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Title:

Second-order matching modulo evaluation -- a technique for reusing proofs

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Abstract 1 We investigate the improvement of theorem provers by reusing previously computed proofs. A proof of a conjecture is generalized by replacing function symbols with function variables. This yields a schematic proof of a schematic conjecture which is instantiated subsequently for obtaining proofs of new, similar conjectures. Our reuse me...

Abstract 1 We investigate the improvement of theorem provers by reusing previously computed proofs. A proof of a conjecture is generalized by replacing function symbols with function variables. This yields a schematic proof of a schematic conjecture which is instantiated subsequently for obtaining proofs of new, similar conjectures. Our reuse method requires solving so-called free function variables, i.e. variables which cannot be instantiated by matching the schematic conjecture with a new conjecture. We develop an algorithm for solving free function variables by combining the techniques of symbolic evaluation and second-order matching. Heuristicsfor controlling the algorithm are presented, and several examples demonstrate their usefulness. We also show how our reuse proposal supports the discovery of useful lemmata. 1 Minimize

Publisher:

Morgan Kaufmann

Contributors:

The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2008-07-17

Source:

http://www.inferenzsysteme.informatik.tu-darmstadt.de/users/walther/Paper/Second-Order-Matching-mod-Eval-IJCAI-1995.pdf

http://www.inferenzsysteme.informatik.tu-darmstadt.de/users/walther/Paper/Second-Order-Matching-mod-Eval-IJCAI-1995.pdf Minimize

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text

Language:

en

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Title:

ARTIFICIAL INTELLIGENCE A Mechanical Solution of Schubert's Steamroller by Many-Sorted Resolution

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We demonstrate the advantage of using a many-sorted resolution calculus by a mechanical solulion of automated a challenge theorem problem. provers This before. problem Our known solution as clearly 'Schubert's demonstrates Steamroller ' the power had of been a many-so unsolvedt ed bY resolution calculus. The proposed method is applicable to all ...

We demonstrate the advantage of using a many-sorted resolution calculus by a mechanical solulion of automated a challenge theorem problem. provers This before. problem Our known solution as clearly 'Schubert's demonstrates Steamroller ' the power had of been a many-so unsolvedt ed bY resolution calculus. The proposed method is applicable to all resolution-based inference systems. In 1978, problem I. Schubert's Problem Schubert of the University of Alberta set up the following challenge Wolves, foxes, birds, caterpillars, and snails are animals, and there are some of each of them. Also there are some grains, and grains are plants. Every animal either likes to eat all plants or all animals much smaller than itself that like to eat some plants. Gaterpillars and snails are much smaller than birds, which are much: ' smaller than foxes, which in turn are much smaller than wolves. Wolves do not like to eat foxes or grains, while birds like to eat caterpillars but not snails. Caterpillars and snails like to eat some plants. Therefore there is an animal that likes to eat a grain-eating animal. This problem became well known since in spite of its apparent simplicity it turned out to be too hard for existing theorem provers because the search space is just too big. Using the following predicates as abbreviations: A(x): x is an animal, W(x): x is a wolf, F(x): x is a fox, B(x): x is a bird, C(x): x is a caterpillar, S(x): x is a snail, G(x): x is a grain, P(x): x is a plant, M(xy): x is much smaller than y, E(xy): x likes to eat y Minimize

Contributors:

The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2008-07-01

Source:

http://www.inferenzsysteme.informatik.tu-darmstadt.de/users/walther/Paper/Schuberts_Steamroller_by_Many-Sorted_Resolution-AIJ-25-2-1985.pdf

http://www.inferenzsysteme.informatik.tu-darmstadt.de/users/walther/Paper/Schuberts_Steamroller_by_Many-Sorted_Resolution-AIJ-25-2-1985.pdf Minimize

Document Type:

text

Language:

en

DDC:

630 Agriculture & related technologies *(computed)*

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Metadata may be used without restrictions as long as the oai identifier remains attached to it. Minimize

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Title:

Proof Management and Retrieval

Description:

Automated theorem provers might be improved if they reuse previously computed proofs. Our approach for reuse is based on so-called proof shells which are obtained from computed proofs by second-order generalization. Each proof shell represents a schematic proof of a schematic conjecture and applies for each instance of the schematic conjecture y...

