L. Wos. The Automation of Reasoning: An Experimenter's Notebook with OTTER Tutorial. Academic Press, 1996.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....hereafter) states that local con uence implies con uence provided there are no in nite paths. We have automated the combinatorial core of Huet s [5] proof of NL using the resolution theorem prover Otter [11] Otter is not the fastest theorem prover anymore, but is by far the best documented, see [13, 14]. We discuss the various sensitivities regarding the precise formulation in relation to the theorem proving procedure in Section 3. Geometric logic is introduced in Section 4, its proof theory in Sections 5 and 6, and the semantics and the completeness results in Section 7. 2 Local con uence is ....

L. Wos, The Automation of Reasoning: an Experimenter's Notebook with Otter Tutorial, Academic Press, 1996.

....interaction from the user may be required to adjust the weightings of strategies or input the theorems in a particular order. Automated theorem proving generally can be classified into two disciplines: search based theorem proving founded on resolution [Rob65] such as Argonne s OTTER system [Wos96] and Bledsoe s knowledge based theorem proving [Ble77] New directions in automated theorem proving, such as proof planning [Ker97] may provide program specialisers with the ability to generate rules during the transformation. The field of automatic theorem proving should be watched closely; ....

L. Wos. The Automation of Reasoning: An Experimenter's Notebook with OTTER Tutorial. Academic Press, 1996.

....original proof, which was found with the standard strategy with maxweight=24, changelimitafter=50, and newmaxweight=17, is 183 steps and was found in about 15 minutes. We asked Larry Wos to try some of his new methods for shortening proofs through proof checking with the resonance strategy [75], and he found the following 113 step proof. Proof (found by Otter 3.0.4 on gyro at 165.96 seconds) 3,2 x x = x 4 x y = y x 6,5 (x y) z = x (y z) 8,7 x x = x 9 x y = y x 11,10 (x y) z = x (y z) 12 (x (y z) x y) x (y z) 15,14 (x (y z) x y) x (y z) 16 ....

....of the absorption laws. Otter s original proof, which was found with the standard strategy with maxweight=28 and maxmem=28000, is 816 steps and was found in a few hours. We asked Larry Wos to try some of his new methods for shortening proofs through proof checking with the resonance strategy [75], and he found the following 99 step proof. Proof (found by Otter 3.0.4 on gyro at 8.56 seconds) 1 (A B) Delta B 6= B 2 x Delta (y z) x Delta y) x Delta z) 3 x (y Delta z) x y) Delta (x z) 4 x x 0 = 1 5 x Delta x 0 = 0 7 x Delta (y z) x Delta y) x ....

L. Wos. The Automation of Reasoning: An Experimenter's Notebook with Otter Tutorial. Academic Press, 1996. To appear.

....and (S) means that the program ran out of inferences to make, usually because the weight limit was too low for the strategy. The smallest time(s) for each problem is set in a box. The proof lengths are listed because there has been recent interest in strategies for finding short proofs [19, 18]. The length includes paramodulation inferences and steps to flip equations, but it does not include demodulation steps. Thus, comparing lengths on the same theorem can be misleading because paramodulation steps in one proof can correspond to demodulation proofs in another. Nevertheless, it is ....

....for AC problems. ffl The tables in Section 4.6 include data on proof length. We found substantial variations in proof length, but we have not been able to draw any conclusions about which strategies lead to short proofs. We advise users seeking short proofs to consult Larry Wos s recent work [19, 18] and to experiment with a variety of strategies. The following results are surprising to us. ffl For selecting the next unit of work, we had previously assumed that the given clause algorithm is much better for non AC problems and that the pair algorithm is much 32 Chapter 4 better for AC ....

L. Wos. The Automation of Reasoning: An Experimenter's Notebook with Otter Tutorial. Academic Press, New York, 1996. To appear.

....touched on the problem; and later in the seminar, Lincoln led a panel discussion on the topic. Such analysis and formalization of proof search are clearly important steps toward automating the achievement of well behaved search. Larry Wos s goal of a self analytical automated reasoning system [10, 11], which can monitor its progress and dynamically adjust the search parameters, is also closely related to the topic of well behaved search. Input Files, Proofs, and EQP Many input files and computer proofs from my Robbins experiments are available on the Web at the following location. ....

L. Wos. The Automation of Reasoning: An Experimenter's Notebook with Otter Tutorial. Academic Press, New York, 1996. This article was processed using the L A T E X macro package with LLNCS style

....the output in question by merely manipulating symbols in accordance with the knowledge bases, algorithms, and code in question. We give three examples of this kind of failure. 8 For a real life counterpart, we have otter s settling the Robbins Problem, presented as an open question in (Wos 1996). 9 4.1 brutus Let s turn first to the brutus system (Bringsjord Ferrucci 2000) This is a system designed to appear to be literarily creative to others. To put the point in the spirit of TT, brutus reflects a multi year attempt to build a system able to play the short short story game, or S ....

