메뉴 건너뛰기




Volumn 7788, Issue , 2013, Pages 240-257

Theorem proving in large formal mathematics as an emerging AI Field

Author keywords

[No Author keywords available]

Indexed keywords

AUTOMATION; SEMANTICS;

EID: 85040513258     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-642-36675-8_13     Document Type: Article
Times cited : (23)

References (51)
  • 1
    • 84875989925 scopus 로고
    • The QED Manifesto Springer, Heidelberg
    • The QED Manifesto. In: Bundy, A. ed.) CADE 1994. LNCS, vol. 814, pp. 238-251. Springer, Heidelberg 1994
    • (1994) CADE 1994. LNCS , vol.814 , pp. 238-251
    • Bundy, A.1
  • 3
    • 84858328940 scopus 로고    scopus 로고
    • Automated and human proofs in general mathematics: An initial comparison
    • Bj?ner, N., Voronkov, A. eds. Springer, Heidelberg
    • Alama, J., Kühlwein, D., Urban, J.: Automated and Human Proofs in General Mathematics: An Initial Comparison. In: Bj?ner, N., Voronkov, A. eds.) LPAR- 18. LNCS, vol. 7180, pp. 37-45. Springer, Heidelberg 2012
    • (2012) LPAR- 18. LNCS , vol.7180 , pp. 37-45
    • Alama, J.1    Kühlwein, D.2    Urban, J.3
  • 4
    • 76649095631 scopus 로고    scopus 로고
    • Superposition modulo linear arithmetic supla
    • Ghilardi, S., Sebastiani, R. eds. Springer, Heidelberg
    • Althaus, E., Kruglov, E.,Weidenbach, C.: Superposition Modulo Linear Arithmetic SUPLA). In: Ghilardi, S., Sebastiani, R. eds.) FroCoS 2009. LNCS, vol. 5749, pp. 84-99. Springer, Heidelberg 2009
    • (2009) FroCoS 2009. LNCS , vol.5749 , pp. 84-99
    • Althaus, E.1    Kruglov, E.2    Weidenbach, C.3
  • 5
    • 84875982204 scopus 로고    scopus 로고
    • On the characterizations of compactness
    • Bancerek, G., Endou, N., Sakai, Y.: On the characterizations of compactness. Formalized Mathematics 94), 733-738 2001
    • (2001) Formalized Mathematics , vol.9 , Issue.4 , pp. 733-738
    • Bancerek, G.1    Endou, N.2    Sakai, Y.3
  • 6
    • 53049084608 scopus 로고    scopus 로고
    • Leo-ii - a cooperative automatic theorem prover for classical higher-order logic system description
    • Armando, A., Baumgartner, P., Dowek, G. eds. Springer, Heidelberg
    • Benzmüller, C.E., Paulson, L.C., Theiss, F., Fietzke, A.: LEO-II - A Cooperative Automatic Theorem Prover for Classical Higher-Order Logic System Description). In: Armando, A., Baumgartner, P., Dowek, G. eds.) IJCAR 2008. LNCS LNAI), vol. 5195, pp. 162-170. Springer, Heidelberg 2008
    • (2008) IJCAR 2008. LNCS LNAI , vol.5195 , pp. 162-170
    • Benzmüller, C.E.1    Paulson, L.C.2    Theiss, F.3    Fietzke, A.4
  • 7
    • 24344470890 scopus 로고    scopus 로고
    • Interactive theorem proving and program development - coq'art: The calculus of inductive constructions
    • Texts in Springer
    • Bertot, Y., Casteran, P.: Interactive Theorem Proving and Program Development - Coq'Art: The Calculus of Inductive Constructions. Texts in Theoretical Computer Science. Springer 2004
    • (2004) Theoretical Computer Science
    • Bertot, Y.1    Casteran, P.2
  • 8
    • 80051549826 scopus 로고    scopus 로고
    • On deciding satisfiability by theorem proving with speculative inferences
