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31
Analogy in Inductive Theorem Proving
, 1998
"... This paper investigates analogydriven proof plan construction in inductive theorem proving. We identify constraints of secondorder mappings that enable a replay of the plan of a source theorem to produce a similar plan for the target theorem. In some cases, differences between the source and ..."
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Cited by 25 (8 self)
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This paper investigates analogydriven proof plan construction in inductive theorem proving. We identify constraints of secondorder mappings that enable a replay of the plan of a source theorem to produce a similar plan for the target theorem. In some cases, differences between the source and target theorem mean that the target proof plan has to be reformulated. These reformulations are suggested by the mappings. The analogy procedure, implemented in ABALONE, is particularly useful for overriding the default control and suggesting lemmas. Employing analogy has extended the problem solving horizon of the proof planner CLAM : with analogy, some theorems could be proved that neither CLAM nor NQTHM could prove automatically.
Secondorder matching modulo evaluation  A technique for reusing proofs
 Proceedings of IJCAI 95
, 1995
"... in our prototype of a learning prover, the PLAGlATORsystem [Brauburger, 1994], has proved successful for many examples, including those from Table 1. Hence we are able to verify these conjectures by automatically reusing the proofs of previously proved, similar conjectures. As a side effect useful ..."
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Cited by 18 (5 self)
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in our prototype of a learning prover, the PLAGlATORsystem [Brauburger, 1994], has proved successful for many examples, including those from Table 1. Hence we are able to verify these conjectures by automatically reusing the proofs of previously proved, similar conjectures. As a side effect useful lemmata are speculated by our method. Table 1 also suggests a recursive organization of the reuse procedure as the proof obligations returned by our solution algorithm may also be proved by reuse. The (heuristic) control of this recursion for avoiding nontermination by cyclic reuses is subject to future work. Another future topic is concerned with the management of learned schematic proofs for an efficient selection of the proof shell which is to be reused for a
Reuse of proofs in software verification
 Foundations of Software Technology and Theoretical Computer Science
, 1993
"... This paper presents a method for automated reuse of proofs in software verication. Proofs about programs as well as proof attempts are used to guide the verification of modified programs, particularly of program corrections. We illustrate the phenomenon of reusability, present an evolutionary verifi ..."
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Cited by 18 (6 self)
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This paper presents a method for automated reuse of proofs in software verication. Proofs about programs as well as proof attempts are used to guide the verification of modified programs, particularly of program corrections. We illustrate the phenomenon of reusability, present an evolutionary verification process model and discuss theoretical and technical aspects. Finally, we report on case studies with an implementation of this method in the Karlsruhe Interactive Verifier (KIV).
Some Experiments on the Applicability of Folding Architecture Networks to Guide Theorem Proving
, 1997
"... One of the major problems in theorem proving is control of the proof search. A promising approach is the application of machine learning techniques for the acquisition of search control knowledge by learning from successful proof searches. In this paper we briefly discuss this idea and existing mach ..."
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Cited by 17 (6 self)
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One of the major problems in theorem proving is control of the proof search. A promising approach is the application of machine learning techniques for the acquisition of search control knowledge by learning from successful proof searches. In this paper we briefly discuss this idea and existing machine learning techniques for this task. We suggest neural folding architecture networks together with supervised training algorithms as a very promising candidate for learning search control knowledge. This suggestion is based on two sets of experiments in which we applied folding architecture networks to term ordering problems and clause classification tasks resulting from the proof search of the equational theorem prover DISCOUNT. 1 INTRODUCTION Currently, automated theorem provers (ATP systems) and similar deductive systems are being introduced into more and more application areas, e.g. deductive databases, verification problems, or computer algebra systems. However, the power of current ...
High Performance ATP Systems by Combining Several AI Methods
 IN PROC. FIFTEENTH INTERNATIONAL JOINT CONFERENCE ON ARTIFICIAL INTELLIGENCE (IJCAI ’97
, 1997
"... We present a concept for an automated theorem prover that employs a search control based on ideas from several areas of artificial intelligence (AI). The combination of casebased reasoning, several similarity concepts, a cooperation concept of distributed AI and reactive planning enables a system u ..."
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Cited by 17 (1 self)
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We present a concept for an automated theorem prover that employs a search control based on ideas from several areas of artificial intelligence (AI). The combination of casebased reasoning, several similarity concepts, a cooperation concept of distributed AI and reactive planning enables a system using our concept to learn form previous successful proof attempts. In a kind of bootstrapping process easy problems are used to solve more and more complicated ones. We provide case studies from two domains of interest in pure equational theorem proving taken from the TPTP library. These case studies show that an instantiation of our architecture achieves a high grade of automation and outperforms stateoftheart conventional theorem provers.