Wos, L. (1996), The Automation of Reasoning: An Experimenter's Notebook with otter Tutorial, Academic Press, San Diego, CA.

....and (S) means that the program ran out of inferences to make, usually because the weight limit was too low for the strategy. The smallest time(s) for each problem is set in a box. The proof lengths are listed because there has been recent interest in strategies for finding short proofs [21, 20]. The length includes paramodulation inferences and steps to flip equations, but it does not include demodulation steps. Thus, 84 Chapter 5 comparing lengths on the same theorem can be misleading because paramodulation steps in one proof can correspond to demodulation proofs in another. ....

....for AC problems. ffl The tables in Section 5.6 include data on proof length. We found substantial variations in proof length, but we have not been able to draw any conclusions about which strategies lead to short proofs. We advise users seeking short proofs to consult Larry Wos s recent work [21, 20] and to experiment with a variety of strategies. The following results are surprising to us. ffl For selecting the next unit of work, we had previously assumed that the given clause algorithm is much better for non AC problems and that the pair algorithm is much better for AC problems. But for ....

L. Wos. The Automation of Reasoning: An Experimenter's Notebook with OTTER Tutorial. Academic Press, New York, 1996.

....how to use them. Theorem Provers The Boyer Moore Theorem Prover (BMTP) 10] is one of the most powerful automated reasoning systems dealing with computationally definable objects represented as Lisp functions. It can apply induction schemes to recursively defined data types and functions. Otter [67] is one of the most important resolution based theorem provers for first order logic with equality. SETHEO ( SEquential THEOrem prover ) 48] is a top down theorem prover of similar performance based on the so called connection tableau method. There exist also parallel versions called PARTHEO [62] ....

L. Wos. The Automation of Reasoning: An Experimenter's Notebook with Otter Tutorial. Academic Press, 1996.

....of paramodulation have led to fruitful theoretical and practical research on paramodulation based theorem proving. Concerning the practical research, a large number of experiments with paramodulation have been performed at the Argonne group by Wos, Overbeek, Henschen and others (see, e.g. [Wos88, Wos96] for references) and especially by McCune with his provers Otter [McC94] and EQP [McC97a] and his recent automated proof of the Robbins conjecture [McC97c, McC97b] 2.2.1 Extending the unit equality case: ordered paramodulation An important tool in paramodulation is the use of term orderings ....

Larry Wos. The Automation of Reasoning: An Experimenter's Notebook with OTTER Tutorial. Academic Press, 1996.

....paramodulation have led to fruitful theoretical and practical research on paramodulation based theorem proving. Concerning the practical research, a large number of experiments with paramodulation have been performed at the Argonne group by Wos, Overbeek, Henschen and others (see, e.g. Wos 1988, Wos 1996] for references) and especially by McCune with his provers Otter [McCune 1994] and EQP [McCune 1997a] and his recent automated proof of the Robbins conjecture [McCune 1997b, McCune 1997c] Concerning the theoretical research, the main techniques are reviewed in this chapter, and some aspects of ....

Wos L. [1996], The Automation of Reasoning: An Experimenter's Notebook with OTTER Tutorial, Academic Press.

....and (S) means that the program ran out of inferences to make, usually because the weight limit was too low for the strategy. The smallest time(s) for each problem is set in a box. The proof lengths are listed because there has been recent interest in strategies for finding short proofs [20, 19]. The length includes paramodulation inferences and steps to flip equations, but it does not include demodulation steps. Thus, 14 Chapter 4 comparing lengths on the same theorem can be misleading because paramodulation steps in one proof can correspond to demodulation proofs in another. ....

....for AC problems. ffl The tables in Section 4.6 include data on proof length. We found substantial variations in proof length, but we have not been able to draw any conclusions about which strategies lead to short proofs. We advise users seeking short proofs to consult Larry Wos s recent work [20, 19] and to experiment with a variety of strategies. The following results are surprising to us. 32 Chapter 4 ffl For selecting the next unit of work, we had previously assumed that the given clause algorithm is much better for non AC problems and that the pair algorithm is much better for AC ....

