diff --git a/thys/GoedelGod/ROOT b/thys/GoedelGod/ROOT --- a/thys/GoedelGod/ROOT +++ b/thys/GoedelGod/ROOT @@ -1,7 +1,8 @@ chapter AFP session "GoedelGod" (AFP) = "HOL" + options [timeout = 600] theories GoedelGod document_files "root.tex" + "root.bib" diff --git a/thys/GoedelGod/document/root.bib b/thys/GoedelGod/document/root.bib new file mode 100644 --- /dev/null +++ b/thys/GoedelGod/document/root.bib @@ -0,0 +1,2167 @@ +@article{J52, + Author = {Christoph Benzm\"uller and David Fuenmayor}, + Journal = {Bulletin of the Section of Logic}, + Publisher = {Department of Logic, University of Lodz}, + Keywords = {own, Ontological Argument, Computational + Metaphysics, Higher Order Logic, Semantic Embedding, + Modal Logics, Automated Reasoning, Ontology + Reasoning}, + Title = {Computer-supported Analysis of Positive Properties, Ultrafilters and Modal Collapse in Variants of {G\"odel's} Ontological Argument}, + OPTUrl = {https://czasopisma.uni.lodz.pl/bulletin/}, + Year = 2020, + Volume = {49}, + Number = {2}, + Doi = {10.18778/0138-0680.2020.08}, + OPTAddendum = {Preprint: \url{https://www.researchgate.net/publication/336742445}}, + Pages = {127-148}, +} + +@InProceedings{C85, + Keywords = {own, Ontological Argument, Computational + Metaphysics, Higher Order Logic, Semantic Embedding, + Modal Logics, Automated Reasoning, Ontology + Reasoning}, + title = {{A (Simplified) Supreme Being Necessarily Exists, says the Computer: Computationally Explored Variants of Gödel's Ontological Argument}}, + author = {Benzmüller, Christoph}, + booktitle = {{Proceedings of the 17th International Conference on Principles of Knowledge Representation and Reasoning, KR 2020}}, + pages = {779--789}, + year = {2020}, + month = {9}, + doi = {10.24963/kr.2020/80}, + url = {https://doi.org/10.24963/kr.2020/80}, + publisher = {{IJCAI} organization}, +} + +@article{J48, +Author = {Benzm{\"u}ller, Christoph and Parent, Xavier and van + der Torre, Leendert}, + Keywords = {own, Normative Reasoning, Deontic Logic, Machine Ethics, Formal Methods, Automated Reasoning, ProoF Assistants, Explainable AI}, +Journal = {Artificial Intelligence (accepted for publication)}, +Publisher = {Elsevier}, +Title = {Designing Normative Theories for Ethical and Legal Reasoning: + LogiKEy Framework, Methodology, and Tool Support}, +Year = 2020, +Pages = {1--50}, +Addendum = {Preprint: \url{https://www.researchgate.net/publication/331986665}}, +} + + +@InCollection{odifreddi00:_ultraf_dictat_gods, + author = {Piergiorgio Odifreddi}, + title = {Ultrafilters, Dictators, and Gods}, + booktitle = {Finite Versus Infinite. Discrete Mathematics and Theoretical Computer Science}, + publisher = {Springer, London}, + year = 2000, + editor = {Cristian Calude and Gheorghe Paun}, + pages = {239-245}} + +@book{1965proslogion, + title={Proslogion}, + author={Charlesworth, M.J.}, + lccn=65005321, + url={https://books.google.lu/books?id=TtFDAQAAMAAJ}, + year=1965, + publisher={Clarendon Press} +} + +@Article{bjoerdal18, + author = {Frode Alfson Bj{\o}rdal}, + title = {All Properties are Divine or God Exists -- The Sacred Thesis and its Ontological Argument}, + journal = {Logic and Logical Philosophy}, + year = 2018, + volume = 27, + number = 3} + +@Unpublished{Swietorzecka19, + author = {Kordula \'Swi\c etorzecka}, + title = {Identity or equality of {Gödelian} God}, + note = {Draft paper, private communication}, + month = {May}, + year = 2019} + +@article{J35, + Author = {David Fuenmayor and Christoph Benzm{\"u}ller}, + Journal = {Archive of Formal Proofs}, + Keywords = {own, Automated Reasoning, Interactive Proof, + Ontology Reasoning, Higher Order Logic, + Computational Metaphysics}, + Note = {Note: verified data publication}, + Title = {{Types, Tableaus and G{\"o}del's God in + Isabelle/HOL}}, + Url = + {http://afp.sourceforge.net/entries/Types_Tableaus_and_Goedels_God.shtml}, + Year = 2017, + Pages = {1--34}, +} + + + +@inproceedings{R74, + Author = {Benzm{\"u}ller, Christoph}, + Title = {Computational Metaphysics: New Insights on {G{\"o}del's} Ontological Argument and Modal Collapse}, + Editor = {Sr\'{e}cko Kova\v{c} and Kordula Swietorzecka}, + Booktitle = {Formal Methods and Science in Philosophy III, Informal Proceedings}, + Year = 2019, + Pages = {3--4}, + Address = {Dubrovnik, Croatia}, + Url = {http://christoph-benzmueller.de/papers/2019-FMSPh-Proceedings.pdf}, +} + +@incollection{Kovacs2012, + year = 2012, + editor = {Miroslaw Szatkowski}, + pages = {50--323}, + author = {Sr\'{e}cko Kova\v{c}}, + booktitle = {Ontological Proofs Today}, + publisher = {Ontos Verlag}, + title = {Modal Collapse in {G\"odel's} Ontological Proof} +} + +@InCollection{sep-logic-modal, + author = {Garson, James}, + title = {Modal Logic}, + booktitle = {The Stanford Encyclopedia of Philosophy}, + editor = {Edward N. Zalta}, + howpublished = {\url{https://plato.stanford.edu/archives/fall2018/entries/logic-modal/}}, + year = {2018}, + edition = {Fall 2018}, + publisher = {Metaphysics Research Lab, Stanford University} +} + +@article{J47, +Author = {Kirchner, Daniel and Benzm{\"u}ller, Christoph and Zalta, Edward N.}, +Journal = {Open Philosophy}, +Title = {Computer Science and Metaphysics: A Cross-Fertilization}, +Editor = {Patrick Grim}, +Year = 2019, +Volume = 2, +Issue = 1, +Pages = {230–251}, +Doi = {10.1515/opphil-2019-0015}, +OPTNote = {Preprint: \url{http://doi.org/10.13140/RG.2.2.25229.18403}}, +OPTUrl = {https://arxiv.org/abs/1905.00787}, +} + +@InCollection{J43, + author = {Benzm\"uller, Christoph and Andrews, Peter}, + title = {Church's Type Theory}, + booktitle = {The Stanford Encyclopedia of Philosophy}, + editor = {Edward N. Zalta}, + howpublished = {\url{https://plato.stanford.edu/entries/type-theory-church/}}, + year = 2019, + edition = {Summer 2019}, + OPTpages = {pp.~1--62 (in pdf version)}, + publisher = {Metaphysics Research Lab, Stanford University}, + url = {https://plato.stanford.edu/entries/type-theory-church/}, +} + +@InCollection{Lowe2013, + author= {Lowe, Edward Jonathan}, + editor= {Moreland, J. P. and Sweis, K. A. and Meister, C. V.}, + title= {A Modal Version of the Ontological Argument}, + booktitle = {Debating Christian Theism}, + publisher = {Oxford University Press}, + year = {2013}, + chapter= {4}, + pages= {61--71}, + isbn = {9780199981434} +} + +@article{zalta1999, + Author = {Edward N. Zalta}, + Title = {{Natural Numbers and Natural Cardinals as Abstract Objects: +A Partial Reconstruction of {Frege's} Grundgesetze in Object +Theory}}, + Journal = {Journal of Philosophical Logic}, + volume = {28}, + number = {6}, + year = {1999}, + pages = {619--660} +} + +@article{zalta1993, + Author = {Edward N. Zalta}, + Title = {{Twenty-Five Basic Theorems in Situation and World Theory}}, + Journal = {Journal of Philosophical Logic}, + volume = {22}, + number = {4}, + year = {1993}, + pages = {385--428} +} + +@article{OppenheimerZalta1991, + author = {Paul E. Oppenheimer and Edward N. Zalta}, + title = {On the Logic of the Ontological Argument}, + volume = {5}, + journal = {Philosophical Perspectives}, + year = {1991}, + pages = {509--529} +} + +@article{PelletierZalta, + Author = {Francis J. Pelletier and Edward N. Zalta}, + Title = {{How to Say Goodbye to the Third Man}}, + Journal = {No\^us}, + volume = {34}, + number = {2}, + year = {2000}, + pages = {165--202} +} + + + +@inproceedings{C74, + Author = {Christoph Benzm{\"u}ller and Fuenmayor, David}, + Booktitle = {Mathematics and Reality, Proceedings of the 11th All India Students' Conference on Science \& Spiritual Quest (AISSQ), 6-7 October, 2018, IIT Bhubaneswar, Bhubaneswar, India}, + Editor = {Gosh, Sudipto and Uppalari, Ramgopal and Rao, K. Vasudeva and Agarwal, Varun and Sharma, Sushant}, + Keywords = {own, Ontological Argument, Computational Metaphysics, Higher Order Logic, Semantic Embedding, Modal Logics, Automated Reasoning, Ontology Reasoning}, + Publisher = {The Bhaktivedanta Institute, Kolkata, \url{www.binstitute.org}}, + Title = {Can Computers Help to Sharpen our Understanding of Ontological Arguments?