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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*...##
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Experiments on Supporting Interactive Proof Using Resolution
[chapter]

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 ...

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

2015
*
Annals of Mathematics and Artificial Intelligence
*

We tried

doi:10.1007/s10472-014-9443-5
fatcat:orr4s7dpwfdftewqqv6dddi5je
*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. ...##
###
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]

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. ...

##
###
Planning diagonalization proofs
[chapter]

1997
*
Lecture Notes in Computer Science
*

It is now widely

doi:10.1007/3540634932_31
fatcat:vfa5mksr6jcuzoyobtypqbpyxy
*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] . ...##
###
Extracting verified decision procedures: DPLL and Resolution

2015
*
Logical Methods in Computer Science
*

We also

doi:10.2168/lmcs-11(1:6)2015
fatcat:v77khapeqzghhhxduaxephewwq
*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. ...##
###
Automatic Proof and Disproof in Isabelle/HOL
[chapter]

2011
*
Lecture Notes in Computer Science
*

Isabelle/HOL is a popular interactive

doi:10.1007/978-3-642-24364-6_2
fatcat:y4crzmmegfhybfp5xu2bwlxoae
*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. ...##
###
Inducing students to induct
[chapter]

1995
*
Lecture Notes in Computer Science
*

As examples, we

doi:10.1007/3-540-60675-0_44
fatcat:z3rf7xtf2bgj5ezkcjrylxhski
*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). ...##
###
Three Tactic Theorem Proving
[chapter]

1999
*
Lecture Notes in Computer Science
*

We take a somewhat radical approach

doi:10.1007/3-540-48256-3_14
fatcat:pbtt3abttndwro6q6fldjn5274
*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 ...##
###
An overview of the Tecton proof system

1994
*
Theoretical Computer Science
*

The Tecton proof system is an experimental tool

doi:10.1016/0304-3975(94)90192-9
fatcat:fnkjdxg2lbf5xl7axzibotkkba
*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 ...##
###
Deriving and applying logic program transformers
[chapter]

1995
*
Lecture Notes in Computer Science
*

We present a methodology

doi:10.1007/3-540-60688-2_52
fatcat:kowfxyecfjadnb63frzrv65hdi
*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. ...##
###
On the Mechanization of the Proof of Hessenberg's Theorem in Coherent Logic

2007
*
Journal of automated reasoning
*

We propose

doi:10.1007/s10817-007-9086-x
fatcat:qd6qknicmve5rfrllkwn3rio2u
*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*). ...##
###
SAD as a mathematical assistant—how should we go from here to there?

2006
*
Journal of Applied Logic
*

is applied

doi:10.1016/j.jal.2005.10.009
fatcat:yzxc73hb2fhmjciwukuq6ii4bu
*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. ...##
###
Knowledge-based proof planning

1999
*
Artificial Intelligence
*

We demonstrate our approach

doi:10.1016/s0004-3702(99)00076-4
fatcat:f4ux6wsnvnaf3eipgpvrot7tme
*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. ...
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