D. A. Plaisted. A simplified problem reduction format. Artificial Intelligence, 2(10):227--261, 192.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....24 Table 6 2: The Order in which non Horn problems appear on the x axes of figures 6 3 and 6 4 55 6. 3 Disjunctions that form a Contradiction An interesting class of problems to look at are those called Disjunctions that form a Contradiction by the TPTP database and coming originally from [Plaisted 92] These are Horn sets, but all possible Lush resolution branches can lead to a contradiction so Semantic Lush resolution was ineffective and its results are not considered here. The syntactic names of the ones tested were SYN005 1.002, SYN0051. 003, SYN005 1.006. In general SYN005 1.00N is ....

....resolution (even with a bad choice of indices) and SL resolution generate search spaces of size polynomial in n, but positive unit resolution, all negative resolution, set of support strategy, ancestry filter form, and input resolution all generate search spaces of size exponential in n. Plaisted 92] This is born out by the comparisons of cpu time and search space in figures 6 5 and 6 6. Looking at the output for SYN005 3 it becomes clearer what is happening. lush(test, disjunction) r(1,disjunction,f(1,p1) r(1,disjunction,f(1,p2) r(1,disjunction,f(1,p3) ....

D. A. Plaisted. A simplified problem reduction format. Artificial Intelligence, 2(10):227--261, 192.

....were deferred, the proof is reattempted, this time with goals being solvable by matching them to deferred heads. When no goals or deferred heads remain, the query has been solved. Plaisted has implemented a new theorem prover using a new method based on his simplified problem reduction format [27]. His system also does not require contrapositives. Plaisted emphasizes the unnatural backward chaining searches that can result from the use of contrapositives. For example, solving and(a,b) by and(X,Y) X, Y seems natural, but use of the contrapositive X and(X,Y) Y is procedurally ....

Plaisted, D.A. A simplified problem reduction format. Artificial Intelligence 18, 2 (March 1982), 227--261.

....reduce inner loop processing time. More specifically, the preprocessing reduces the penalty in inner loop speed for the use of a stronger proof procedure. This variant is actually closer in structure to systems proposed by others, notably N Prolog [3, 2] and the Simplified Problem Reduction Format [9, 10] (hereafter referenced as SPRF) than to nH Prolog, as we note later. We present the variant here, discuss some of its characteristics, particularly those distinct from nH Prolog, and establish soundness and completeness properties for this variant. The variant that we consider is Inheritance ....

....can realize on occasion. In addition, InH Prolog turns out to be a quite natural formulation of the near Horn Prolog approach to extending Prolog, an impression that is reinforced by the observation that InH Prolog has natural counterparts in a sequent style theorem proving procedure (SPRF [9, 10]) and a Prolog for hypothetical implication (N Prolog [3, 2] see Program: p(X) q(a) q(b) r(b) p(X) q(X) s(X) s(c) p(c) Query: q(X) i.e. FALSE : q(X) Deduction using weak cancellation: FALSE : q(X) # f0:p(Y)g where X = a restart : FALSE # p(Y) q(X1) # p(Y) ....

David Plaisted. A simplified problem reduction format. Artif. Intell, 18:227--261, 1982.

....are identical, it is necessary to permit the alternative of not factoring, i.e. a choice point must be established. This increases the size of the search space. Of the chain format systems mentioned above, only SL resolution incorporates a separate factoring operation. It has been noted by Plaisted [1982, p. 235] that . the failure to economise on repeated subgoals seems to be a serious problem with SL resolution . Lemmas The truncation operation of the ME procedure includes a mechanism by which lemma chains can be produced and added to the input set. The literals that consitute a lemma ....

Plaisted D.A. (1982), A Simplified Problem Reduction Format, In Artificial Intelligence 18, Elsevier Science, Amsterdam, The Netherlands, 227-261.

....: General [HW92] ATP [Qua92b] PLA Planning. Planning is the process of determining the sequence of actions to be performed by an agent, to reach a desired state. The initial state and the desired state are provided. Indices : DDC 006.3; MSC 68T99. References : General [AKPT91] ATP [Pla81, Pla82] PRV Program Verification. Program verification formally establishes that a computer program does the task it is designed for. Indices : DDC 005.14; MSC 68Q60. References : General , ATP [WOLB92, MOW76] PUZ Puzzles. Puzzles are designed to test the ingenuity of humans. Indices : DDC 510, ....

D.A. Plaisted. A Simplified Problem Reduction Format. Artificial Intelligence, 18:227--261, 1982.

....establish that the query 9 L is proved whenever it should be provable. Before stating the completeness theorem, we address several points worth noting or recalling. Regarding the result, the assertion is very close to completeness results for similar systems, in particular the SPRF procedure [Pla82, Pla88] and the N Prolog procedure [GR84, Gab85] see chapter 6) The key difference is the inclusion here of the cancellation pruning rule, which demands the use of the distinguished head within its block. As we have previously stated, this provides a strong pruning rule, although its optimal use does ....

....refutation in which the goal atom is selected for reduction cancellation. The subtree with root sequent FALSE # h 2 corresponds to the restart block in the linear refutation. 6. 2 SPRF The first system we will consider is the Simplified Problem Reduction Format (SPRF) developed by Plaisted [Pla82, Pla88]. The SPRF is a Gentzenstyle axiom system that employs sequents of the form Gamma L where Gamma is a sequence of atoms and L is an atom. The axioms for the system are of the form Gamma L for L 2 Gamma. The input set is expected to be in clausal form with negative facts positively ....

