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"Handbook of Practical Logic and Automated Reasoning," by John R. Harrison, Cambridge University Press, 2009

Freek Wiedijk
2012 Journal of automated reasoning  
The prover from the book implements first order logic, while HOL Light is higher order. In fact the book only briefly mentions higher order logic on page 122.  ...  Almost all interesting proof automation apparently can be presented in the domain of first order logic.  ... 
doi:10.1007/s10817-012-9251-8 fatcat:skyan2eawbchfoqgybnqsdkruu

Deduction Beyond First-Order Logic (Dagstuhl Seminar 17371)

Jasmin Christian Blanchette, Carsten Fuhs, Viorica Sofronie-Stokkermans, Cesare Tinelli, Marc Herbstritt
2018 Dagstuhl Reports  
Other practical problems need a mixture of first-order proof search and some more advanced reasoning (for instance, about higher-order formulas), or simply higher-level reasoning steps.  ...  Much research in the past two decades was dedicated to automating first-order logic with equality. However, applications often need reasoning beyond this logic.  ...  We discussed different abstractions and refinement strategies for reasoning with large first-order theories.  ... 
doi:10.4230/dagrep.7.9.26 dblp:journals/dagstuhl-reports/BlanchetteFST17 fatcat:yfc3wk2fwngc3i2dmjwrz3gsgi

Page 1973 of Mathematical Reviews Vol. , Issue 2001C [page]

2001 Mathematical Reviews  
“In this paper, we exemplify the methods and proof- and model- theoretic tools needed for extending first-order automated theo- rem proving to higher-order logic.  ...  .” 2001¢:68114 68T15 03B35 Kohlhase, Michael (D-SAAR-I; Saarbriicken) Higher-order automated theorem proving.  ... 

Automation of Higher-Order Logic [chapter]

Christoph Benzmüller, Dale Miller
2014 Handbook of the History of Logic  
We thank Chad Brown for sharing notes that he has written related to the material in this chapter.  ...  The first author has been supported by the German Research Foundation under Heisenberg grant BE2501/9-1 and the second author has been supported by the ERC Advanced Grant ProofCert.  ...  In the deduction-modulo approach to theorem proving (Dowek et al., 2003) , a first-order presentation of (intensional) higher-order logic can be exploited to automate higher-order reasoning .  ... 
doi:10.1016/b978-0-444-51624-4.50005-8 fatcat:jfcztdvymjfujg3bzb2rq2qyzy

Formalization, Mechanization and Automation of Gödel's Proof of God's Existence [article]

Christoph Benzmüller, Bruno Woltzenlogel Paleo
2013 arXiv   pre-print
G\"odel's ontological proof has been analysed for the first-time with an unprecedent degree of detail and formality with the help of higher-order theorem provers.  ...  A formalization using the Isabelle proof assistant, where the theorems (and some additional lemmata) have been automated with Sledgehammer and Metis.  ...  This work attests the maturity of contemporary interactive and automated deduction tools for classical higher-order logic and demonstrates the elegance and practical relevance of the embeddings-based approach  ... 
arXiv:1308.4526v4 fatcat:cgfnwih4vfg37gqdqvw635mvim

Page 1604 of Mathematical Reviews Vol. , Issue 92c [page]

1992 Mathematical Reviews  
Summary: “A technique for establishing completeness results for theorem-proving systems in first-order logic with equality is pre- sented.  ...  Summary: “The combination of higher-order and first-order unifi- cation algorithms is studied.  ... 

Progress in the Development of Automated Theorem Proving for Higher-Order Logic [chapter]

Geoff Sutcliffe, Christoph Benzmüller, Chad E. Brown, Frank Theiss
2009 Lecture Notes in Computer Science  
The Thousands of Problems for Theorem Provers (TPTP) problem library is the basis of a well established infrastructure supporting research, development, and deployment of first-order Automated Theorem  ...  Motivation and History There is a well established infrastructure that supports research, development, and deployment of first-order Automated Theorem Proving (ATP) systems, stemming from the Thousands  ...  Thanks to Jasmin Blanchette for explaining how to implement IsabelleM. Thanks to Andrei Tchaltsev and Alexandre Riazanov for developing the first-order parts of the Java parser for the TPTP language.  ... 
doi:10.1007/978-3-642-02959-2_8 fatcat:osm5sbcmnbg6nn3cdwqgunwkle

JProver: Integrating Connection-Based Theorem Proving into Interactive Proof Assistants [chapter]