    • Bonacina, M.P., Lynch, C., de Moura, L.M.: On deciding satisfiability by theorem proving with speculative inferences. J. Autom. Reasoning 472), 161-189 2011
    • (2011) J. Autom. Reasoning , vol.472 , pp. 161-189
    • Bonacina, M.P.1    Lynch, C.2    De Moura, L.M.3
  • 9
    • 84863632508 scopus 로고    scopus 로고
    • Satallax: An automatic higher-order prover
    • Gramlich, B., Miller, D., Sattler, U. eds.Springer, Heidelberg
    • Brown, C.E.: Satallax: An Automatic Higher-Order Prover. In: Gramlich, B., Miller, D., Sattler, U. eds.) IJCAR 2012. LNCS, vol. 7364, pp. 111-117. Springer, Heidelberg 2012
    • (2012) IJCAR 2012. LNCS , vol.7364 , pp. 111-117
    • Brown, C.E.1
  • 12
    • 0345231602 scopus 로고    scopus 로고
    • First order proof problems extracted from an article in the mizar mathematical library
    • Bonacina, M.P., Furbach, U. eds. RISC-Linz Report Series No. 97-50, vol. Johannes Keler Universitát Linz Austria
    • Dahn, I., Wernhard, C.: First order proof problems extracted from an article in the MIZAR Mathematical Library. In: Bonacina, M.P., Furbach, U. eds.) Int. Workshop on First-Order Theorem Proving FTP 1997). RISC-Linz Report Series No. 97-50, vol. 97-50), pp. 58-62. Johannes Kepler Universitát, Linz, Austria 1997
    • (1997) Int. Workshop on First-Order Theorem Proving FTP 1997 , vol.50 , pp. 58-62
    • Dahn, I.1    Wernhard, C.2
  • 14
    • 15544380712 scopus 로고    scopus 로고
    • Common syntax of the dfgschwerpunktprogramm deduction
    • Fakultát für Informatik, Universát Karlsruhe, Karlsruhe, Germany
    • Háhnle, R., Kerber, M., Weidenbach, C.: Common Syntax of the DFGSchwerpunktprogramm Deduction. Technical Report TR 10/96, Fakultát für Informatik, Universát Karlsruhe, Karlsruhe, Germany 1996
    • (1996) Technical Report TR 10/96
    • Háhnle, R.1    Kerber, M.2    Weidenbach, C.3
  • 15
    • 79955003612 scopus 로고    scopus 로고
    • Introduction to the flyspeck project
    • Coquand, T., Lombardi, H., Roy, M.-F. eds. Internationales Begegnungs- und Forschungszentrum für Informatik IBFI), Schloss Dagstuhl, Germany
    • Hales, T.C.: Introduction to the Flyspeck project. In: Coquand, T., Lombardi, H., Roy, M.-F. eds.) Mathematics, Algorithms, Proofs. Dagstuhl Seminar Proceedings, vol. 05021, Internationales Begegnungs- und Forschungszentrum für Informatik IBFI), Schloss Dagstuhl, Germany 2005
    • (2005) Mathematics, Algorithms, Proofs. Dagstuhl Seminar Proceedings , vol.5021
    • Hales, T.C.1
  • 16
    • 84957700828 scopus 로고    scopus 로고
    • HOL light: A tutorial introduction
    • Srivas, M., Camilleri, A. eds. Springer, Heidelberg
    • Harrison, J.: HOL Light: A Tutorial Introduction. In: Srivas, M., Camilleri, A. eds.) FMCAD 1996. LNCS, vol. 1166, pp. 265-269. Springer, Heidelberg 1996
    • (1996) FMCAD 1996. LNCS , vol.1166 , pp. 265-269
    • Harrison, J.1
  • 17
    • 33745644363 scopus 로고
    • On the rules of suppositions
    • Jaskowski, S.: On the rules of suppositions. Studia Logica, 1 1934
    • (1934) Studia Logica , vol.1
    • Jaskowski, S.1
  • 18
    • 38049091964 scopus 로고    scopus 로고