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D. Plaisted. A simplified problem reduction format. Artificial Intelligence, 18:227--261, 1982.

....11YXX. References : General [HW92] ATP [Qua92b] PLA Planning. Planning is the process of determining the sequence of actions to be performed by an agent, to reach a specified desired state from a specified initial state. Indices : DDC 006.3; MSC 68T99. References : General [AKPT91] ATP [Pla81, Pla82] PRV Program Verification. Program verification formally establishes that a computer program does the task it is designed for. Indices : DDC 005.14; MSC 68Q60. References : General , ATP [WOEB92, MOW76] PUZ Puzzles. Puzzles are designed to test the ingenuity of humans. Indices : DDC 510, ....

D.A. Plaisted. A Simplified Problem Reduction Format. Artificial Intelligence, 18:227--261, 1982.

....MSC 11YXX. References : General [35] ATP [86] PLA Planning. Planning is the process of determining the sequence of actions to be performed by an agent, to reach a desired state. The initial state and the desired state are provided. Indices : DDC 006.3; MSC 68T99. References : General [2] ATP [79, 80]. PRV Program Verification. Program verification formally establishes that a computer program does the task it is designed for. Indices : DDC 005.14; MSC 68Q60. References : General , ATP [136, 61] PUZ Puzzles. Puzzles are designed to test the ingenuity of humans. Indices : DDC 510, 793.73; ....

\Phi D.A. Plaisted. A Simplified Problem Reduction Format. Artificial Intelligence, 18:227--261, 1982.

....References : General [HW92] ATP [Qua92b] PLA Planning. Planning is the process of determining the sequence of actions to be performed by an agent, to reach a specified desired state from a specified initial state. Indices : DDC 006.3; MSC 68T99. References : General [AKPT91] ATP [Pla81, Pla82] PRV Program Verification. Program verification formally establishes that a computer program does the task it is designed for. Indices : DDC 005.14; MSC 68Q60. References : General , ATP [WOEB92, MOW76] PUZ Puzzles. Puzzles are designed to test the ingenuity of humans. Indices : DDC 510, ....

D.A. Plaisted. A Simplified Problem Reduction Format. Artificial Intelligence, 18:227--261, 1982.

....We would like to find a back chaining strategy that is efficient on Horn clauses, based on unification, and still always permits instances to be deleted. Some such strategies exist; they are the MESON strategy, model elimination [Lov78] and the simple and modified problem reduction formats [Pla82, Pla88], all with caching. However, of these, either caching of unit lemmas and subgoals is not complete for first order logic, as for the first two, or the strategies have propositional inefficiencies for non Horn problems, as for the second two. For the MESON strategy and model elimination, if caching ....

....MESON strategy, unit lemmas result in behavior like that of model elimination with unit lemmas. The MESON strategy with unit lemmas and caching has behavior like model elimination with unit lemmas and caching. 5. 16 Problem reduction formats The simplified and modified problem reduction formats [Pla82, Pla88] simulate Prolog s back chaining mechanism, but are complete for first order logic. The simplified problem reduction format [Pla82] without caching is much the same as model elimination, for Horn clauses. The simplified problem reduction format generates formulae called decompositions. For Horn ....

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D. Plaisted. A simplified problem reduction format. Artificial Intelligence, 18:227--261, 1982. 39

....clauses and rapidly find those that were relevant for a particular query. I then wanted to develop this into a general first order theorem prover based on unification, but this was not to be until Shie Jue s clause linking theorem prover implementation. The simplified problem reduction format of [Pla82] was an attempt to improve on the SL resolution idea by performing back chaining in a more efficient manner, and was seen as an extension of Prolog s search strategy to full first order logic, with caching incorporated. It is a goal oriented strategy that avoids repeated work for Horn clauses. ....

....of [Pla94b] and [Pla94c] which give sets of clauses on which well known strategies perform asymptotically very bad. There, we show that only a small number of strategies are both goal sensitive and propositionally efficient. We note that some of these complexity issues were addressed already in [Pla82]. A further evidence for the search inefficiencies of resolution and other common strategies is the superior performance of CLIN S on some problems, as mentioned in [CP94] and confirmed by our tests of this prover on other examples as well. We note that term rewriting based theorem provers also ....

D. Plaisted. A simplified problem reduction format. Artificial Intelligence, 18:227--261, 1982.

....are from Stickel s paper [Sti86] The problem example is a theorem presented by Pellitier and Rudnicki in AAR Newsletter No. 6, 1986. The problem exx5 is a verification condition from Hoare s FIND program [Ble77] The problem exx7 is a situation calculus theorem developed by David Plaisted [Pla82] latinsq is the latin square problem from [Rob63] liar is the truthtellers and liars problem [LO85] salt is the salt and mustard problem from Lewis Carroll [LO85] The problem schubert is Schubert s steamroller [Wal84] The stack problem is a proof of a trivial property of push down ....

D. Plaisted. A simplified problem reduction format. Artificial Intelligence, 18:227--261, 1982.

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