}, + Url = {http://christoph-benzmueller.de/papers/C74.pdf}, + pages = {195-226}, + isbn = {81-89635-31-X}, + Comment = {DOI (preprint): 10.13140/RG.2.2.31921.84323}, + Doi = {10.13140/RG.2.2.31921.84323}, + Year = 2018, +} + +@inproceedings{HuffmanK13, + author = {Brian Huffman and + Ondrej Kuncar}, + title = {Lifting and Transfer: {A} Modular Design for Quotients in {Isabelle/HOL}}, + booktitle = {Certified Programs and Proofs --- Third International Conference, {CPP} + 2013, Melbourne, VIC, Australia, December 11-13, 2013, Proceedings}, + pages = {131--146}, + year = {2013}, + editor = {Georges Gonthier and + Michael Norrish}, + series = {Lecture Notes in Computer Science}, + volume = {8307}, + publisher = {Springer}, +} + + +@inproceedings{C70, + Author = {Alexander Steen and Christoph Benzm{\"u}ller}, + Booktitle = {Automated Reasoning. IJCAR 2018}, + Editor = {Didier Galmiche and Stephan Schulz and Roberto Sebastiani}, + Keywords = {own, Higher Order Logic, Automated Reasoning, LEO Prover}, + Publisher = {Springer, Cham}, + Series = {Lecture Notes in Computer Science}, + Title = {The Higher-Order Prover {Leo-III}}, + Url = {http://christoph-benzmueller.de/papers/C70.pdf}, + volume = 10900, + pages = {108-116}, + doi = {10.1007/978-3-319-94205-6_8}, + isbn = {978-3-319-94204-9}, + Year = 2018, +} + +@article{J30, + Author = {Christoph Benzm{\"u}ller and Nik Sultana and Lawrence C. Paulson and Frank Thei{\ss}}, + Doi = {10.1007/s10817-015-9348-y}, + Journal = {Journal of Automated Reasoning}, + Keywords = {own, Automated Reasoning, Interactive Proof, Ontology Reasoning, LEO Prover, Higher Order Logic, DFG-2501-Selected}, + Number = 4, + Pages = {389-404}, + Title = {The Higher-Order Prover {LEO-II}}, + Url = {http://christoph-benzmueller.de/papers/J30.pdf}, + Volume = 55, + Year = 2015, +} + +@inproceedings{Nunchaku, + author = {Cruanes, Simon and + Blanchette, Jasmin C.}, + title = {Extending Nunchaku to Dependent Type Theory}, + booktitle = {Proceedings First International Workshop on Hammers for Type Theories, + HaTT@IJCAR 2016, Coimbra, Portugal, July 1, 2016.}, + pages = {3--12}, + year = {2016}, + doi = {10.4204/EPTCS.210.3}, + series = {{EPTCS}}, + volume = {210}, + url = {https://doi.org/10.4204/EPTCS.210}, +} + + +@misc{W62, + Author = {Benzm\"uller, Christoph and Farjami, Ali and Parent, Xavier}, + OPTBooktitle = {MIREL 2018}, + OPTEditor = {}, + Keywords = {own, Dyadic Deontic Logic E, Preference Models, Higher Order Logic, Semantic Embedding, Automated Reasoning}, + Note = {MIREL 2018 workshop on MIning and REasoning with Legal texts; available online at \url{http://orbilu.uni.lu/handle/10993/37014}}, + Url = {http://orbilu.uni.lu/handle/10993/37014}, + Title = {Aqvist's Dyadic Deontic Logic {E} in {HOL}}, + Year = 2018, +} + + +@misc{W63, + Author = {Farjami, Ali and Meder, Paul and Parent, Xavier and Benzm\"uller, Christoph}, + OPTBooktitle = {MIREL 2018}, + OPTEditor = {}, + Keywords = {own, Input/Output Logic, Higher Order Logic, Semantic Embedding, Automated Reasoning, General Data Protection Regulation}, + Note = {MIREL 2018 workshop on MIning and REasoning with Legal texts; available online at \url{http://orbilu.uni.lu/handle/10993/37013}}, + Title = { {I/O} Logic in {HOL}}, + Year = 2018, +} + +@inproceedings{C71, + Author = {Benzm{\"u}ller, Christoph and Farjami, Ali and Parent, Xavier}, + Booktitle = {Deontic Logic and Normative Systems --- 14th International Conference, DEON 2018, Utrecht, The Netherlands, 3-6 July, 2018}, + Editor = {Jan Broersen and Cleo Condoravdi and Shyam Nair and Gabriella Pigozzi}, + Keywords = {own, Higher Order Logic, Deontic Logic, + Automated Reasoning, Universal Reasoning}, + Publisher = {College Publications}, + pages = {33-50}, + OPTSeries = {}, + Title = {A Dyadic Deontic Logic in {HOL}}, + Url = {http://christoph-benzmueller.de/papers/C71.pdf}, + OPTVolume = 9706, + Year = 2018, + isbn = {978-1-84890-278-7}, + note = {(John-Jules Meyer Best Paper Award)}, +} + +@article{J41, + author = {Christoph Benzm{\"u}ller}, + title = {Universal (Meta-)Logical Reasoning: Recent Successes}, + journal = {Science of Computer Programming}, + year = 2019, + volume = 172, + month = {3}, + pages = {48-62}, + OPTnote = {DOI (preprint): \url{http://dx.doi.org/10.13140/RG.2.2.11039.61609/2}}, + doi = {10.1016/j.scico.2018.10.008}, + url = {https://doi.org/10.1016/j.scico.2018.10.008} +} + + +@inproceedings{C47, + Address = {Berlin, Germany}, + Author = {Christoph Benzm{\"u}ller and Maximilian Claus and Nik Sultana}, + Booktitle = {PxTP 2015}, + Comment = {slides}, + Doi = {10.4204/EPTCS.186.5}, + Editor = {Cezary Kaliszyk and Andrei Paskevich}, + Issn = {2075-2180}, + Keywords = {own, Automated Reasoning, Interactive Proof, Ontology Reasoning, LEO Prover, Higher Order Logic}, + Pages = {27-41}, + Publisher = {EPTCS}, + Title = {Systematic Verification of the Modal Logic Cube in {Isabelle/HOL}}, + Url = {http://christoph-benzmueller.de/papers/C47.pdf}, + Volume = 186, + Year = 2015, +} + +@inproceedings{C72, + Author = {Benzm{\"u}ller, Christoph}, + Booktitle = {Deontic Logic and Normative Systems --- 14th International Conference, DEON 2018, Utrecht, The Netherlands, 3-6 July, 2018}, + Editor = {Jan Broersen and Cleo Condoravdi and Shyam Nair and Gabriella Pigozzi}, + Keywords = {own, Higher Order Logic, Deontic Logic, + Automated Reasoning, Universal Reasoning}, + Publisher = {College Publications}, + pages = 7, + Title = {A Flexible Infrastructure for Normative Reasoning (invited keynote abstract)}, + Url = {http://christoph-benzmueller.de/papers/C72.pdf}, + Volume = 9706, + Year = 2018, + isbn = {978-1-84890-278-7}, +} + +@inproceedings{C44, + Author = {Christoph Benzm{\"{u}}ller and Woltzenlogel Paleo, Bruno}, + Booktitle = {Computer Science --- Theory and Applications --- 10th International Computer Science Symposium in Russia, {CSR} 2015, Listvyanka, Russia, July 13-17, 2015, Proceedings}, + Doi = {10.1007/978-3-319-20297-6_25}, + Editor = {Lev D. Beklemishev and Daniil V. Musatov}, + Keywords = {own, Automated Reasoning, Interactive Proof, Ontology Reasoning, LEO Prover, Higher Order Logic, Computational Metaphysics}, + Pages = {398--411}, + Publisher = {Springer}, + Series = {Lecture Notes in Computer Science}, + Title = {Interacting with Modal Logics in the {Coq} Proof Assistant}, + Url = {http://christoph-benzmueller.de/papers/C44.pdf}, + Volume = 9139, + Year = 2015 +} + +@article{B17, + Author = {David Fuenmayor and Christoph Benzm\"uller}, + Journal = {Journal of Applied Logic - IfCoLoG Journal of Logics + and their Applications (special issue on Formal + Approaches to the Ontological Argument)}, + Volume = 5, + Number = 7, + Pages = {1567-1603}, + Editors = {Silvestre, Ricardo and B\'{e}ziau, Jean-Yves}, + Keywords = {own, Automated Reasoning, Interactive Proof, + Ontology Reasoning, Higher Order Logic, + Computational Metaphysics}, + Title = {A Case Study On Computational Hermeneutics: + {E.~J.~Lowe's} Modal Ontological Argument}, + Year = 2018, +} + + + +@book{lambek86:_introd_higher_order_categ_logic, + author = {Lambek, J. and Scott, P.J.}, + publisher = {Cambridge University Press}, + title = {Introduction to Higher Order Categorical Logic}, + year = {1986}, +} + +@book{jacobs99:_categ_logic_type_theor, + author = {B. Jacobs}, + publisher = {North Holland, Elsevier}, + series = {Studies in Logic and the Foundations of Mathematics}, + title = {Categorical Logic and Type Theory}, + volume = {141}, + year = {1999}, +} + +@book{andreka17:_univer_algeb_logic, + author = {Andreka, H. and N\'emeti, I. and Sain, I.}, + publisher = {Birkh\"auser Basel}, + series = {Studies in Universal Logic}, + title = {Universal Algebraic Logic}, + year = {2017}, +} + +@article{moss99:_coalg_logic, + author = {L.S. Moss}, + journal = {Annals of Pure and Applied Logic}, + number = {1-3}, + pages = {277-317}, + title = {Coalgebraic Logic}, + volume = {96}, + year = {1999}, +} + +@article{rutten00:_univer, + author = {J.J.M.M. Rutten}, + journal = {Theoretical Computer Science}, + number = {1}, + pages = {3-80}, + title = {Universal coalgebra: a theory of systems}, + volume = {249}, + year = {2000}, +} + +@inproceedings{DBLP:conf/icfem/GuttmannSW11, + author = {Walter Guttmann and Georg Struth and Tjark Weber}, + booktitle = {Proc. of ICFEM 2011}, + editor = {Shengchao Qin and Zongyan Qiu}, + pages = {617-632}, + publisher = {Springer}, + series = {Lecture Notes in Computer Science}, + title = {Automating Algebraic Methods in {Isabelle}}, + volume = {6991}, + year = {2011}, +} + +@article{foster15:_fine_struc_regul_algeb, + author = {S. Foster and G. Struth}, + journal = {Journal of Automated Reasoning}, + number = {2}, + pages = {165-197}, + title = {On the Fine-Structure of Regular Algebra}, + volume = {54}, + year = {2015}, +} + +@article{Church40, + author = {Alonzo Church}, + journal = {Journal of Symbolic Logic}, + pages = {56--68}, + title = {A Formulation of the Simple Theory of Types}, + volume = {5}, + year = {1940}, +} + +@InCollection{AndrewsSEP, + author = {Andrews, Peter}, + title = {Church's Type Theory}, + booktitle = {The Stanford Encyclopedia of Philosophy}, + editor = {Edward N. Zalta}, + howpublished = {\url{https://plato.stanford.edu/archives/sum2018/entries/type-theory-church/}}, + year = {2018}, + edition = {Summer 2018}, + publisher = {Metaphysics Research Lab, Stanford University} +} + +@incollection{B5, + author = {Christoph Benzm{\"u}ller and Dale Miller}, + booktitle = {Handbook of the History of Logic, Volume 9 --- + Computational Logic}, + editor = {Gabbay, Dov M. and Siekmann, J\"org H. and + Woods, John}, + pages = {215-254}, + publisher = {North Holland, Elsevier}, + title = {Automation of Higher-Order Logic}, + year = {2014}, + doi = {10.1016/B978-0-444-51624-4.50005-8}, + isbn = {978-0-444-51624-4}, + OPTurl = {http://christoph-benzmueller.de/papers/B5.pdf}, +} + +@article{J23, + author = {Christoph Benzm{\"u}ller and Lawrence Paulson}, + journal = {Logica Universalis}, + number = {1}, + pages = {7-20}, + title = {Quantified Multimodal Logics in Simple Type Theory}, + volume = {7}, + year = {2013}, + doi = {10.1007/s11787-012-0052-y}, + OPTurl = {http://christoph-benzmueller.de/papers/J23.pdf}, +} + +@book{frege79:_begrif, + author = {Gottlob Frege}, + publisher = {Halle}, + title = {Begriffsschrift. Eine der arithmetischen + nachgebildete Formelsprache des reinen Denkens}, + year = {1879}, +} + +@article{J6, + author = {Christoph Benzm{\"u}ller and Chad Brown and + Michael Kohlhase}, + journal = {Journal of Symbolic Logic}, + number = {4}, + pages = {1027-1088}, + title = {Higher-Order Semantics and Extensionality}, + volume = {69}, + year = {2004}, + doi = {10.2178/jsl/1102022211}, + OPTurl = {http://christoph-benzmueller.de/papers/J6.pdf}, +} + +@book{andrews2002introduction, + author = {Peter B Andrews}, + publisher = {Springer}, + series = {Applied Logic Series}, + title = {An Introduction to Mathematical Logic and Type + Theory: To Truth Through Proof}, + volume = {27}, + year = {2002}, +} + +@book{Isabelle2, + author = {Nipkow, Tobias and Paulson, Lawrence C. and + Wenzel, Makarius}, + volume = {2283}, + publisher = {Springer}, + series = {LNCS}, + title = {{{Isabelle/HOL: A Proof Assistant for Higher-Order + Logic}}}, + year = {2002}, +} + +@book{Coq, + author = {Bertot, Y. and Casteran, P.}, + publisher = {Springer}, + title = {{Interactive Theorem Proving and Program + Development}}, + year = {2004}, +} + + + + +@inproceedings{Satallax, + author = {Chad E. Brown}, + booktitle = {Automated Reasoning --- 6th International Joint + Conference, {IJCAR} 2012, Manchester, UK, June 26-29, + 2012. Proceedings}, + editor = {Bernhard Gramlich and Dale Miller and Uli Sattler}, + pages = {111--117}, + publisher = {Springer}, + series = {Lecture Notes in Computer Science}, + title = {Satallax: An Automatic Higher-Order Prover}, + volume = {7364}, + year = {2012}, + isbn = {978-3-642-31364-6}, +} + +@inproceedings{Nitpick, + author = {Jasmin C. Blanchette and Tobias Nipkow}, + booktitle = {Interactive Theorem Proving --- {ITP} 2010}, + editor = {M.~Kaufmann and L.~C.~Paulson}, + pages = {131--146}, + publisher = {Springer}, + series = {LNCS}, + title = {Nitpick: {A} Counterexample Generator for + Higher-Order Logic Based on a Relational Model + Finder}, + volume = {6172}, + year = {2010}, +} + +@article{Sledgehammer, + author = {Blanchette, Jasmin C. and B\"ohme, Sascha and + Paulson, Lawrence C.}, + journal = {Journal of Automated Reasoning}, + number = {1}, + pages = {109-128}, + publisher = {Springer}, + title = {Extending {Sledgehammer} with {SMT} Solvers}, + volume = {51}, + year = {2013}, + issn = {0168-7433}, + language = {English}, +} + +@inproceedings{E, + author = {Stephan Schulz}, + booktitle = {Logic for Programming, Artificial Intelligence, and + Reasoning -- 19th International Conference, LPAR-19, + Stellenbosch, South Africa, December 14-19, 2013. + Proceedings}, + editor = {Kenneth L. McMillan and Aart Middeldorp and + Andrei Voronkov}, + pages = {735--743}, + publisher = {Springer}, + series = {Lecture Notes in Computer Science}, + title = {System Description: {E} 1.8}, + volume = {8312}, + year = {2013}, + doi = {10.1007/978-3-642-45221-5}, + isbn = {978-3-642-45220-8}, + OPTurl = {http://dx.doi.org/10.1007/978-3-642-45221-5}, +} + +@inproceedings{CVC4, + author = {Morgan Deters and Andrew Reynolds and Tim King and + Clark W. Barrett and Cesare Tinelli}, + booktitle = {Formal Methods in Computer-Aided Design, {FMCAD} + 2014, Lausanne, Switzerland, October 21-24, 2014}, + editor = {Koen Claessen and Viktor Kuncak}, + pages = {7}, + publisher = {{IEEE}}, + title = {A tour of {CVC4:} {How} it works, and how to use it}, + year = {2014}, + isbn = {978-0-9835678-4-4}, +} + +@InProceedings{Z3, +author="de Moura, Leonardo +and Bj{\o}rner, Nikolaj", +editor="Ramakrishnan, C. R. +and Rehof, Jakob", +title="Z3: An Efficient SMT Solver", +booktitle="Tools and Algorithms for the Construction and Analysis of Systems", +year="2008", +publisher="Springer Berlin Heidelberg", +address="Berlin, Heidelberg", +pages="337--340", +abstract="Satisfiability Modulo Theories (SMT) problem is a decision problem for logical first order formulas with respect to combinations of background theories such as: arithmetic, bit-vectors, arrays, and uninterpreted functions. Z3 is a new and efficient SMT Solver freely available from Microsoft Research. It is used in various software verification and analysis applications.", +isbn="978-3-540-78800-3" +} + +@inproceedings{Spass, + author = {Jasmin C. Blanchette and Andrei Popescu and + Daniel Wand and Christoph Weidenbach}, + booktitle = {Interactive Theorem Proving --- Third International + Conference, {ITP} F2012, Princeton, NJ, USA, August + 13-15, 2012. Proceedings}, + editor = {Lennart Beringer and Amy P. Felty}, + pages = {345--360}, + publisher = {Springer}, + series = {Lecture Notes in Computer Science}, + title = {{More {SPASS} with Isabelle -- Superposition with + Hard Sorts and Configurable Simplification}}, + volume = {7406}, + year = {2012}, + isbn = {978-3-642-32346-1}, +} + +@inproceedings{Vampire, + author = {Laura Kov{\'{a}}cs and Andrei Voronkov}, + booktitle = {Computer Aided Verification - 25th International + Conference, {CAV} 2013, Saint Petersburg, Russia, + July 13-19, 2013. Proceedings}, + editor = {Natasha Sharygina and Helmut Veith}, + pages = {1--35}, + publisher = {Springer}, + series = {Lecture Notes in Computer Science}, + title = {{First-Order Theorem Proving and Vampire}}, + volume = {8044}, + year = {2013}, + isbn = {978-3-642-39798-1}, +} + +@phdthesis{BaldoniPhD, + author = {Matteo Baldoni}, + note = {(Revised version dated July 9, 2003)}, + school = {Dipartimento di Informatica, Universit\'a degli Studi + di Torino}, + title = {Normal Multimodal Logics: Automatic Deduction and + Logic Programming Extension}, + year = {2003}, +} + +@book{fagin04:_reason_about_knowl, + author = {Ronald Fagin and Halpern, Joseph Y. and Yoram Moses and + Moshe Vardi}, + publisher = {The MIT Press}, + title = {Reasoning About Knowledge}, + year = {2004}, +} + +@incollection{DBLP:books/el/RV01/OhlbachNRG01, + author = {Ohlbach, H.J. and Nonnengart, A. and de Rijke, M. and + Gabbay, D.M.}, + booktitle = {Handbook of Automated Reasoning (in 2 volumes)}, + editor = {J.A. Robinson and A. Voronkov}, + pages = {1403--1486}, + publisher = {Elsevier and {MIT} Press}, + title = {Encoding Two-Valued Nonclassical Logics in Classical + Logic}, + year = {2001}, +} + +@article{J25, + author = {Christoph Benzm{\"u}ller}, + journal = {Annals of Mathematics and Artificial Intelligence}, + number = {1--2}, + pages = {103-128}, + title = {Combining and Automating Classical and Non-Classical + Logics in Classical Higher-Order Logic}, + volume = {62}, + year = {2011}, + doi = {10.1007/s10472-011-9249-7}, + OPTurl = {http://christoph-benzmueller.de/papers/J25.pdf}, +} + +@misc{sergot08:_epist_logic_common_knowl, + author = {Marek Sergot}, + howpublished = {Lecture Course Notes, Department of Computing + Imperial College, London, + \url{https://www.doc.ic.ac.uk/~mjs/teaching/ModalTemporal499/Epistemic_499_v0809_2up.pdf}}, + title = {Epistemic Logic and ‘Common Knowledge’}, + year = {2008}, +} + +@incollection{sep-dynamic-epistemic, + author = {Baltag, Alexandru and Renne, Bryan}, + booktitle = {The Stanford Encyclopedia of Philosophy}, + edition = {Winter 2016}, + editor = {Edward N. Zalta}, + howpublished = + {\url{https://plato.stanford.edu/archives/win2016/entries/dynamic-epistemic/}}, + publisher = {Metaphysics Research Lab, Stanford University}, + title = {Dynamic Epistemic Logic}, + year = {2016}, +} + +@article{J22, + author = {Geoff Sutcliffe and Christoph Benzm{\"u}ller}, + journal = {Journal of Formalized Reasoning}, + number = {1}, + pages = {1-27}, + title = {Automated Reasoning in Higher-Order Logic using the + {TPTP THF} Infrastructure}, + volume = {3}, + year = {2010}, + issn = {1972-5787}, + OPTurl = {http://christoph-benzmueller.de/papers/J22.pdf}, +} + +@article{J5, + author = {Christoph Benzm{\"u}ller}, + journal = {Synthese}, + number = {1-2}, + pages = {203-235}, + title = {Comparing Approaches to Resolution based Higher-Order + Theorem Proving}, + volume = {133}, + year = {2002}, + abstract = {We investigate several approaches to resolution based + automated theorem proving in classical higher-order + logic (based on Church's simply typed lambda + calculus) and discuss their requirements with respect + to Henkin completeness and full extensionality. In + particular we focus on Andrews' higher-order + resolution [Andrews71], Huet's constrained resolution + [Huet72], higher-order $E$-resolution, and + extensional higher-order resolution + [BenzmuellerKohlhase98]. With the help of examples we + illustrate the parallels and differences of the + extensionality treatment of these approaches and + demonstrate that extensional higher-order resolution + is the sole approach that can completely avoid + additional extensionality axioms.