    • Integrating linear arithmetic into superposition calculus
    • Duparc, J., Henzinger, T.A. eds. Springer, Heidelberg
    • Korovin, K., Voronkov, A.: Integrating Linear Arithmetic into Superposition Calculus. In: Duparc, J., Henzinger, T.A. eds.) CSL 2007. LNCS, vol. 4646, pp. 223-237. Springer, Heidelberg 2007
    • (2007) CSL 2007. LNCS , vol.4646 , pp. 223-237
    • Korovin, K.1    Voronkov, A.2
  • 21
    • 9444271076 scopus 로고    scopus 로고
    • Mace4 reference manual and guide
    • Argonne National Laboratory, Argonne, USA
    • McCune, W.W.: Mace4 Reference Manual and Guide. Technical Report ANL/MCS-TM-264, Argonne National Laboratory, Argonne, USA 2003
    • (2003) Technical Report ANL/MCS-TM-264
    • McCune, W.W.1
  • 22
    • 15244350579 scopus 로고    scopus 로고
    • Otter 3.3 reference manual
    • Argonne National Laboratory, Argonne, USA
    • McCune, W.W.: Otter 3.3 Reference Manual. Technical Report ANL/MSC-TM- 263, Argonne National Laboratory, Argonne, USA 2003
    • (2003) Technical Report ANLMSC-TM- 263
    • McCune, W.W.1
  • 23
    • 58549087405 scopus 로고    scopus 로고
    • Lightweight relevance filtering for machine-generated resolution problems
    • Meng, J., Paulson, L.C.: Lightweight relevance filtering for machine-generated resolution problems. J. Applied Logic 71), 41-57 2009
    • (2009) J. Applied Logic , vol.7 , Issue.1 , pp. 41-57
    • Meng, J.1    Paulson, L.C.2
  • 25
    • 0348126394 scopus 로고    scopus 로고
    • Isabelle/hol - a proof assistant for higher-order logic
    • Springer, Heidelberg
    • Nipkow, T., Paulson, L.C., Wenzel, M.T.: Isabelle/HOL - A Proof Assistant for Higher-Order Logic. LNCS, vol. 2283. Springer, Heidelberg 2002
    • (2002) LNCS , vol.2283
    • Nipkow, T.1    Paulson, L.C.2    Wenzel, M.T.3
  • 26
    • 15544368828 scopus 로고    scopus 로고
    • Computing small clause normal forms
    • Elsevier and MIT Press
    • Nonnengart, A., Weidenbach, C.: Computing small clause normal forms. In: Handbook of Automated Reasoning, vol. I, pp. 335-367. Elsevier and MIT Press 2001
    • (2001) Handbook of Automated Reasoning , vol.1 , pp. 335-367
    • Nonnengart, A.1    Weidenbach, C.2
  • 27
    • 30244551599 scopus 로고    scopus 로고
    • Leancop: Lean connection-based theorem proving
    • Otten, J., Bibel, W.: LeanCoP: Lean Connection-Based Theorem Proving. Journal of Symbolic Computation 361-2), 139-161 2003
    • (2003) Journal of Symbolic Computation , vol.361 , Issue.2 , pp. 139-161
    • Otten, J.1    Bibel, W.2
  • 28
    • 79959729624 scopus 로고    scopus 로고
    • SPASS+T
    • Sutcliffe, G., Schmidt, R., Schulz, S. eds
    • Prevosto, V., Waldmann, U.: SPASS+T. In: Sutcliffe, G., Schmidt, R., Schulz, S. eds.) ESCoR 2006. CEUR, vol. 192, pp. 18-33 2006
    • (2006) ESCoR 2006. CEUR , vol.192 , pp. 18-33
    • Prevosto, V.1    Waldmann, U.2
  • 29
    • 0006763226 scopus 로고
    • Automated deduction in von neumann-bernays-godel set theory
    • Quaife, A.: Automated Deduction in von Neumann-Bernays-Godel Set Theory. Journal of Automated Reasoning 81), 91-147 1992
    • (1992) Journal of Automated Reasoning , vol.81 , pp. 91-147
