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== References == === Notes === {{notelist}} === Citations === {{reflist}} === Sources === {{refbegin|30em}} * {{cite book |last1=Akiba |first1=Ken |title=Indeterminacy, Vagueness, and Truth: The Boolean Many-valued Approach |publisher=Springer Nature |isbn=978-3-031-74175-3 |url=https://books.google.com/books?id=ftksEQAAQBAJ&pg=PA7 |language=en |date=2024 }} * {{cite book |last1=Arthur |first1=Richard T. W. |title=An Introduction to Logic - Second Edition: Using Natural Deduction, Real Arguments, a Little History, and Some Humour |publisher=Broadview Press |isbn=978-1-77048-648-5 |language=en |date=2016 }} * {{cite book |last1=Asprino |first1=L. |title=Engineering Background Knowledge for Social Robots |publisher=IOS Press |isbn=978-1-64368-109-2 |url=https://books.google.com/books?id=H6EGEAAAQBAJ&pg=PA4 |language=en |date=2020 }} * {{cite book |last1=Audi |first1=Robert |title=The Cambridge Dictionary of Philosophy |publisher=Cambridge University Press |chapter=Philosophy of Logic |year=1999 |isbn=978-1-107-64379-6 }} * {{cite book |last1=Bacon |first1=Andrew |title=A Philosophical Introduction to Higher-order Logics |publisher=Routledge |isbn=978-1-000-92575-3 |url=https://books.google.com/books?id=qa3WEAAAQBAJ&pg=PA423 |language=en |date=2023 }} * {{cite book |last1=Baker |first1=Gordon P. |last2=Hacker |first2=P. M. S. |title=Wittgenstein: Rules, Grammar and Necessity: Volume 2 of an Analytical Commentary on the Philosophical Investigations, Essays and Exegesis 185-242 |publisher=John Wiley & Sons |isbn=978-1-118-85459-4 |url=https://books.google.com/books?id=vEFVAgAAQBAJ&pg=PA88 |language=en |date=2014 }} * {{cite web |last1=Beall |first1=Jc |last2=Restall |first2=Greg |last3=Sagi |first3=Gil |title=Logical Consequence |url=https://plato.stanford.edu/entries/logical-consequence/ |website=The Stanford Encyclopedia of Philosophy |publisher=Metaphysics Research Lab, Stanford University |date=2024 }} * {{cite book |last1=Boyer |first1=Robert S. |last2=Moore |first2=J. Strother |title=A Computational Logic Handbook: Formerly Notes and Reports in Computer Science and Applied Mathematics |publisher=Academic Press |isbn=978-1-4832-7778-3 |url=https://books.google.com/books?id=eMHSBQAAQBAJ&pg=PA144 |language=en |date=2014 }} * {{cite web |last1=Burris |first1=Stanley |title=George Boole |url=https://plato.stanford.edu/entries/boole/ |website=The Stanford Encyclopedia of Philosophy |publisher=Metaphysics Research Lab, Stanford University |access-date=31 March 2025 |date=2024 }} * {{cite book |last1=Butterfield |first1=Andrew |last2=Ngondi |first2=Gerard Ekembe |title=A Dictionary of Computer Science |publisher=Oxford University Press |isbn=978-0-19-968897-5 |url=https://books.google.com/books?id=GDgICwAAQBAJ&pg=PA1 |language=en |date=2016 }} * {{cite book |last1=Cannon |first1=Douglas |title=Deductive Logic in Natural Language |publisher=Broadview Press |isbn=978-1-77048-113-8 |url=https://books.google.com/books?id=79qb93CQE2AC&pg=PA14 |language=en |date=2002 }} * {{cite book |last1=Carlson |first1=Robert |title=A Concrete Introduction to Real Analysis |publisher=CRC Press |isbn=978-1-4987-7815-2 |language=en |date=2017 }} * {{cite book |last1=Cohen |first1=Elliot