now wellestablished mechanism for restricting resolution operations whilst searching for a proof. It has been very successful, being central to a number of theorem-proving systems, in particular Otter [15], the predominant system for classical first-order logic.…”

Section: Sos In Classical Resolutionmentioning

confidence: 99%

“…Identifying a suitable set of support affects both the completeness and the efficiency of the method. In classical resolution work has been carried out on using both semantic and syntactic methods to choose the set of support [22]. We anticipate that extensions of these methods can be adopted.…”

Section: Limitationsmentioning

confidence: 99%

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The Set of Support strategy in temporal resolution

Dixon

Fisher

Proceedings. Fifth International Workshop on Temporal Representation and Reasoning (Cat. No.98EX157)

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A variety of proof methods have been developed to support the effective mechanisation of temporal logic. While clausal temporal resolution has been successfully employed for a range of problems, a number of improvements are still required. In particular, as there is no consistent control strategy underlying the method, a large amount of irrelevant information may sometimes be generated.Following on from classical resolution, where the Set of Support strategy has been used very successfully, we here introduce, justify and apply a temporal version of this strategy, thus allowing the supporting set to be carried over between the different phases of the resolution method. This not only restricts the production of irrelevant information but, under certain conditions, retains the completeness of the refutation process.

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Efficiency and Completeness of the Set of Support Strategy in Theorem Proving

Cited by 242 publications

References 1 publication

Experiment with an automatic theorem-prover having partial ordering inference rules

Experiment with an automatic theorem-prover having partial ordering inference rules

Paramodulation and Theorem-proving in First-Order Theories with Equality

The Set of Support strategy in temporal resolution

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