Automated theorem provers might be improved if they reuse previously computed proofs. Our approach for reuse is based on so-called proof shells which are obtained from computed proofs by second-order generalization. Each proof shell represents a schematic proof of a schematic conjecture and applies for each instance of the schematic conjecture yielding (first-order) proof obligations justifying a successful proof reuse. But since there may be different proofs for different instances of a schematic conjecture, we have to select a reusable proof shell among the applicable proof shells for a new conjecture. For supporting such a retrieval efficiently, the set of computed proof shells is organized by so-called proof volumes and a proof dictionary. All applicable proof shells can be accessed by searching for the right proof volume in the proof dictionary, if the applicability of proof shells is determined by so-called simple second-order matchers. Minimize

Contributors:

The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2009-05-25

Source:

http://www.informatik.uni-freiburg.de/~koehler/ijcai-95/ijcai-ws/kolbe.ps.gz

http://www.informatik.uni-freiburg.de/~koehler/ijcai-95/ijcai-ws/kolbe.ps.gz Minimize

Document Type:

text

Language:

en

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Title:

Patching Proofs for Reuse

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. 1 We investigate the application of machine learning paradigms in automated reasoning in order to improve a theorem prover by reusing previously computed proofs. Our reuse procedure generalizes a previously computed proof of a conjecture yielding a schematic proof which can be instantiated subsequently if a new, similar conjecture is given. We...

. 1 We investigate the application of machine learning paradigms in automated reasoning in order to improve a theorem prover by reusing previously computed proofs. Our reuse procedure generalizes a previously computed proof of a conjecture yielding a schematic proof which can be instantiated subsequently if a new, similar conjecture is given. We show that for exploiting the full flexibility of second-order instantiations the instantiated schematic proof has to be patched such that a proof of the new conjecture is obtained. We develop an algorithm which computes patched proofs showing thereby that proof patching is always possible in a uniform way. This enables a further processing of the obtained proof, justifies the soundness of our proposal for reusing proofs, and provides a key for comparing our method with other reuse paradigms. 1 Introduction Several machine learning paradigms aim to improve a problem solver by reusing previously computed solutions, e.g. explanation-based learn. Minimize

Contributors:

The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2009-04-12

Source:

http://kirmes.inferenzsysteme.informatik.th-darmstadt.de/~kolbe/patProRep.ps.Z

http://kirmes.inferenzsysteme.informatik.th-darmstadt.de/~kolbe/patProRep.ps.Z Minimize

Document Type:

text

Language:

en

DDC:

004 Data processing & computer science *(computed)*

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Title:

Adaptation of Proofs for Reuse

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Automated theorem provers might be improved if they are enabled to reuse previously computed proofs. Our approach for reuse is based on generalizing computed proofs by replacing function symbols with function variables. This yields a schematic proof which is instantiated subsequently for obtaining proofs of new, similar conjectures. Our reuse me...

Automated theorem provers might be improved if they are enabled to reuse previously computed proofs. Our approach for reuse is based on generalizing computed proofs by replacing function symbols with function variables. This yields a schematic proof which is instantiated subsequently for obtaining proofs of new, similar conjectures. Our reuse method, which requires no human support, demands two steps of proof adaptation, viz. solution of so-called free function variables and patching of completely instantiated proofs. We develop algorithms for solving free function variables and for computing patched proofs and demonstrate their usefulness with several examples. Minimize

Contributors:

The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2009-05-25

Source:

http://www.aic.nrl.navy.mil/~aha/aaai95-fss/papers/kolbe.ps.Z

http://www.aic.nrl.navy.mil/~aha/aaai95-fss/papers/kolbe.ps.Z Minimize

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text

Language:

en

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Title:

A Machine-Verified Code Generator

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We consider the machine-supported verification of a code syntax trees which may be obtained by a parser from programs of an imperative programming language. We motivate the representation of states developed for the verification, which is crucial for success, as the interpretation of tree-structured WHILE-programs differs significantly in its op...

