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Page 6373 of Mathematical Reviews Vol. , Issue 97J [page]

1997 Mathematical Reviews  
{For the entire collection see MR 97i:00014. } 97j:68112 68T15 03B35 Kerber, Manfred (4-BIRM-SC; Birmingham); Pracklein, Axel Using tactics to reformulate formulae for resolution theorem proving.  ...  We show the conceptual power of the new definition by showing how it unifies known elimination operators such as resolution in theorem proving, joins in relational databases, and variable elimination for  ... 

Experiments on Supporting Interactive Proof Using Resolution [chapter]

Jia Meng, Lawrence C. Paulson
2004 Lecture Notes in Computer Science  
Resolution theorem provers are automatic and powerful, but they are designed to be used for very different applications.  ...  Interactive theorem provers can model complex systems, but require much effort to prove theorems.  ...  Acknowledgements We are grateful to the Vampire team (Alexandre Riazanov and Andrei Voronkov) for their co-operation and to Gernot Stenz and Geoff Sutcliffe for running some of our problems on their reasoning  ... 
doi:10.1007/978-3-540-25984-8_28 fatcat:cih6ysuuvvb6zj2jbemcqhz75a

Automated generation of machine verifiable and readable proofs: A case study of Tarski's geometry

Sana Stojanović Ðurđević, Julien Narboux, Predrag Janičić
2015 Annals of Mathematics and Artificial Intelligence  
We tried to automatically generate such proofs for the theorems from this book using resolution theorem provers and a coherent logic theorem prover.  ...  from the Coq formalization for each theorem.  ...  We are grateful to Stephan Schulz for his help and comments about using the prover E, and to Filip Marić for his advice about Isabelle proofs and his feedback on earlier versions of this paper.  ... 
doi:10.1007/s10472-014-9443-5 fatcat:orr4s7dpwfdftewqqv6dddi5je

Page 5118 of Mathematical Reviews Vol. , Issue 911 [page]

1991 Mathematical Reviews  
As a corollary from the completeness theorem we obtain a small model theorem and an algorithm for checking the validity of PAL formulas.”  ...  Several design tactics have been implemented in the KIDS/CYPRESS system and have been used to derive many algorithms semiautomatically.” 91i:68099 68060 03B70 Walukiewicz, Igor (PL-WASW-1) Gentzen type  ... 

Presenting intuitive deductions via symmetric simplification [chapter]

Frank Pfenning, Dan Nesmith
1990 Lecture Notes in Computer Science  
For most of today's automated theorem proving systems, this requires a non-trivial translation procedure to extract human-oriented deductions from machine-oriented proofs.  ...  We present an algorithm, symmetric simplification, for discovering useful lemmas in deductions of theorems in first-and higher-order logic.  ...  The disadvantage of this approach is that, to date, other theorem proving procedures are superior in that they can prove more theorems, and can prove them faster.  ... 
doi:10.1007/3-540-52885-7_98 fatcat:nllnavbdwvdzzai2mllqm2vilq

Planning diagonalization proofs [chapter]

Lassaad Cheikhrouhou
1997 Lecture Notes in Computer Science  
It is now widely used as a proof technique for unsolvability results and metamathematical arguments.  ...  The diagonalization proof technique is a well-known method in theoretical computer science and in mathematics that originated with Cantor, who used it to show his seminal uncountability results.  ...  In mega, we use a declarative representation as much as possible for methods, such that meta-methods can be employed to reformulate methods for example for analogy-driven theorem proving 18] .  ... 
doi:10.1007/3540634932_31 fatcat:vfa5mksr6jcuzoyobtypqbpyxy

Extracting verified decision procedures: DPLL and Resolution

Ulrich Berger, Andrew Lawrence, Fredrik Nordvall Forsberg, Monika Seisenberger, Daniel Leivant
2015 Logical Methods in Computer Science  
We also prove the equivalence between the resolution proof system and the DPLL proof system with a bound on the size of the resulting resolution proof.  ...  We use non-computational quantifiers to remove redundant computational content from the extracted program and translate it into Haskell to improve performance.  ...  We would like to thank the anonymous referees for their constructive comments. The financial support of Invensys Rail/Siemens Rail Automation is gratefully acknowledged.  ... 
doi:10.2168/lmcs-11(1:6)2015 fatcat:v77khapeqzghhhxduaxephewwq

Automatic Proof and Disproof in Isabelle/HOL [chapter]