}, + doi = {10.1023/A:1020840027781}, + issn = {0039-7857}, + OPTurl = {http://christoph-benzmueller.de/papers/J5.pdf}, +} + +@article{J12, + author = {J{\"o}rg Siekmann and Christoph Benzm{\"u}ller and + Serge Autexier}, + journal = {Journal of Applied Logic}, + number = {4}, + pages = {533-559}, + title = {Computer Supported Mathematics with {OMEGA}}, + volume = {4}, + year = {2006}, + doi = {10.1016/j.jal.2005.10.008}, + OPTurl = {http://christoph-benzmueller.de/papers/J12.pdf}, +} + +@incollection{B10, + author = {Serge Autexier and Christoph Benzm\"uller and + Dominik Dietrich and J\"org Siekmann}, + booktitle = {Resource-Adaptive Cognitive Processes}, + editor = {Matthew W. Crocker and J\"org Siekmann}, + pages = {389-423}, + publisher = {Springer}, + series = {Cognitive Technologies}, + title = {{OMEGA}: Resource-Adaptive Processes in an Automated + Reasoning Systems}, + year = {2010}, + doi = {10.1007/978-3-540-89408-7_17}, + isbn = {978-3-540-89407-0}, + OPTurl = {http://christoph-benzmueller.de/papers/B10.pdf}, +} + +@incollection{B1, + author = {J{\"o}rg Siekmann and Christoph Benzm{\"u}ller and + Armin Fiedler and Andreas Meier and Immanuel Normann and + Martin Pollet}, + booktitle = {Thirty Five Years of Automating Mathematics}, + editor = {Fairouz Kamareddine}, + pages = {271-314}, + publisher = {Kluwer Academic Publishers}, + series = {Applied Logic series (28)}, + title = {Proof Development in {OMEGA}: The Irrationality of + Square Root of 2}, + year = {2003}, + doi = {10.1007/978-94-017-0253-9_11}, + isbn = {978-1-402-01656-1}, + OPTurl = {http://christoph-benzmueller.de/papers/B1.pdf}, +} + +@incollection{B11, + author = {Christoph Benzm\"uller and Marvin Schiller and + J\"org Siekmann}, + booktitle = {Resource-Adaptive Cognitive Processes}, + editor = {Matthew W. Crocker and J\"org Siekmann}, + pages = {291-311}, + publisher = {Springer}, + series = {Cognitive Technologies}, + title = {Resource-Bounded Modelling and Analysis of + Human-Level Interactive Proofs}, + year = {2010}, + doi = {10.1007/978-3-540-89408-7_13}, + isbn = {978-3-540-89407-0}, + OPTurl = {http://christoph-benzmueller.de/papers/B11.pdf}, +} + +@article{J27, + author = {Christoph Benzm{\"u}ller and Adam Pease}, + journal = {Journal of Web Semantics}, + pages = {104-117}, + title = {Higher-order Aspects and Context in {SUMO}}, + volume = {12-13}, + year = {2012}, + doi = {10.1016/j.websem.2011.11.008}, + OPTurl = {http://christoph-benzmueller.de/papers/J27.pdf}, +} + +@incollection{B9, + author = {Christoph Benzm{\"u}ller and Lawrence Paulson}, + booktitle = {Reasoning in Simple Type Theory --- Festschrift in + Honor of {Peter B. Andrews} on His 70th Birthday}, + editor = {Christoph Benzm{\"u}ller and Chad Brown and + J{\"o}rg Siekmann and Richard Statman}, + note = {(Superseded by 2013 article in Logica Universalis)}, + pages = {386-406}, + publisher = {College Publications}, + series = {Studies in Logic, Mathematical Logic and Foundations}, + title = {Exploring Properties of Normal Multimodal Logics in + Simple Type Theory with {LEO-II}}, + year = {2008}, + isbn = {978-1-904987-70-3}, + OPTurl = {http://christoph-benzmueller.de/papers/B9.pdf}, +} + +@article{J21, + author = {Christoph Benzm{\"u}ller and Lawrence Paulson}, + journal = {The Logic Journal of the IGPL}, + number = {6}, + pages = {881-892}, + title = {Multimodal and Intuitionistic Logics in Simple Type + Theory}, + volume = {18}, + year = {2010}, + doi = {10.1093/jigpal/jzp080}, + OPTurl = {http://christoph-benzmueller.de/papers/J21.pdf}, +} + +@unpublished{zalta16:_princ_logic_metap, + author = {Edward N. Zalta}, + note = {Preprint available at + \url{https://mally.stanford.edu/principia.pdf}}, + title = {{Principia Logico-Metaphysica (Draft/Excerpt)}}, + year = {2018}, +} + +@book{stalnaker12:_mere_possin, + author = {Robert C. Stalnaker}, + publisher = {Princeton University Press}, + title = {Mere Possibilities: Metaphysical Foundations of Modal + Semantics}, + year = {2012}, +} + +@book{williamson13, + author = {T. Williamson}, + publisher = {Oxford:OUP}, + title = {Modal Logic as Metaphysics}, + year = {2013}, +} + +@article{FitelsonZalta, + author = {Branden Fitelson and Edward N. Zalta}, + journal = {Journal Philosophical Logic}, + number = {2}, + pages = {227--247}, + title = {Steps Toward a Computational Metaphysics}, + volume = {36}, + year = {2007}, + doi = {10.1007/s10992-006-9038-7}, +} + +@article{OppenheimerZalta2011, + author = {P. E. Oppenheimer and Edward N. Zalta}, + journal = {Australasian Journal of Philosophy}, + number = {2}, + pages = {333-349}, + title = {A Computationally-Discovered Simplification of the + Ontological Argument}, + volume = {89}, + year = {2011}, +} + +@inproceedings{AlamaZalta2015, + author = {Jesse Alama and Oppenheimer, Paul E. and + Zalta, Edward N.}, + booktitle = {Automated Deduction -- {CADE-25}}, + OPTeditor = {A.~P.~Felty and A.~Middeldorp}, + pages = {73--97}, + publisher = {Springer}, + series = {LNCS}, + title = {Automating Leibniz's Theory of Concepts}, + volume = {9195}, + year = {2015}, +} + + +@inproceedings{C40, + author = {Christoph Benzm{\"u}ller and + Woltzenlogel Paleo, Bruno}, + booktitle = {ECAI 2014}, + OPTeditor = {T. Schaub and et al.}, + pages = {93--98}, + publisher = {IOS Press}, + series = {Frontiers in Artificial Intelligence and + Applications}, + title = {Automating {G\"{o}del's} Ontological Proof of {God}'s + Existence with Higher-order Automated Theorem + Provers}, + volume = {263}, + year = {2014}, + doi = {10.3233/978-1-61499-419-0-93}, + OPTurl = {http://christoph-benzmueller.de/papers/C40.pdf}, +} + +@inproceedings{C55, + author = {Christoph Benzm{\"u}ller and + Woltzenlogel Paleo, Bruno}, + booktitle = {{IJCAI} 2016}, + editor = {S.~Kambhampati}, + pages = {936-942}, + publisher = {AAAI Press}, + title = {The Inconsistency in {G{\"o}del's} Ontological + Argument: A Success Story for {AI} in Metaphysics}, + volume = {1-3}, + year = {2016}, + isbn = {978-1-57735-770-4}, + url = {http://www.ijcai.org/Proceedings/16/Papers/137.pdf}, +} + +@inproceedings{C60, + address = {Berlin, Germany}, + author = {Christoph Benzm{\"u}ller and + Woltzenlogel Paleo, Bruno}, + booktitle = {{KI 2016}: Advances in Artificial Intelligence, + Proceedings}, + editor = {Malte Helmert and Franz Wotawa}, + pages = {244-250}, + publisher = {Springer}, + series = {Lecture Notes in Computer Science}, + title = {An Object-Logic Explanation for the Inconsistency in + {G\"odel's} Ontological Theory (Extended Abstract, + Sister Conferences)}, + year = {2016}, + doi = {10.1007/978-3-319-46073-4}, + OPTurl = {http://christoph-benzmueller.de/papers/C60.pdf}, +} + +@inCollection{GoedelNotes, + author = {Kurt G\"odel}, + OPTbooktitle = {Logic and Theism: Arguments for and Against Beliefs + in God}, + editor = {Sobel, J.H.}, + pages = {144--145}, + OPTpublisher = {Cambridge University Press}, + title = {{Appendix A. Notes in Kurt G\"odel's Hand}}, + OPTchapter = {Appendix A. Notes in Kurt G\"odel's Hand}, + year = {1970}, + isbn = {9781139449984}, + crossref = {sobel2004logic}, +} + +@inCollection{ScottNotes, + author = {Dana S. Scott}, + OPTbooktitle = {Logic and Theism: Arguments for and Against Beliefs + in God}, + editor = {Sobel, J.H.}, + pages = {145-146}, + OPTpublisher = {Cambridge U. Press}, + title = {{Appendix B: Notes in Dana Scott's Hand}}, + OPTchapter = {Appendix B: Notes in Dana Scott's Hand}, + year = 1972, + isbn = 9781139449984, + crossref = {sobel2004logic}, +} + +@book{BC04, + author = {Bertot, Y. and Casteran, P.