    • Quaife, A.1
  • 32
    • 0036327027 scopus 로고    scopus 로고
    • The design and implementation of vampire
    • Riazanov, A., Voronkov, A.: The Design and Implementation of Vampire. AI Communications 152-3), 91-110 2002
    • (2002) AI Communications , vol.152 , pp. 91-110
    • Riazanov, A.1    Voronkov, A.2
  • 33
    • 0036323940 scopus 로고    scopus 로고
    • E: A brainiac theorem prover
    • Schulz, S.: E: A Brainiac Theorem Prover. AI Communications 152-3), 111-126 2002
    • (2002) AI Communications , vol.152 , pp. 111-126
    • Schulz, S.1
  • 35
    • 35148824106 scopus 로고    scopus 로고
    • Srass - a semantic relevance axiom selection system
    • Pfenning, F. ed. Springer, Heidelberg
    • Sutcliffe, G., Puzis, Y.: SRASS - A Semantic Relevance Axiom Selection System. In: Pfenning, F. ed.) CADE 2007. LNCS LNAI), vol. 4603, pp. 295-310. Springer, Heidelberg 2007
    • (2007) CADE 2007. LNCS LNAI , vol.4603 , pp. 295-310
    • Sutcliffe, G.1    Puzis, Y.2
  • 36
    • 63849210284 scopus 로고    scopus 로고
    • The 4th IJCAR automated theorem proving system competition - CASC-J4
    • Sutcliffe, G.: The 4th IJCAR automated theorem proving system competition - CASC-J4. AI Commun. 221), 59-72 2009
    • (2009) AI Commun , vol.221 , pp. 59-72
    • Sutcliffe, G.1
  • 37
    • 78650810189 scopus 로고    scopus 로고
    • The tptp world - infrastructure for automated reasoning
    • Clarke, E.M., Voronkov, A. eds. Springer, Heidelberg
    • Sutcliffe, G.: The TPTP World - Infrastructure for Automated Reasoning. In: Clarke, E.M., Voronkov, A. eds.) LPAR-16 2010. LNCS, vol. 6355, pp. 1-12. Springer, Heidelberg 2010
    • (2010) LPAR-16 2010. LNCS , vol.6355 , pp. 1-12
    • Sutcliffe, G.1
  • 38
    • 21144440096 scopus 로고    scopus 로고
    • Translating mizar for first order theorem provers
    • Asperti, A., Buchberger, B., Davenport, J.H. eds. Springer, Heidelberg
    • Urban, J.: Translating Mizar for First Order Theorem Provers. In: Asperti, A., Buchberger, B., Davenport, J.H. eds.) MKM 2003. LNCS, vol. 2594, pp. 203-215. Springer, Heidelberg 2003
    • (2003) MKM 2003. LNCS , vol.2594 , pp. 203-215
    • Urban, J.1
  • 39
    • 15544376440 scopus 로고    scopus 로고
    • Mptp - motivation, implementation, first experiments
    • Urban, J.: MPTP - Motivation, Implementation, First Experiments. Journal of Automated Reasoning 333-4), 319-339 2004
    • (2004) Journal of Automated Reasoning , vol.333 , pp. 319-339
    • Urban, J.1
  • 40
    • 33745672083 scopus 로고    scopus 로고
    • Xml-izing mizar: Making semantic processing and Presentation of MML Easy
    • Kohlhase, M. ed. Springer, Heidelberg
    • Urban, J.: XML-izing Mizar: Making Semantic Processing and Presentation of MML Easy. In: Kohlhase, M. ed.) MKM 2005. LNCS LNAI), vol. 3863, pp. 346- 360. Springer, Heidelberg 2006
    • (2006) MKM 2005. LNCS LNAI , vol.3863 , pp. 346-360
    • Urban, J.1
  • 42
    • 33846474906 scopus 로고    scopus 로고
    • MPTP 0.2: Design, implementation, and initial experiments
    • Urban, J.: MPTP 0.2: Design, Implementation, and Initial Experiments. Journal of Automated Reasoning 371-2), 21-43 2007