L. Wos. The Automation of Reasoning: An Experimenter's Notebook with Otter Tutorial. Academic Press, New York, 1996.

....of 900,000 clauses or with the use of 20,000 demodulators (rewrite rules) OTTER s performance is not substantially less than with far smaller numbers. If one is interested in seeing how OTTER is used in research, The Automation of Reasoning: An Experimenter s Notebook with OTTER Tutorial [Wos, 1996] is an excellent resource. The book present both successes and failures from numerous experiments with OTTER. Two other reasoning programs deserve mention. The first is ACL2 (A Computational Logic for Applicative Common Lisp) which incorporates an industrial strength version of the BoyerMoore ....

L. Wos. The automation of reasoning: An experimenter's notebook with OTTER tutorial. Academic Press, New York, 1996.

....original proof, which was found with the standard strategy with maxweight=24, changelimitafter=50, and newmaxweight=17, is 183 steps and was found in about 15 minutes. We asked Larry Wos to try some of his new methods for shortening proofs through proof checking with the resonance strategy [78], and he found the following 113 step proof. Proof (found by Otter 3.0.4 on gyro at 165.96 seconds) 3,2 x x = x 4 x y = y x 6,5 (x y) z = x (y z) 8,7 x x = x 130 6. Lattice Like Algebras 9 x y = y x 11,10 (x y) z = x (y z) 12 (x (y z) x y) x (y z) 15,14 (x (y ....

....z) x y) x z)g. Otter s original proof, which was found with the standard strategy with maxweight=23 and the flag controlmemory, is 125 steps and was found in 914 seconds. Larry Wos, starting with that proof, found the following 30 step proof by proof checking with the resonance strategy [78]) Proof (found by Otter 3.0.4 on gyro at 12.04 seconds) 2 x y = y x 3 x = x 5,4 x x = x 6 x y = y x 8,7 (x y) z = x (y z) 10,9 x x = x 13,12 (x y) z = x (y z) 6.2 Distributivity and Modularity 135 15,14 (x (y z) x y) x (y z) 16 (x (y z) x y) x (y z) ....

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L. Wos. The Automation of Reasoning: An Experimenter's Notebook with Otter Tutorial. Academic Press, 1996. To appear.

....this article in part prompted by the recent activities of chip designers that include Intel and AMD, activities heavily emphasizing the proving of theorems. As for my research that appears to me to be relevant, I have made an intense and most profitable study of finding proofs that are shorter [2, 3], some that avoid the use of various types of term, some that are far less complex than previously known, and the like. Those results suggest to me a strong possible connection between more appealing proofs (in mathematics and in logic) and enhanced and improved design of both hardware and ....

Wos, L.: The Automation of Reasoning: An Experimenter's Notebook with OTTER Tutorial. Academic Press, New York (1996)

....by a harder question, or replace the goal by one that appears to be more unreachable You might wonder why I chose to focus specifically on term avoidance. The main impetus was my success several years ago in finding a proof in many valued sentential calculus with such a constraint (Chapter 11 of [Wos1996], a proof conjectured to be nonexistent. Since then, when studying some problem in a logic calculus, I frequently have attempted 6 to find a proof free of double negation. And so I made such an attempt in my most recent study of the Meredith single axiom (completing with the deduction of the ....

Wos, L., The Automation of Reasoning: An Experimenter's Notebook with OTTER Tutorial, Academic Press, New York, 1996.

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Wos, L., The Automation of Reasoning: An Experimenter's Notebook with OTTER Tutorial, a Academic Press: New York, 1996. See http://www.mcs.anl.gov/people/wos/index.html for input files nd information on shorter proofs.

....Department of Energy, under Contract W 31 109 Eng 38. the most effective approaches where no new information is retained are based on Prolog technology. Among the more effective approaches in which new information is accrued are the computational logic paradigm and the clause language paradigm [14, 15, 18]. The former provides the basis for the Boyer Moore program [1, 2] mainly used for program verification) and the latter (in the Argonne variant) provides the basis for McCune s OTTER [7, 8] Based on my own experiments spread over more than thirty years, and supported by comments from other ....

....is its high weight or complexity. Perhaps in the future, this deficiency will be sharply reduced by having the program automatically (and possibly self analytically) move certain clauses from list(sos) to list(usable) before they are chosen as the focus of attention; see Section 13.4 of [18]. List(sos) is the name of the list of clauses that have not yet been chosen as the focus of attention but are recursively traceable to the initial set of support or were in the initial set of support. List(usable) consists of the input clauses that were part of the problem description but not ....

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Wos, L., The Automation of Reasoning: An Experimenter's Notebook with OTTER Tutorial, Academic Press: New York, 1996 (see http://www.mcs.anl.gov/people/wos/index.html for input files and information on shorter proofs).

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L. Wos. The Automation of Reasoning: An Experimenter's Notebook with OTTER Tutorial. Academic Press, 1996.

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