We consider the machine-supported verification of a code syntax trees which may be obtained by a parser from programs of an imperative programming language. We motivate the representation of states developed for the verification, which is crucial for success, as the interpretation of tree-structured WHILE-programs differs significantly in its operation from the interpretation of the linear machine code. This work has been developed for a course to demonstrate to the students the support gained by computer-aided verification in a central subject of computer science, boiled down to the classroom-level. We report about the insights obtained into the properties of machine code as well as the challenges and efforts encountered when verifying the correctness of the code generator. We also illustrate the performance of the VeriFunsystem that was used for this work. Minimize

Contributors:

The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2009-03-10

Source:

http://www.inferenzsysteme.informatik.tu-darmstadt.de/verifun/archive/lpar-2003-while-code-springer.pdf

http://www.inferenzsysteme.informatik.tu-darmstadt.de/verifun/archive/lpar-2003-while-code-springer.pdf Minimize

Document Type:

text

Language:

en

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Title:

Second-order matching modulo evaluation -- A technique for reusing proofs

Description:

in our prototype of a learning prover, the PLAGlATOR-system [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 a...

in our prototype of a learning prover, the PLAGlATOR-system [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 Minimize

Publisher:

IJCAI, Morgan Kaufmann

Contributors:

The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2012-03-04

Source:

http://ijcai.org/Past%20Proceedings/IJCAI-95-VOL%201/pdf/025.pdf

http://ijcai.org/Past%20Proceedings/IJCAI-95-VOL%201/pdf/025.pdf Minimize

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text

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en

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Title:

Reusing Proofs

Description:

. 1 We develop a learning component for a theorem prover designed for verifying statements by mathematical induction. If the prover has found a proof, it is analyzed yielding a so-called catch. The catch provides the features of the proof which are relevant for reusing it in subsequent verification tasks and may also suggest useful lemmata. Proo...

. 1 We develop a learning component for a theorem prover designed for verifying statements by mathematical induction. If the prover has found a proof, it is analyzed yielding a so-called catch. The catch provides the features of the proof which are relevant for reusing it in subsequent verification tasks and may also suggest useful lemmata. Proof analysis techniques for computing the catch are presented. A catch is generalized in a certain sense for increasing the reusability of proofs. We discuss problems arising when learning from proofs and illustrate our method by several examples. 1 INTRODUCTION The improvement of problem solvers by reusing previously computed solutions is an active research area of Artificial Intelligence, emerging in the methodologies of explanationbased learning (EBL) [11, 4, 5] and analogical reasoning (AR) [2, 7, 12]. In EBL a problem's solution is analyzed, yielding an explanation why the solution succeeds. After generalization, the explanation is used for. Minimize

Publisher:

John Wiley & Sons, Ltd

Contributors:

The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2009-04-12

Source:

http://kbibmp3.ub.uni-kl.de/Preprint_Informatik/PS/no_series_216.ps.gz

http://kbibmp3.ub.uni-kl.de/Preprint_Informatik/PS/no_series_216.ps.gz Minimize

Document Type:

text

Language:

en

DDC:

004 Data processing & computer science *(computed)*

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Title:

Verifying the Modal Logic Cube is an Easy Task (for Higher-Order Automated Reasoners)

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Abstract. Prominent logics, including quantified multimodal logics, can be elegantly embedded in simple type theory (classical higher-order logic). Furthermore, off-the-shelf reasoning systems for simple type type theory exist that can be uniformly employed for reasoning within and about embedded logics. In this paper we focus on reasoning about...

Abstract. Prominent logics, including quantified multimodal logics, can be elegantly embedded in simple type theory (classical higher-order logic). Furthermore, off-the-shelf reasoning systems for simple type type theory exist that can be uniformly employed for reasoning within and about embedded logics. In this paper we focus on reasoning about modal logics and exploit our framework for the automated verification of inclusion and equivalence relations between them. Related work has applied first-order automated theorem provers for the task. Our solution achieves significant improvements, most notably, with respect to elegance and simplicity of the problem encodings as well as with respect to automation performance. 1 Minimize

Contributors:

The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2010-09-28

Source:

http://www.ags.uni-sb.de/%7Echris/papers/B12.pdf

http://www.ags.uni-sb.de/%7Echris/papers/B12.pdf Minimize

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text

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en

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Title:

Termination analysis for functional programs

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Proving termination is a central problem in software development and formal methods for termination analysis are essential for program verification. However, since the halting problem is undecidable and totality of functions is not even semi-decidable, there is no procedure to prove or disprove the

Proving termination is a central problem in software development and formal methods for termination analysis are essential for program verification. However, since the halting problem is undecidable and totality of functions is not even semi-decidable, there is no procedure to prove or disprove the Minimize

Publisher:

Kluwer

Contributors:

The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2009-04-06

Source:

http://www.inferenzsysteme.informatik.tu-darmstadt.de/~giesl/datei.ps

http://www.inferenzsysteme.informatik.tu-darmstadt.de/~giesl/datei.ps Minimize

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text

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en

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