Stephan Schmitt, Lori Lorigo, Christoph Kreitz, Aleksey Nogin
2001 Lecture Notes in Computer Science  
-Proof planning for induction / first-order logic (HOL+CLAM / OMEGA+OTTER) -Decision procedures, e.g. for fragments of arithmetic (HOL, Nuprl, STeP) -Automatic theorem provers for first-order logics  ...  (HOL, Nuprl) • JProver: Constructive logics -Complete theorem prover for first-order intuitionistic logic -Modular interface for connecting to interactive proof assistants -Integrated into Nuprl / MetaPRL  ... 
doi:10.1007/3-540-45744-5_34 fatcat:3bm75w7mbnbefd5zb4safxl5bq

Integrating Automated and Interactive Theorem Proving [chapter]

Ahrendt, Beckert, Hähnle, Menzel, Reif, Schellhorn, Schmitt
1998 Applied Logic Series  
Automated Theorem Prover) is an automated tableau prover for full first-order logic with equality.  ...  The first is a combination of the higher-order logic proof checker LAMBDA with the automatic first-order logic prover SEDUCT.  ... 
doi:10.1007/978-94-017-0435-9_4 fatcat:nsfxar65jbhybcrsdvi2stys6u

An Automated Theorem Proving in First-Order Predicate Calculus using Resolution

Moko Anasuodei, James Godbless Tamaraebi, Federal University Otuoke
2020 International Journal of Engineering Research and  
The project's focus was on the design and implementation of a program for automated theorem proving in first-order logic using the resolution proof procedure for first-order logic.  ...  A key concern of Automated Theorem Proving (ATP) research is the development and use of systems that derives conclusions following inevitably from facts.  ...  ACKNOWLEDGMENT All gratitude goes to God almighty for his infinite provisions, guidance and inspiration.  ... 
doi:10.17577/ijertv9is020301 fatcat:n27iauebrjeuzlvldemztsj3hm

Foreword to the Special Issue on Automated Reasoning

Pascal Fontaine, Cezary Kaliszyk, Stephan Schulz, Josef Urban, Pascal Fontaine, Cezary Kaliszyk, Stephan Schulz, Josef Urban
2018 AI Communications  
More specifically, some suggested topics were: • Automated reasoning in propositional, first-order, higher-order and non-classical logics • AI and big-data methods in theorem proving and mathematics •  ...  , instantiation-based, rewriting, logical frameworks, etc) • Automated reasoning tools for all kinds of practical problems and applications • Methods for large-scale computer understanding of mathematics  ...  More specifically, some suggested topics were: • Automated reasoning in propositional, first-order, higher-order and non-classical logics • AI and big-data methods in theorem proving and mathematics •  ... 
doi:10.3233/aic-180765 fatcat:7shttduixbfj3nwno4g5z7yxeu

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

Comparison of Two Theorem Provers: Isabelle/HOL and Coq [article]

Artem Yushkovskiy
2018 arXiv   pre-print
time, it gave rise to rather practical areas of logic, such as the theory of automated theorem proving.  ...  This paper compares two widespread tools for automated theorem proving, Isabelle/HOL and Coq, with respect to expressiveness, limitations and usability.  ...  Stavros Tripakis for letting me dive into the exciting world of Logic, for providing feedback on my paper at all stages of the work, for answering all my countless questions and supporting me.  ... 
arXiv:1808.09701v2 fatcat:ffesxt4esffgjottsxmwjykjri

The Imandra Automated Reasoning System (System Description) [chapter]

Grant Passmore, Simon Cruanes, Denis Ignatovich, Dave Aitken, Matt Bray, Elijah Kagan, Kostya Kanishev, Ewen Maclean, Nicola Mometto
2020 Lecture Notes in Computer Science  
, and interactive proof assistants for typed higher-order logics.  ...  multisorted first-order logic with theories, including arithmetic and datatypes.  ...  Logic Imandra's logic is built on a mechanized formal semantics for a pure, higher-order subset of OCaml.  ... 
doi:10.1007/978-3-030-51054-1_30 fatcat:rbl5k3rktrcmdl5cl3xhw3nxxu

The Imandra Automated Reasoning System (system description) [article]

Grant Olney Passmore, Simon Cruanes, Denis Ignatovich, Dave Aitken, Matt Bray, Elijah Kagan, Kostya Kanishev, Ewen Maclean, Nicola Mometto
2020 arXiv   pre-print
, and interactive proof assistants for typed higher-order logics.  ...  multi-sorted first-order logic with theories, including arithmetic and datatypes.  ...  typed higher-order logics [4, 5, 7, 8] .  ... 
arXiv:2004.10263v1 fatcat:qpyc56r67jgdxa573iz6ui7gkm
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