}, + publisher = {Springer}, + series = {Texts in Theoretical Computer Science}, + title = {{Interactive Theorem Proving and Program Development + - Coq'Art: The Calculus of Inductive Constructions}}, + year = {2004}, +} + +@incollection{Sobel, + author = {Sobel, Jordan H.}, + booktitle = {{On Being and Saying. Essays for Richard Cartwright}}, + editor = {Judith Jarvis Tomson}, + pages = {241-261}, + publisher = {{MIT Press}}, + title = {G\"odel's Ontological Proof}, + year = {1987}, +} + +@article{Anderson90, + author = {C. Anthony Anderson}, + journal = {Faith and Philosophy}, + number = {3}, + title = {Some emendations of {G{\"o}del's} ontological proof}, + volume = {7}, + year = {1990}, + pages = {291--303} +} + +@incollection{AndersonGettings, + author = {Anderson, C. Anthony and Gettings, M.}, + booktitle = {{G\"odel'96: Logical Foundations of Mathematics, + Computer Science, and Physics: Lecture Notes in Logic + 6}}, + pages = {167-172}, + publisher = {{Springer}}, + title = {{G\"odel}'s Ontological Proof Revisited}, + year = {1996}, +} + +@incollection{Hajek1, + author = {H\'ajek, Petr}, + booktitle = {Logic and algebra}, + editor = {A. Ursini and P. Agliano}, + pages = {125–135}, + publisher = {Dekker, New York etc.}, + title = {Magari and others on {G\"odel’s} ontological proof}, + year = {1996}, +} + +@incollection{Hajek2, + author = {H\'ajek, Petr}, + booktitle = {{Kurt G{\"o}del. Wahrheit und Beweisbarkeit}}, + editor = {Buldt et al., B.}, + note = {ISBN 3-209-03835-X}, + pages = {325-336}, + publisher = {öbv \& hpt Verlagsgesellschaft mbH, Wien}, + title = {{Der Mathematiker und die Frage der Existenz Gottes}}, + year = {2001}, +} + +@article{Hajek3, + author = {Petr H{\'{a}}jek}, + journal = {Studia Logica}, + number = {2}, + pages = {149--164}, + title = {A New Small Emendation of {G{\"{o}}del's} Ontological + Proof}, + volume = {71}, + year = {2002}, +} + +@incollection{Bjordal, + author = {F. Bj{\o}rdal}, + booktitle = {The Logica Yearbook 1998}, + editor = {T. Childers}, + publisher = {Filosofia}, + title = {Understanding {G\"{o}del’s} Ontological Argument}, + pages = {214-217}, + year = {1999}, +} + +@article{J32, + author = {Benzm{\"u}ller, Christoph and Weber, Leon and + Woltzenlogel Paleo, Bruno}, + journal = {Logica Universalis}, + number = {1}, + pages = {139-151}, + title = {Computer-Assisted Analysis of the + {Anderson-H\'{a}jek} Controversy}, + volume = {11}, + year = {2017}, + doi = {10.1007/s11787-017-0160-9}, + OPTurl = {http://christoph-benzmueller.de/papers/J32.pdf}, +} + + +@Article{J36, + Keywords = {own, Automated Reasoning, Intensional Higher-Order Modal + Logic, Higher Order Logic}, + author = {Christoph Benzm{\"u}ller and Woltzenlogel Paleo, + Bruno}, + title = {Experiments in {Computational Metaphysics}: + {G\"odel's} Proof of {God's} Existence}, + journal = {Savijnanam: scientific exploration for a spiritual + paradigm. Journal of the Bhaktivedanta Institute}, + year = 2017, + volume = 9, + pages = {43-57}, + OPTurl = + {https://sites.google.com/binstitute.org/journal/article-3-page-43}, + issn = {0972-6586}, +} + + +@inproceedings{C50, + address = {Wroclaw, Poland}, + author = {Christoph Benzm{\"u}ller}, + booktitle = {TABLEAUX 2015}, + editor = {Hans De Nivelle}, + pages = {213-220}, + publisher = {Springer}, + series = {LNAI}, + title = {Invited Talk: On a (Quite) Universal Theorem Proving + Approach and Its Application in Metaphysics}, + volume = {9323}, + year = {2015}, + doi = {10.1007/978-3-319-24312-2_15}, + OPTurl = {http://christoph-benzmueller.de/papers/C50.pdf}, +} + +@inproceedings{C46, + address = {Berlin, Germany}, + author = {Christoph Benzm{\"u}ller and + Woltzenlogel Paleo, Bruno}, + booktitle = {Reasoning Web 2015}, + editor = {Adrian Paschke and Wolfgang Faber}, + number = {9203}, + pages = {32-74}, + publisher = {Springer}, + series = {Lecture Notes in Computer Science}, + title = {Higher-Order Modal Logics: Automation and + Applications}, + year = {2015}, + doi = {10.1007/978-3-319-21768-0_2}, + OPTurl = {http://christoph-benzmueller.de/papers/C46.pdf}, +} + + + +@article{J28, + author = {Christoph Benzm\"uller and Woltzenlogel Paleo, Bruno}, + journal = {Archive of Formal Proofs}, + OPTnote = {This publication is machine verified with + Isabelle/HOL, but comparably mildly human reviewed}, + title = {{G{\"o}del's God in Isabelle/HOL}}, + volume = {2013}, + year = {2013}, + url = {http://afp.sourceforge.net/entries/GoedelGod.shtml}, +} + +@inproceedings{W55, + address = {Sinaia, Romania}, + author = {Christoph Benzm{\"u}ller and + Woltzenlogel Paleo, Bruno}, + booktitle = {Recent Trends in Algebraic Development Techniques: + 22nd International Workshop, WADT 2014, Sinaia, + Romania, September 4-7, 2014, Revised Selected + Papers}, + editor = {Codescu, Mihai and Diaconescu, Razvan and + Tutu, Ionut}, + number = {9563}, + pages = {3-6}, + publisher = {Springer}, + series = {Lecture Notes in Computer Science}, + title = {On Logic Embeddings and {G\"odel's} {God}}, + year = {2015}, + doi = {10.1007/978-3-319-28114-8_1}, + isbn = {978-3-319-28114-8}, + OPTurl = {http://christoph-benzmueller.de/papers/W55.pdf}, +} + +@incollection{B15, + author = {Benzm{\"u}ller, Christoph and + Woltzenlogel Paleo, Bruno}, + booktitle = {The Square of Opposition: A Cornerstone of Thought + (Collection of papers related to the World Congress + on the Square of Opposition IV, Vatican, 2014)}, + note = {\url{http://www.springer.com/us/book/9783319450612}}, + editor = {B\'{e}ziau, Jean-Yves and Basti, Gianfranco}, + pages = {307-313}, + publisher = {Springer International Publishing Switzerland}, + series = {Studies in Universal Logic}, + title = {The Modal Collapse as a Collapse of the Modal Square + of Opposition}, + year = {2016}, + doi = {10.1007/978-3-319-45062-9_18}, + OPTurl = {http://christoph-benzmueller.de/papers/B15.pdf}, +} + + + +@inproceedings{C56, + address = {Berlin, Germany}, + author = {Alexander Steen and Max Wisniewski and + Christoph Benzm{\"u}ller}, + booktitle = {Mathematical Software -- ICMS 2016, 5th International + Congress, Proceedings}, + editor = {G.-M. Greuel and T. Koch and P. Paule and A. Sommese}, + pages = {75-81}, + publisher = {Springer}, + series = {Lecture Notes in Computer Science}, + title = {Agent-Based {HOL} Reasoning}, + volume = {9725}, + year = {2016}, + doi = {10.1007/978-3-319-42432-3_10}, + isbn = {978-3-319-42431-6}, + OPTurl = {http://christoph-benzmueller.de/papers/C56.pdf}, +} + +@book{fitting02:_types_tableaus_god, + author = {Melvin Fitting}, + publisher = {Kluwer}, + title = {Types, Tableaus, and {G}{\"o}del's God}, + year = {2002}, +} + +@book{Principia, + author = {Alfred North Whitehead and Bertrand Russell}, + publisher = {Cambridge: Cambridge University Press. Second + edition, 1925 (Vol. 1), 1927 (Vols 2, 3). Abridged as + Principia Mathematica to *56, Cambridge: Cambridge + University Press, 1962.}, + title = {Principia Mathematica, 3 vols}, + year = {1910, 1912, 1913}, +} + +@book{zalta1988intensional, + author = {Edward N. Zalta}, + publisher = {MIT Press}, + series = {A Bradford book}, + title = {Intensional Logic and the Metaphysics of + Intentionality}, + year = {1988}, + isbn = {9780262240277}, +} + +@article{zalta1988validity, + author = {Edward N. Zalta}, + journal = {The Journal of Philosophy}, + title = {Logical and Analytic Truths That Are Not Necessary}, + year = {1988}, + volume = {85}, + number = {2}, + pages = {57--74}, +} + +@book{zalta1983abstract, + author = {Edward N. Zalta}, + publisher = {D. Reidel}, + title = {Abstract Objects: An Introduction to Axiomatic + Metaphysics}, + city = {Dordrecht}, + year = {1983}, + isbn = {9789027714749}, + OPTurl = {https://books.google.de/books?id=voCSP6k3FCcC}, +} + +@article{DBLP:journals/logcom/OppenheimerZ11, + author = {Paul E. Oppenheimer and Edward N. Zalta}, + journal = {Journal of Logic and Computation}, + number = 2, + pages = {351--374}, + title = {Relations Versus Functions at the Foundations of + Logic: Type-Theoretic Considerations}, + volume = 21, + year = 2011, + doi = {10.1093/logcom/exq017}, + url = {http://dx.doi.org/10.1093/logcom/exq017}, +} + + + +@article{DBLP:journals/afp/Kirchner17, + author = {Daniel Kirchner}, + journal = {Archive of Formal Proofs}, + title = {Representation and Partial Automation of the + Principia Logico-Metaphysica in {Isabelle/HOL}}, + volume = {2017}, + year = {2017}, + url = {https://www.isa-afp.org/entries/PLM.html}, +} + +@techreport{R60, + author = {Kirchner, Daniel