Jasmin Christian Blanchette, Lukas Bulwahn, Tobias Nipkow
2011 Lecture Notes in Computer Science  
Isabelle/HOL is a popular interactive theorem prover based on higherorder logic. It owes its success to its ease of use and powerful automation.  ...  compiler as a fast evaluator for ground formulas, and its rival Nitpick is based on the model finder Kodkod, which performs a reduction to SAT.  ...  We thank Alexander Krauss, Mark Summerfield, and Thomas Türk for suggesting several textual improvements.  ... 
doi:10.1007/978-3-642-24364-6_2 fatcat:y4crzmmegfhybfp5xu2bwlxoae

Inducing students to induct [chapter]

David Lester, Sava Mintchev
1995 Lecture Notes in Computer Science  
As examples, we use the material that we have developed for an introductory functional programming module; and show how the theorem prover can be of assistance.  ...  In this paper we investigate the use of a theorem prover (written in Haskell) to help students gain con dence in their mathematical abilities.  ...  Assessment The students are assessed by a two hour written examination (counting for 75% of the marks) and by four assessed practicals (counting for 25% of the marks).  ... 
doi:10.1007/3-540-60675-0_44 fatcat:z3rf7xtf2bgj5ezkcjrylxhski

Three Tactic Theorem Proving [chapter]

Don Syme
1999 Lecture Notes in Computer Science  
We take a somewhat radical approach to proof description: proofs are not described with tactics but by using just three expressive o u t l i ning constructs.  ...  We describe the key features of the proof description language of Declare, an experimental theorem prover for higher order logic.  ...  Declarative Theorem Proving Interactive theorem provers combine aspects of formal speci cation, manual proof description and automated reasoning, and they allow us to develop machine checked formalizations  ... 
doi:10.1007/3-540-48256-3_14 fatcat:pbtt3abttndwro6q6fldjn5274

An overview of the Tecton proof system

D. Kapur, X. Nie, D.R. Musser
1994 Theoretical Computer Science  
The Tecton proof system is an experimental tool for constructing proofs of first-order logic formulas and of program specifications expressed using formulas in Hoare's axiomatic proof formalism.  ...  in an easy to comprehend form, using a combination of tabular formats, graphical representations, and hypertext links; and automating substantial parts of proofs through rewriting, induction, case analysis  ...  Acknowledgment Raj Agarwal, Michael Seager, and Changqing Wang have assisted in the implementation of Tecton, particularly of the program parser, Hoare formula generator, and  ... 
doi:10.1016/0304-3975(94)90192-9 fatcat:fnkjdxg2lbf5xl7axzibotkkba

Deriving and applying logic program transformers [chapter]

Penny Anderson, David Basin
1995 Lecture Notes in Computer Science  
We present a methodology for logic program development based on the use of veri ed transformation templates.  ...  We use the Isabelle Logical Framework to formalize transformation templates as inference rules.  ...  reformulated, are also useful for optimizing logic programs.  ... 
doi:10.1007/3-540-60688-2_52 fatcat:kowfxyecfjadnb63frzrv65hdi

On the Mechanization of the Proof of Hessenberg's Theorem in Coherent Logic

Marc Bezem, Dimitri Hendriks
2007 Journal of automated reasoning  
We propose to combine interactive proof construction with proof automation for a fragment of first-order logic called Coherent Logic (CL).  ...  We test our approach with a case study: Hessenberg's theorem, which states that in elementary projective plane geometry Pappus' axiom implies Desargues' axiom.  ...  This places CL somewhere in the middle between resolution logic (using conjunctive normal forms) and tableau methods (using general formulas).  ... 
doi:10.1007/s10817-007-9086-x fatcat:qd6qknicmve5rfrllkwn3rio2u

SAD as a mathematical assistant—how should we go from here to there?

Alexander Lyaletski, Andrey Paskevich, Konstantin Verchinine
2006 Journal of Applied Logic  
is applied to prove end subgoals.  ...  For example, we can handle binders like Σ or lim without resort to second order or to a full-powered set theory.  ...  Acknowledgements We are grateful to the referee for his valuable comments and suggestions which were extremely useful. We thank everybody who took part in the development of the SAD system.  ... 
doi:10.1016/j.jal.2005.10.009 fatcat:yzxc73hb2fhmjciwukuq6ii4bu

Knowledge-based proof planning

Erica Melis, Jörg Siekmann
1999 Artificial Intelligence  
We demonstrate our approach for the mathematical domain of limit theorems, which was proposed as a challenge to automated theorem proving by the late Woody Bledsoe.  ...  Let us pay attention to it. Woody  ...  We thank Jaime Carbonell and Manuela Veloso for discussions about control-rules and Martin Müller for his help to getting started with constraint solving.  ... 
doi:10.1016/s0004-3702(99)00076-4 fatcat:f4ux6wsnvnaf3eipgpvrot7tme
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