Experiments in the Heuristic Use of Past Proof Experience
 Proc. CADE13
, 1996
"... Problems stemming from the study of logic calculi in connection with an inference rule called "condensed detachment" are widely acknowledged as prominent test sets for automated deduction systems and their search guiding heuristics. It is in the light of these problems that we demonstrate the power ..."
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Cited by 16 (4 self)
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Problems stemming from the study of logic calculi in connection with an inference rule called "condensed detachment" are widely acknowledged as prominent test sets for automated deduction systems and their search guiding heuristics. It is in the light of these problems that we demonstrate the power of heuristics that make use of past proof experience with numerous experiments. We present two such heuristics. The first heuristic attempts to reenact a proof of a proof problem found in the past in a flexible way in order to find a proof of a similar problem. The second heuristic employs "features" in connection with past proof experience to prune the search space. Both these heuristics not only allow for substantial speedups, but also make it possible to prove problems that were out of reach when using socalled basic heuristics. Moreover, a combination of these two heuristics can further increase performance. We compare our results with the results the creators of Otter obtained with t...
Learning Proof Heuristics By Adapting Parameters
 In Proc. of the 12th International Workshop on Machine Learning
, 1995
"... We present a method for learning heuristics employed by an automated prover to control its inference machine. The hub of the method is the adaptation of the parameters of a heuristic. Adaptation is accomplished by a genetic algorithm. The necessary guidance during the learning process is provided by ..."
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Cited by 14 (5 self)
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We present a method for learning heuristics employed by an automated prover to control its inference machine. The hub of the method is the adaptation of the parameters of a heuristic. Adaptation is accomplished by a genetic algorithm. The necessary guidance during the learning process is provided by a proof problem and a proof of it found in the past. The objective of learning consists in finding a parameter configuration that avoids redundant effort w.r.t. this problem and the particular proof of it. A heuristic learned (adapted) this way can then be applied profitably when searching for a proof of a similar problem. So, our method can be used to train a proof heuristic for a class of similar problems. A number of experiments (with an automated prover for purely equational logic) show that adapted heuristics are not only able to speed up enormously the search for the proof learned during adaptation. They also reduce redundancies in the search for proofs of similar theorems. This not o...
Annotated Reasoning
 Annals of Mathematics and Artificial Intelligence (AMAI). Special Issue on Strategies in Automated Deduction
, 2000
"... Proof Search According to [12], abstract proof search is a process by which, starting from a representation of a problem at a socalled ground level, we construct a new and simpler representation at a socalled abstract level and use it to solve the original problem. That is, we abstract the given ..."
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Cited by 11 (4 self)
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Proof Search According to [12], abstract proof search is a process by which, starting from a representation of a problem at a socalled ground level, we construct a new and simpler representation at a socalled abstract level and use it to solve the original problem. That is, we abstract the given goal, prove its abstracted version and then use the information about the resulting abstract proof as an outline to construct the proof at the ground level. Dierent techniques to abstract from details have been studied in the literature. The problem is to nd out which details should be abstracted away. On one hand, if we abstract too much information then we often obtain abstract solutions that cannot be transferred to the ground level. Then, planning at the abstract level is even more dicult than planning at the ground level because the abstraction removes necessary control information, or we obtain only little information from the abstract proof how to guide the proof at the ground leve...
Similarities and Reuse of Proofs in Formal Software Verification
, 1998
"... The amount of user interaction is a prime cost factor in interactive program verification. This paper analyzes situations in which the reuse of previous proofs can help reducing these costs. In particular, it describes a technique that reuses subproofs in the verification of invariants of state tran ..."
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Cited by 8 (2 self)
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The amount of user interaction is a prime cost factor in interactive program verification. This paper analyzes situations in which the reuse of previous proofs can help reducing these costs. In particular, it describes a technique that reuses subproofs in the verification of invariants of state transition systems. This technique replays decisions of generalized previous proof attempts from the same overall verification process. As opposed to CBR applications that are justified by the fact that no or insufficient domain knowledge is available to solve a problem from first principles or by saving a huge search effort, our technique aims at saving user interaction. Several case studies provide first proofs of significant savings of user interaction in verification proofs by employing our CBR technique.
Automatic learning of proof methods in proof planning
 L. J. of the IGPL
, 2002
"... Our research interests in this project are in exploring how automated reasoning systems can learn theorem proving strategies. In particular, we are looking into how a proof planning system (Bundy, 1988) can automatically learn ..."
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Cited by 8 (4 self)
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Our research interests in this project are in exploring how automated reasoning systems can learn theorem proving strategies. In particular, we are looking into how a proof planning system (Bundy, 1988) can automatically learn