and Benzm{\"u}ller, Christoph and + Edward N. Zalta}, + institution = {CoRR}, + note = {Preprint of submitted article}, + title = {{Mechanizing Principia Logico-Metaphysica in + Functional Type Theory}}, + year = {2017}, + url = {https://arxiv.org/abs/1711.06542}, +} + +@book{link08:_one_hundr_years_russel_parad, + editor = {Link, Godehard}, + publisher = {De Gruyter}, + title = {One Hundred Years of Russell's Paradox}, + year = {2008}, +} + +@book{Frege1879, + author = {Gottlob Frege}, + note = {Translated in \cite{vanHeijenoort67}}, + publisher = {Halle}, + title = {Begriffsschrift, eine der arithmetischen + nachgebildete Formelsprache des reinen Denkens}, + year = {1879}, +} + +@inproceedings{Lambert60, + author = {Karel Lambert}, + booktitle = {Abstracts: The International Congress for Logic, + Methodology and Philosophy of Science}, + publisher = {Stanford: Stanford University Press}, + title = {The Definition of E(xistence)! in Free Logic}, + year = {1960}, +} + +@incollection{Scott67, + author = {Dana S. Scott}, + booktitle = {Bertrand Russell: Philosopher of the Century}, + editor = {R. Schoenman}, + note = {(Reprinted with additions in: Philosophical + Application of Free Logic, edited by K. Lambert. + Oxford Universitry Press, 1991, pp. 28 - 48)}, + pages = {181-200}, + publisher = {George Allen \& Unwin, London}, + title = {Existence and description in formal logic}, + year = {1967}, +} + +@book{lambert02:_free_logic, + author = {Karel Lambert}, + publisher = {Cambridge: Cambridge University Press}, + title = {Free Logic: Selected Essays}, + year = {2002}, +} + +@InCollection{sep-logic-free, + author = {Nolt, John}, + title = {Free Logic}, + booktitle = {The Stanford Encyclopedia of Philosophy}, + editor = {Edward N. Zalta}, + howpublished = {\url{https://plato.stanford.edu/archives/fall2018/entries/logic-free/}}, + year = {2018}, + edition = {Fall 2018}, + publisher = {Metaphysics Research Lab, Stanford University} +} + + +@techreport{R58, + author = {Christoph Benzm{\"u}ller and Scott, Dana S.}, + institution = {CoRR}, + title = {Axiomatizing Category Theory in Free Logic}, + year = {2016}, + url = {http://arxiv.org/abs/1609.01493}, +} + +@inproceedings{C57, + address = {Berlin, Germany}, + author = {Christoph Benzm{\"u}ller and Scott, Dana S.}, + booktitle = {Mathematical Software -- ICMS 2016, 5th International + Congress, Proceedings}, + editor = {G.-M. Greuel and T. Koch and P. Paule and A. Sommese}, + pages = {43-50}, + publisher = {Springer}, + series = {Lecture Notes in Computer Science}, + title = {Automating Free Logic in {Isabelle/HOL}}, + volume = {9725}, + year = {2016}, + doi = {10.1007/978-3-319-42432-3_6}, + isbn = {978-3-319-42431-6}, + OPTurl = {http://christoph-benzmueller.de/papers/C57.pdf}, +} + + +@article{J39, + author = {Christoph Benzm{\"u}ller and Scott, Dana S.}, + title = {Axiom Systems for Category Theory in Free Logic}, + journal = {Archive of Formal Proofs}, + month = may, + year = 2018, + note = {\url{http://isa-afp.org/entries/AxiomaticCategoryTheory.html}, + Formal proof development}, + ISSN = {2150-914x}, +} + +@book{FreydScedrov90, + author = {Peter Freyd and Andre Scedrov}, + publisher = {North Holland}, + title = {Categories, Allegories}, + year = {1990}, +} + +@incollection{Scott79, + author = {Scott, Dana S.}, + booktitle = {Applications of Sheaves: Proceedings of the Research + Symposium on Applications of Sheaf Theory to Logic, + Algebra, and Analysis, Durham, July 9--21, 1977}, + editor = {Fourman, Michael and Mulvey, Christopher and + Scott, Dana}, + pages = {660--696}, + publisher = {Springer}, + series = {Lecture Notes in Mathematics}, + title = {Identity and existence in intuitionistic logic}, + volume = {752}, + year = {1979}, +} + +@article{J31, + author = {Christoph Benzm{\"u}ller}, + journal = {Journal of Philosophical Logic}, + number = {3}, + pages = {333-353}, + title = {Cut-Elimination for Quantified Conditional Logic}, + volume = {46}, + year = {2017}, + doi = {10.1007/s10992-016-9403-0}, + OPTurl = {http://christoph-benzmueller.de/papers/J31.pdf}, +} + +@incollection{Stalnaker68, + author = {Robert C. Stalnaker}, + booktitle = {Studies in Logical Theory}, + pages = {98--112}, + publisher = {Blackwell}, + title = {A Theory of Conditionals}, + year = {1968}, +} + +@article{Chellas75, + author = {Chellas, B.F.}, + journal = {Journal of Philosophical Logic}, + number = {2}, + pages = {133-153}, + title = {Basic Conditional Logic}, + volume = {4}, + year = {1975}, +} + +@article{delgrande98, + author = {J.P. Delgrande}, + journal = {Artificial Intelligence}, + number = {1-2}, + pages = {105-137}, + title = {On First-Order Conditional Logics}, + volume = {105}, + year = {1998}, +} + +@article{delgrande87, + author = {J.P. Delgrande}, + journal = {Artificial Intelligence}, + number = {1}, + pages = {105-130}, + title = {A First-Order Conditional Logic for Prototypical + Properties}, + volume = {33}, + year = {1987}, +} + +@article{DBLP:journals/tocl/FriedmanHK00, + author = {N. Friedman and J.Y. Halpern and D. Koller}, + journal = {ACM Transactions on Computational Logic}, + number = {2}, + pages = {175-207}, + title = {First-order conditional logic for default reasoning + revisited}, + volume = {1}, + year = {2000}, +} + +@article{DBLP:journals/corr/abs-1011-3479, + author = {Dirk Pattinson and Lutz Schr{\"{o}}der}, + journal = {Logical Methods in Computer Science}, + number = {1}, + title = {Generic Modal Cut Elimination Applied to Conditional + Logics}, + volume = {7}, + year = {2011}, + bibOPTurl = {http://dblp.uni-trier.de/rec/bib/journals/corr/abs-1011- + 3479}, + doi = {10.2168/LMCS-7(1:4)2011}, +} + +@article{DBLP:journals/apal/Rasga07, + author = {Jo{\~{a}}o Rasga}, + journal = {Ann. Pure Appl. Logic}, + number = {1-3}, + pages = {81--99}, + title = {Sufficient conditions for cut elimination with + complexity analysis}, + volume = {149}, + year = {2007}, + bibOPTurl = {http://dblp.uni-trier.de/rec/bib/journals/apal/Rasga07}, + doi = {10.1016/j.apal.2007.08.001}, +} + +@inproceedings{C37, + address = {Beijing, China}, + author = {Christoph Benzm{\"u}ller}, + booktitle = {23rd International Joint Conference on Artificial + Intelligence ({IJCAI-13})}, + editor = {Francesca Rossi}, + pages = {746-753}, + publisher = {AAAI Press}, + title = {Automating Quantified Conditional Logics in {HOL}}, + year = {2013}, + isbn = {978-1-57735-633-2}, + OPTurl = {http://christoph-benzmueller.de/papers/C37.pdf}, +} + +@article{J18, + author = {Christoph Benzm{\"u}ller and Chad Brown and + Michael Kohlhase}, + journal = {Logical Methods in Computer Science}, + number = {1:6}, + pages = {1-21}, + title = {Cut-Simulation and Impredicativity}, + volume = {5}, + year = {2009}, + doi = {10.2168/LMCS-5(1:6)2009}, + OPTurl = {http://christoph-benzmueller.de/papers/J18.pdf}, +} + +@inproceedings{C58, + OPTaddress = {Potsdam}, + author = {Max Wisniewski and Alexander Steen and + Christoph Benzm{\"u}ller}, + booktitle = {Hochschuldidaktik der Informatik: 7. Fachtagung des + GI-Fachbereichs Informatik und Ausbildung/Didaktik + der Informatik}, + editor = {Andreas Schwill and Ulrike Lucke}, + pages = {81-92}, + publisher = {Universit{\"a}tsverlag Potsdam}, + series = {Commentarii informaticae didacticae (CID)}, + title = {{Einsatz von Theorembeweisern in der Lehre}}, + year = {2016}, + isbn = {978-3-86956-376-3}, + issn = {1868-0844}, + OPTurl = {https://publishup.uni-potsdam.de/opus4-ubp/frontdoor/index/ + index/docId/9485}, +} + +@unpublished{R57, + author = {Christoph Benzm{\"u}ller and Max Wisniewski and + Alexander Steen}, + note = {This lecture course proposal received the 2015 + central teaching award of FU Berlin}, + title = {{Computational Metaphysics}}, + year = {2015}, + url = {http://christoph-benzmueller.de/papers/R57.pdf}, +} + +@incollection{B16, + author = {Bentert, Matthias and Benzm{\"u}ller, Christoph and + Streit, David and Woltzenlogel Paleo, Bruno}, + booktitle = {Death and Anti-Death, Volume 14: Four Decades after + Michael Polanyi, Three Centuries after G.W. Leibniz}, + editor = {Tandy, Charles}, + note = {Preprint: + \url{https://www.researchgate.net/publication/311456135}}, + publisher = {Ria University Press}, + title = {Analysis of an Ontological Proof Proposed by + {Leibniz}}, + year = {2016}, + isbn = {978-1934297254}, + OPTurl = {https://philpapers.org/rec/TANDAA-10}, +} + +@inproceedings{C63, + author = {David Fuenmayor and Christoph Benzm{\"u}ller and + Alexander Steen and Max Wisniewski}, + booktitle = {Handbook of the 2nd World Congress on Logic and + Religion, Warsaw, Poland}, + editor = {Stanislaw Krajewski