    • (2007) Journal of Automated Reasoning , vol.371 , pp. 21-43
    • Urban, J.1
  • 43
    • 38149064402 scopus 로고    scopus 로고
    • Atp cross-verification of the mizar mptp challenge problems
    • Dershowitz, N., Voronkov, A. eds. Springer, Heidelberg
    • Urban, J., Sutcliffe, G.: ATP Cross-Verification of the Mizar MPTP Challenge Problems. In: Dershowitz, N., Voronkov, A. eds.) LPAR 2007. LNCS LNAI), vol. 4790, pp. 546-560. Springer, Heidelberg 2007
    • (2007) LPAR 2007. LNCS LNAI , vol.4790 , pp. 546-560
    • Urban, J.1    Sutcliffe, G.2
  • 45
    • 84863609884 scopus 로고    scopus 로고
    • An overview of methods for large-theory automated theorem proving invited paper
    • Höfner, A., McIver, G. eds. CEUR
    • Urban, J.: An overview of methods for large-theory automated theorem proving invited paper). In: Höfner, A., McIver, G. eds.) ATEWorkshop. CEURWorkshop Proceedings, vol. 760, pp. 3-8. CEUR-WS.org 2011
    • (2011) ATEWorkshop. CEURWorkshop Proceedings , vol.760 , pp. 3-8
    • Urban, J.1
  • 46
    • 77954871167 scopus 로고    scopus 로고
    • Awiki for mizar: Motivation, considerations, and initial prototype
    • Autexier, S., Calmet, J., Delahaye, D., Ion, P.D.F., Rideau, L., Rioboo, R., Sexton, A.P. eds. Springer, Heidelberg
    • Urban, J., Alama, J., Rudnicki, P., Geuvers, H.: AWiki for Mizar: Motivation, Considerations, and Initial Prototype. In: Autexier, S., Calmet, J., Delahaye, D., Ion, P.D.F., Rideau, L., Rioboo, R., Sexton, A.P. eds.) AISC 2010. LNCS, vol. 6167, pp. 455-469. Springer, Heidelberg 2010
    • (2010) AISC 2010. LNCS , vol.6167 , pp. 455-469
    • Urban, J.1    Alama, J.2    Rudnicki, P.3    Geuvers, H.4
  • 47
    • 84875991525 scopus 로고    scopus 로고
    • Atp and presentation service for mizar formalizations
    • Urban, J., Rudnicki, P., Sutcliffe, G.: ATP and Presentation Service for Mizar Formalizations. J. Autom. Reasoning 502), 229-241 2013
    • (2013) J. Autom. Reasoning , vol.502 , pp. 229-241
    • Urban, J.1    Rudnicki, P.2    Sutcliffe, G.3
  • 48
    • 53049092451 scopus 로고    scopus 로고
    • Malarea sg1 - machine learner for automated reasoning with semantic guidance
    • Armando, A., Baumgartner, P., Dowek, G. eds. Springer, Heidelberg
    • Urban, J., Sutcliffe, G., Pudlák, P., Vysköcil, J.: MaLARea SG1 - Machine Learner for Automated Reasoning with Semantic Guidance. In: Armando, A., Baumgartner, P., Dowek, G. eds.) IJCAR 2008. LNCS LNAI), vol. 5195, pp. 441-456. Springer, Heidelberg 2008
    • (2008) IJCAR 2008. LNCS LNAI , vol.5195 , pp. 441-456
    • Urban, J.1    Sutcliffe, G.2    Pudlák, P.3    Vysköcil, J.4
  • 49
    • 79959744394 scopus 로고    scopus 로고
    • Malecop machine learning connection prover
    • Brünnler, K., Metcalfe, G. eds.Springer, Heidelberg
    • Urban, J., Vysköcil, J., ?St?epánek, P.: MaLeCoP Machine Learning Connection Prover. In: Brünnler, K., Metcalfe, G. eds.) TABLEAUX 2011. LNCS, vol. 6793, pp. 263-277. Springer, Heidelberg 2011
    • (2011) TABLEAUX 2011. LNCS , vol.6793 , pp. 263-277
    • Urban, J.1    Vysköcil, J.2    Stepánek, P.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.