and Piotr Balcerowicz}, + pages = {3}, + title = {The Virtues of Automated Theorem Proving in + Metaphysics --- A Case Study: {E. J. Lowe's} Modal + Ontological Argument}, + year = {2017}, + OPTurl = {http://christoph-benzmueller.de/papers/C63.pdf}, +} + +@inproceedings{C65, + author = {David Fuenmayor and Christoph Benzm{\"u}ller}, + booktitle = {KI 2017: Advances in Artificial Intelligence}, + pages = {114-127}, + publisher = {Springer}, + series = {LNAI}, + title = {Automating Emendations of the Ontological Argument in + Intensional Higher-Order Modal Logic}, + volume = {10505}, + year = {2017}, + doi = {10.1007/978-3-319-67190-1_9}, + isbn = {978-3-319-67189-5}, + OPTurl = {http://christoph-benzmueller.de/papers/C65.pdf}, +} + + +@article{J37, + author = {David Fuenmayor and Christoph Benzm\"uller}, + journal = {Archive of Formal Proofs}, + OPTnote = {This publication is machine verified with + Isabelle/HOL, but comparably mildly human reviewed}, + title = {{Computer-assisted Reconstruction and Assessment of + E. J. Lowe's Modal Ontological Argument}}, +volume = {2017}, + year = {2017}, + url = {https://www.isa-afp.org/entries/Lowe_Ontological_Argument.html}, +} + + + +@MastersThesis{BScMakarenko, + author = {Irina Makarenko}, + school = {Department of Mathematics and Computer Science, Freie + Universit{\"a}t Berlin}, + type = {Bachelor's Thesis}, + title = {Automatisierung von freier Logik in Logik h{\"o}herer + Stufe}, + year = {2016}, +} + +@MastersThesis{BScFuenmayor, + author = {David Fuenmayor}, + school = {Department of Philosophy, Freie Universit{\"a}t + Berlin}, + type = {Bachelor's Thesis}, + title = {Computational Hermeneutics: Using Computers to + Understand Philosophical Arguments}, + year = {2017}, +} + +@MastersThesis{BScGleissner, + author = {Tobias Gleissner}, + school = {Department of Mathematics and Computer Science, Freie + Universit{\"a}t Berlin}, + type = {Bachelor's Thesis}, + title = {Converting Higher-Order Modal Logic Problems into + Classical Higher-Order Logic}, + year = {2017}, +} + +@MastersThesis{MScSchuetz, + author = {Fabian Sch{\"u}tz}, + school = {Department of Mathematics and Computer Science, Freie + Universit{\"a}t Berlin}, + type = {Master's Thesis}, + title = {{Wahrhaftiger Toren Zorn - Repr{\"a}sentation und + Interpretation von Argumenten}}, + year = {2017}, +} + +@article{J33, + author = {Steen, Alexander and Benzm{\"u}ller, Christoph}, + journal = {Logic and Logical Philosophy}, + pages = {535-554}, + title = {Sweet {SIXTEEN}: Automation via Embedding into + Classical Higher-Order Logic}, + volume = {25}, + year = {2016}, + doi = {10.12775/LLP.2016.021}, + issn = {1425-3305}, + OPTurl = {http://christoph-benzmueller.de/papers/J33.pdf}, +} + +@inproceedings{wisniewski14:_embed_quant_higher_order_nomin, + author = {Max Wisniewski and Alexander Steen}, + booktitle = {1st International Workshop on Automated Reasoning in + Quantified Non-Classical Logics (ARQNL 2014), Vienna, + Austria, Proceedings}, + editor = {Christoph Benzm\"uller and Jens Otten}, + pages = {59-64}, + publisher = {EasyChair Publications}, + series = {EasyChair Proceedings in Computing}, + title = {Embedding of Quantified Higher-Order Nominal Modal + Logic into Classical Higher-Order Logic}, + volume = {33}, + year = {2014}, +} + +@MastersThesis{MScClaus, + author = {Maximilian Claus}, + school = {Department of Mathematics and Computer Science, Freie + Universit{\"a}t Berlin}, + type = {Master's Thesis}, + title = {Software Model Checking With Higher-Order Automated + Theorem Provers: A Logic Embedding Approach}, + year = {2015}, +} + +@book{boolos93:_logic_provab, + author = {George Boolos}, + publisher = {Cambridge University Press}, + title = {The Logic of Provability}, + year = {1993}, +} + +@article{bostrom03:_are_we_livin_comput_simul, + author = {Nick Bostrom}, + journal = {The Philosophical Quarterly}, + number = {211}, + pages = {243–255}, + title = {Are We Living in a Computer Simulation?}, + volume = {53}, + year = {2003}, + doi = {10.1111/1467-9213.00309}, +} + +@techreport{R59, + author = {Christoph Benzm{\"u}ller}, + institution = {CoRR}, + title = {Universal Reasoning, Rational Argumentation and + Human-Machine Interaction}, + year = {2017}, + url = {http://arxiv.org/abs/1703.09620}, +} + +@book{gabbay13:_handb_deont_logic_normat_system, + editor = {Dov Gabbay and John Horty and Xavier Parent and + van der Meyden, Ron and van der Torre, Leendert}, + publisher = {College Publications}, + title = {Handbook of Deontic Logic and Normative Systems}, + year = {2013}, +} + +@article{DBLP:journals/jphil/MakinsonT00, + author = {David Makinson and Leendert W. N. van der Torre}, + journal = {Journal of Philosophical Logic}, + number = {4}, + pages = {383--408}, + title = {Input/Output Logics}, + volume = {29}, + year = {2000}, + biburl = {http://dblp.uni-trier.de/rec/bib/journals/jphil/ + MakinsonT00}, + doi = {10.1023/A:1004748624537}, + OPTurl = {http://dx.doi.org/10.1023/A:1004748624537}, +} + +@article{DBLP:journals/logcom/CarmoJ13, + author = {Jos{\'{e}} Carmo and Andrew J. I. Jones}, + journal = {Journal of Logic and Computation}, + number = {3}, + pages = {585--626}, + title = {Completeness and decidability results for a logic of + contrary-to-duty conditionals}, + volume = {23}, + year = {2013}, + biburl = {http://dblp.uni-trier.de/rec/bib/journals/logcom/CarmoJ13}, + doi = {10.1093/logcom/exs009}, + OPTurl = {http://dx.doi.org/10.1093/logcom/exs009}, +} + +@inproceedings{C69, + author = {Benzm{\"u}ller, Christoph and Parent, Xavier and + van der Torre, Leendert}, + booktitle = {14th Conference on Computability in Europe, CiE 2018, + Kiel, Germany, July 30-August, 2018, Proceedings}, + editor = {Manea, Florin and Miller, Russell G. and + Nowotka, Dirk}, + pages = {60-69}, + publisher = {Springer}, + series = {Lecture Notes in Computer Science}, + title = {A Deontic Logic Reasoning Infrastructure}, + volume = {10936}, + year = {2018}, + doi = {10.1007/978-3-319-94418-0_6}, + isbn = {978-3-319-67189-5}, + OPTurl = {http://christoph-benzmueller.de/papers/C69.pdf}, +} + +@techreport{R66, + author = {Benzm{\"u}ller, Christoph and Parent, Xavier}, + institution = {CoRR}, + title = {First Experiments with a Flexible Infrastructure for + Normative Reasoning}, + year = {2018}, + url = {http://arxiv.org/abs/1804.02929}, +} + +@techreport{R65, + author = {Benzm{\"u}ller, Christoph and Parent, Xavier}, + institution = {CoRR}, + + title = {{I/O} Logic in {HOL} --- First Steps}, + year = {2018}, + url = {http://arxiv.org/abs/1803.09681}, +} + +@techreport{R63, + author = {Benzm{\"u}ller, Christoph and Farjami, Ali and + Parent, Xavier}, + institution = {CoRR}, + title = {Faithful Semantical Embedding of a Dyadic Deontic + Logic in {HOL}}, + year = {2018}, + url = {https://arxiv.org/abs/1802.08454}, +} + +@inproceedings{C62, + address = {Maun, Botswana}, + author = {Tobias Glei{\ss}ner and Alexander Steen and + Christoph Benzm{\"u}ller}, + booktitle = {LPAR-21. 21st International Conference on Logic for + Programming, Artificial Intelligence and Reasoning}, + editor = {Thomas Eiter and David Sands}, + pages = {14-30}, + publisher = {EasyChair}, + series = {EPiC Series in Computing}, + title = {Theorem Provers for Every Normal Modal Logic}, + volume = {46}, + year = {2017}, + doi = {10.29007/jsb9}, + issn = {2398-7340}, + OPTurl = {https://easychair.org/publications/paper/340346}, +} + +@inproceedings{W56, + author = {Max Wisniewski and Alexander Steen and + Christoph Benzm\"uller}, + booktitle = {ARQNL 2016. Automated Reasoning in Quantified + Non-Classical Logics}, + editor = {Christoph Benzm{\"u}ller and Jens Otten}, + pages = {51-65}, + publisher = {CEUR Workshop Proceedings, http://ceur-ws.org}, + title = {{TPTP} and Beyond: Representation of Quantified + Non-Classical Logics}, + volume = {1770}, + year = {2016}, + OPTurl = {http://ceur-ws.org/Vol-1770/}, +} + +@inproceedings{C38, + address = {Stellenbosch, South Africa}, + author = {Christoph Benzm{\"u}ller and Thomas Raths}, + booktitle = {Proceedings of the 19th International Conference on + Logic for Programming, Artificial Intelligence and + Reasoning (LPAR)}, + editor = {Kenneth L. McMillan and Aart Middeldorp and + Andrei Voronkov}, + pages = {127-136}, + publisher = {Springer}, + series = {Lecture Notes in Computer Science}, + title = {{HOL} based First-order Modal Logic Provers}, + volume = {8312}, + year = {2013}, + doi = {10.1007/978-3-642-45221-5_9}, + isbn = {978-3-642-45220-8}, + OPTurl = {http://christoph-benzmueller.de/papers/C38.pdf}, +} + +@inproceedings{C34, + address = {Montpellier, France}, + author = {Christoph Benzm{\"u}ller and Jens Otten and + Thomas Raths}, + booktitle = {ECAI 2012}, + editor = {Luc De Raedt and Christian Bessiere and Didier Dubois and + Patrick Doherty and Paolo Frasconi and Fredrik Heintz and + Peter Lucas}, + pages = {163-168}, + publisher = {IOS Press}, + series = {Frontiers in Artificial Intelligence and + Applications}, + title = {Implementing and Evaluating Provers for First-order + Modal Logics}, + volume = {242}, + year = {2012}, + doi = {10.3233/978-1-61499-098-7-163}, + isbn = {978-1-61499-097-0}, + OPTurl = {http://christoph-benzmueller.de/papers/C34.pdf}, +} + +@inproceedings{C64, + address = {Maun, Botswana}, + author = {Christoph Benzm{\"u}ller and Alexander Steen and + Max Wisniewski}, + booktitle = {IWIL@LPAR 2017 Workshop and {LPAR-21} Short + Presentations, Maun, Botswana, May 7-12, 2017}, + editor = {Thomas Eiter and David Sands and Geoff Sutcliffe and + Andrei Voronkov}, + pages = {11-61}, + publisher = {EasyChair}, + series = {Kalpa Publications in Computing}, + title = {{Leo-III} Version 1.1 (System description)}, + volume = {1}, + year = {2017}, + OPTurl = {http://www.easychair.org/publications/paper/342979}, +} + +@inproceedings{W57, + address = {Maun, Botswana}, + author = {Alexander Steen and Max Wisniewski and + Christoph Benzm{\"u}ller}, + booktitle = {IWIL@LPAR 2017 Workshop and {LPAR-21} Short + Presentations, Maun, Botswana, May 7-12, 2017}, + editor = {Thomas Eiter and David Sands and Geoff Sutcliffe and + Andrei Voronkov}, + pages = {100-112}, + publisher = {EasyChair}, + series = {Kalpa Publications in Computing}, + title = {Going Polymorphic - {TH1} Reasoning for {Leo-III}}, + volume = {1}, + year = {2017}, + OPTurl = {http://www.easychair.org/publications/paper/346851}, +} + +@book{vanHeijenoort67, + address = {Cambridge, MA}, + author = {Jean van Heijenoort}, + edition = {3rd printing, 1997}, + publisher = {Harvard Univ. Press}, + series = {Source books in the history of the sciences series}, + title = {From {F}rege to {G}{\"o}del: {A} Source Book in + Mathematics, 1879-1931}, + year = {1967}, + isbn = {0-674-32450-1}, +} + +@article{J38, + Author = {David Fuenmayor and Christoph Benzm\"uller}, + Journal = {Journal of Applied Logic - IfCoLoG Journal of Logics and their Applications (special issue on Formal Approaches to the Ontological Argument)}, + Editors = {Silvestre, Ricardo and B\'{e}ziau, Jean-Yves}, + Keywords = {own, Automated Reasoning, Interactive Proof, Ontology + Reasoning, Higher Order Logic, Computational + Metaphysics}, + Title = {A Case Study On Computational Hermeneutics: {E.J. Lowe's Modal} Ontological Argument}, + Year = 2018, + Url = {http://christoph-benzmueller.de/papers/J38.pdf}, + Note = {Accepted for publication; to be published also as chapter in the book 'Beyond Faith and Rationality: Essays on Logic, Religion and Philosophy' printed in the Springer book series 'Sophia Studies in Cross-cultural Philosophy of Traditions and Cultures'}, +} + +@Article{MacLane48, + author = {Saunders MacLane}, + title = {Groups, Categories and Duality}, + journal = {Proceedings of the National Academy of Sciences}, + year = 1948, + volume = 34, + number = 6, + pages = {263-267}} + +@article{J42, + author = {David Fuenmayor and Christoph Benzmüller}, + title = {{Formalisation and Evaluation of Alan Gewirth's Proof for the Principle of Generic Consistency in Isabelle/HOL}}, + journal = {Archive of Formal Proofs}, + month = oct, + year = 2018, + note = {\url{http://isa-afp.org/entries/GewirthPGCProof.html}, + Formal proof development}, + ISSN = {2150-914x}, +} + +@Book{Isabelle, + author = {Tobias Nipkow and Lawrence C. Paulson and Markus Wenzel}, + title = {{Isabelle/HOL} --- A Proof Assistant for Higher-Order Logic}, + publisher = {Springer}, + series = {LNCS}, + volume = 2283, + year = 2002} + +@article{J50, + Author = {Kirchner, Daniel and Benzm{\"u}ller, Christoph and + Zalta, Edward N.}, + Keywords = {own, Higher Order Logic, Higher Order Modal Logic, + Universal Reasoning, Computational Metaphysics}, + Title = {Mechanizing Principia Logico-Metaphysica in + Functional Type Theory}, + Journal = {Review of Symbolic Logic}, + Volume = {13}, + Number = {1}, + Publisher = {Cambridge University Press}, + Doi = {10.1017/S1755020319000297}, + pages = {206-218}, + Addendum = {Preprint: \url{https://www.researchgate.net/publication/321160582}}, + Year = 2020, +} + +@article{Thesis, + author = {Daniel Kirchner}, + title = {{Representation and Partial Automation of the Principia Logico-Metaphysica in Isabelle/HOL}}, + journal = {Archive of Formal Proofs}, + month = sep, + year = 2017, + note = {\url{http://isa-afp.org/entries/PLM.html}, + Formal proof development}, + ISSN = {2150-914x}, +} +@Article{rtt, + author = {Oppenheimer, Paul E. and Zalta, Edward N.}, + title = {{Relations Versus Functions at the Foundations of Logic: Type-Theoretic Considerations}}, + journal = {Journal of Logic and Computation}, + year = 2011, + volume = 21, + number = 2, + pages = {351--374} +} +@article{Andrews89, + author = {Peter B. Andrews}, + title = {On Connections and Higher-Order Logic}, + journal = {Journal of Automated Reasoning}, + volume = {5}, + number = {3}, + pages = {257--291}, + year = {1989}, + url = {https://doi.org/10.1007/BF00248320}, + doi = {10.1007/BF00248320}, + timestamp = {Sat, 20 May 2017 00:22:32 +0200}, + biburl = {https://dblp.org/rec/bib/journals/jar/Andrews89}, + bibsource = {dblp computer science bibliography, https://dblp.org} +} + + + + +@book{BurrisSankappanavar1981, + author = {Burris, S. and Sankap\-panavar, H.P.}, + owner = 23, + publisher = {Springer}, + title = {A Course in Universal Algebra}, + url = {http://www.math.uwaterloo.ca/~snburris/htdocs/ualg.html}, + year = 1981 +} + +@article{Kanckos2017VariantsOG, + title={Variants of {G{\"o}del}’s Ontological Proof in a Natural Deduction Calculus}, + author={Annika Kanckos and Woltzenlogel Paleo, Bruno}, + journal={Studia Logica}, + year={2017}, + volume={105}, + pages={553-586} +} + + +@Article{Rushby, + author = {John Rushby}, + title = {A Mechanically Assisted Examination of Begging the Question in {Anselm's} Ontological Argument}, + journal = {J. Applied Logics}, + year = 2018, + volume = 5, + number = 7, + pages = {1473--1496}} + + +@Article{Blumson, + author = {Ben Blumson}, + title = {{Anselm's God in Isabelle/HOL}}, + journal = {Archive of Formal Proofs}, + year = 2017} + + +@article{KanckosLethen19, +title = "The Development of {G{\"o}del}'s ontological Proof", +keywords = "611 Philosophy", +author = "Annika Kanckos and Tim Lethen", +year = "2019", +month = "11", +day = "15", +doi = "10.1017/S1755020319000479", +language = "English", +OPTpages = "1 -- 19", +journal = "The Review of Symbolic Logic", +issn = "1755-0203", +publisher = "Cambridge University Press", +} + + +@InProceedings{C78, + Keywords = {own, Automated Reasoning, Free Logic, Higher Order + Logic, Category Theory, Algebraic Structures, Modeloids}, + Author = {Lucca Tiemens and Dana S. Scott and Christoph Benzm\"uller and Miroslav Benda}, + title = {Computer-supported Exploration of a Categorical Axiomatization of Modeloids}, + booktitle = {Relational and Algebraic Methods in Computer Science -- 18th International Conference, RAMiCS 2020}, + editors = {Uli Fahrenberg and Peter Jipsen and Michael Winter}, + year = 2020, + series = {LNCS}, + url = {https://www.springerprofessional.de/computer-supported-exploration-of-a-categorical-axiomatization-o/17853766}, + publisher = {Springer}, + volume = 12062, + pages = {302--317}, + doi = {10.1007/978-3-030-43520-2_19}, + addendum = {Preprint (with proofs): \url{https://www.researchgate.net/publication/336838722}}, +} + + +@article{J40, + author = {Christoph Benzm{\"u}ller and Scott, Dana S.}, + Keywords = {own, Automated Reasoning, Free Logic, Higher Order + Logic, Category Theory}, + title = {Automating Free Logic in {HOL}, with an Experimental + Application in Category Theory}, + volume = 64, + number = 1, + pages = {53--72}, + year = 2020, + url = {http://doi.org/10.13140/RG.2.2.11432.83202}, + journal = {Journal of Automated Reasoning}, + publisher = {Springer Netherlands}, + doi = {10.1007/s10817-018-09507-7}, + Addendum = {Preprint: + \url{http://doi.org/10.13140/RG.2.2.11432.83202}}, +} + + +@book{sobel2004logic, + author = {Sobel, Jordan H.}, + booktitle = {Logic and Theism: Arguments for and Against Beliefs + in {God}}, + OPTeditor = {Sobel, J.H.}, + publisher = {Cambridge University Press}, + title = {Logic and Theism: Arguments for and Against Beliefs + in God}, + year = {2004}, + isbn = {9781139449984}, +} \ No newline at end of file