D. |title=Critical Thinking Unleashed |publisher=Rowman & Littlefield |isbn=978-0-7425-6432-9 |url=https://books.google.com/books?id=4aGIsKmkODgC&pg=PA254 |language=en |date=2009 }} * {{cite book |last1=Cook |first1=Roy T. |title=Dictionary of Philosophical Logic |publisher=Edinburgh University Press |isbn=978-0-7486-3197-1 |language=en |date=2009 }} * {{cite book |last1=Copi |first1=Irving |last2=Cohen |first2=Carl |last3=Flage |first3=Daniel |title=Essentials of Logic |publisher=Routledge |isbn=978-1-315-38900-4 |language=en |date=2016 }} * {{cite book |last1=Copi |first1=Irving M. |last2=Cohen |first2=Carl |last3=Rodych |first3=Victor |title=Introduction to Logic |date=2019 |publisher=Routledge |isbn=978-1-351-38697-5 |language=en }} * {{cite book |last1=Corcoran |first1=John |editor1-last=Martínez |editor1-first=Concha |editor2-last=Falguera |editor2-first=José L. |editor3-last=Sagüillo |editor3-first=José M. |title=Current Topics in Logic and Analytic Philosophy |publisher=Universidade de Santiago de Compostela |isbn=978-84-9750-811-7 |chapter-url=https://books.google.com/books?id=9IMEm4dYQXUC&pg=PA146 |language=en |chapter=Notes on the Founding of Logics and Metalogic: Aristotle, Boole, and Tarski |date=2007 |pages=143–176}} * {{cite book |last1=Dent |first1=David |title=The Nature of Scientific Innovation, Volume I: Processes, Means and Impact |publisher=Palgrave Macmillan |isbn=978-3-031-75212-4 |url=https://books.google.com/books?id=NbA0EQAAQBAJ&pg=PA36 |language=en |date=2024 }} *{{cite book |last1=Dowden |first1=Bradley H. |title=Logical Reasoning |date=2020 |url=https://www.csus.edu/indiv/d/dowdenb/4/logical-reasoning-archives/Logical-Reasoning-2020-05-15.pdf }} (for an earlier version, see: {{cite book |last1=Dowden |first1=Bradley Harris |title=Logical Reasoning |date=1993 |publisher=Wadsworth Publishing Company |isbn=978-0-534-17688-4 |language=en |ref=none }}) * {{cite web |last1=Egré |first1=Paul |last2=Rott |first2=Hans |title=The Logic of Conditionals |url=https://plato.stanford.edu/entries/logic-conditionals/ |website=The Stanford Encyclopedia of Philosophy |publisher=Metaphysics Research Lab, Stanford University |access-date=24 March 2025 |date=2021 }} * {{cite book |last1=Evans |first1=J. S. B. T. |editor1-last=Holyoak |editor1-first=Keith J. |editor2-last=Morrison |editor2-first=Robert G. |title=The Cambridge Handbook of Thinking and Reasoning |publisher=Cambridge University Press |isbn=978-0-521-82417-0 |language=en |chapter=Deductive Reasoning |date=2005 |pages=169–184}} * {{cite book |last1=Fetzer |first1=James H. |editor1-last=Paul |editor1-first=Ellen Frankel |editor2-last=Miller |editor2-first=Fred Dycus |editor3-last=Paul |editor3-first=Jeffrey |title=Scientific Innovation, Philosophy, and Public Policy: Volume 13, Part 2 |publisher=Cambridge University Press |isbn=978-0-521-58994-9 |chapter-url=https://books.google.com/books?id=JbNI3b-j0mkC&pg=PA241 |language=en |chapter=Computer Reliability and Public Policy: Limits of Knowledge of Computer-Based Systems |date=1996 |pages=229–266}} * {{cite book |last1=Fitting |first1=M. |last2=Mendelsohn |first2=Richard L. |title=First-Order Modal Logic |publisher=Springer Science & Business Media |isbn=978-94-011-5292-1 |url=https://books.google.com/books?id=5IxqCQAAQBAJ&pg=PA68 |language=en |date=2012 }} * {{cite web |last1=Garson |first1=James |title=Modal Logic |url=https://plato.stanford.edu/entries/logic-modal/ |website=The Stanford Encyclopedia of Philosophy |publisher=Metaphysics Research Lab, Stanford University |access-date=22 March 2025 |date=2024 }} * {{cite book |last1=Gensler |first1=Harry J. |title=Introduction to Logic |publisher=Routledge |isbn=978-1-136-99453-1 |url=https://books.google.com/books?id=jpteBwAAQBAJ&pg=PA362 |language=en |date=2012 }} * {{cite book |last1=Gossett |first1=Eric |title=Discrete Mathematics with Proof |publisher=John Wiley & Sons |isbn=978-0-470-45793-1 |url=https://books.google.com/books?id=NuFeW8N2hlkC&pg=PA50 |language=en |date=2009 }} * {{cite web |last1=Gottwald |first1=Siegfried |title=Many-Valued Logic |url=https://plato.stanford.edu/entries/logic-manyvalued/ |website=The Stanford Encyclopedia of Philosophy |publisher=Metaphysics Research Lab, Stanford University |access-date=24 March 2025 |date=2022 }} * {{cite book |last1=Grandy |first1=R. E. |title=Advanced Logic for Applications |publisher=D. Reidel Publishing Company |isbn=978-90-277-1034-5 |url=https://books.google.com/books?id=ItgJhsGE-RAC&pg=PA122 |language=en |date=1979 }} * {{cite web |last1=Groarke |first1=Louis F. |title=Aristotle: Logic |url=https://iep.utm.edu/aristotle-logic/ |website=Internet Encyclopedia of Philosophy |access-date=24 March 2025}} * {{cite book |last1=Haack |first1=Susan |author-link=Susan Haack |title=Philosophy of Logics |date=1978 |publisher=Cambridge University Press |chapter=1. 'Philosophy of Logics' |isbn=978-0-521-29329-7 |pages=1–10 }} * {{cite book |last1=Hintikka |first1=Jaakko |title=Inquiry as Inquiry: A Logic of Scientific Discovery |publisher=Springer Science & Business Media |isbn=978-94-015-9313-7 |url=https://books.google.com/books?id=rUDsCAAAQBAJ&pg=PA98 |language=en |date=2013 }} * {{cite web |last1=Hintikka |first1=Jaakko J. |author-link=Jaakko Hintikka |title=Philosophy of logic |url=https://www.britannica.com/topic/philosophy-of-logic |website=Encyclopædia Britannica |access-date=21 November 2021 |language=en |archive-date=28 April 2015 |archive-url=https://web.archive.org/web/20150428101732/http://www.britannica.com/EBchecked/topic/346240/philosophy-of-logic |url-status=live |date=2019 }} * {{cite book |last1=Hintikka |first1=Jaakko |last2=Sandu |first2=Gabriel |editor-last1=Jacquette |editor-first1=Dale |title=Philosophy of Logic |date=2006 |publisher=North Holland |chapter=What Is Logic? |isbn=978-0-444-51541-4 |pages=13–39}} * {{cite web |last1=Hintikka |first1=Jaakko J. |last2=Spade |first2=Paul Vincent |title=History of logic: Ancient, Medieval, Modern, & Contemporary Logic |url=https://www.britannica.com/topic/history-of-logic |website=Encyclopædia Britannica |access-date=30 March 2025 |language=en |date=2020 }} * {{cite book |last1=Hodel |first1=Richard E. |title=An Introduction to Mathematical Logic |publisher=Dover Publications |isbn=978-0-486-49785-3 |url=https://books.google.com/books?id=SxRYdzWio84C&pg=PA7 |language=en |date=2013 }} * {{cite book |last1=Hodges |first1=Wilfrid |editor-last1=Honderich |editor-first1=Ted |title=The Oxford Companion to Philosophy |date=2005 |publisher=Oxford University Press |chapter=Logic, Modern |isbn=978-0-19-926479-7 |pages=533–536}} * {{cite web |last1=Horsten |first1=Leon |title=Philosophy of Mathematics |url=https://plato.stanford.edu/entries/philosophy-mathematics/ |website=The Stanford Encyclopedia of Philosophy |publisher=Metaphysics Research Lab, Stanford University |access-date=28 March 2025 |date=2023 }} * {{cite book |last1=Hurley |first1=Patrick J. |title=Logic: The Essentials |publisher=Cengage Learning |isbn=978-1-4737-3630-6 |language=en |date=2016 }} * {{cite book |last1=Hurley |first1=Patrick J. |last2=Watson |first2=Lori |title=A Concise Introduction to Logic |publisher=Cengage Learning |isbn=978-1-305-95809-8 |edition=13 |date=2018 }} * {{cite book |last1=Jacquette |first1=Dale |editor-last1=Jacquette |editor-first1=Dale |title=Philosophy of Logic |date=2006 |publisher=North Holland |chapter=Introduction: Philosophy of Logic Today |isbn=978-0-444-51541-4 |pages=1–12}} * {{cite journal |last1=Johnson |first1=Ralph H. |title=The Relation Between Formal and Informal Logic |journal=Argumentation |year=1999 |volume=13 |issue=3 |pages=265–274 |doi=10.1023/A:1007789101256 |s2cid=141283158 }} * {{cite book |last1=Kirwan |first1=Christopher |chapter=Laws of Thought |editor1-last=Honderich |editor1-first=Ted |title=The Oxford Companion to Philosophy |date=2005 |publisher=Oxford University Press |isbn=978-0-19-926479-7 |page=507 }} * {{cite book |last1=Kleene |first1=S. C. |editor1-last=Beklemishev |editor1-first=Lev D. |title=The Foundations of Intuitionistic Mathematics |publisher=Elsevier |isbn=978-0-08-095759-3 |chapter-url=https://books.google.com/books?id=q-LG8Ep7WFcC&pg=PA81 |language=en |chapter=II. Various Notions of Realizability |date=2000 }} * {{cite web |last1=Klement |first1=Kevin C. |title=Propositional Logic |url=https://iep.utm.edu/propositional-logic-sentential-logic/ |website=Internet Encyclopedia of Philosophy |access-date=24 March 2025}} * {{cite book |last1=Linnebo |first1=Øystein |editor1-last=Horsten |editor1-first=Leon |editor2-last=Pettigrew |editor2-first=Richard |title=The Bloomsbury Companion to Philosophical Logic |publisher=Bloomsbury Publishing |isbn=978-1-4725-2829-2 |chapter-url=https://books.google.com/books?id=EKZOBAAAQBAJ&pg=PA123 |language=en |chapter=Higher-Order Logic |date=2014 |pages=105–127 }} * {{cite book |last1=Lowe |first1=E. J. |editor-last1=Honderich |editor-first1=Ted |title=The Oxford Companion to Philosophy |date=2005 |publisher=Oxford University Press |chapter=Philosophical Logic |isbn=978-0-19-926479-7 |pages=699–701}} * {{cite book |last1=Magnus |first1=P. D. |last2=Button |first2=Tim |title=forall x: Calgary: An Introduction to Formal |publisher=University of Calgary |isbn=979-8-5273-4950-4 |date=2021 }} * {{cite web |last1=McKeon |first1=Matthew |title=Logical Consequence |url=https://iep.utm.edu/logcon/ |website=Internet Encyclopedia of Philosophy |access-date=28 March 2025}} * {{cite book |last1=McKeon |first1=Matthew W. |title=The Concept of Logical Consequence: An Introduction to Philosophical Logic |publisher=Peter Lang |isbn=978-1-4331-0645-3 |language=en |date=2010 }} * {{cite book |last1=Metcalfe |first1=George |last2=Paoli |first2=Francesco |last3=Tsinakis |first3=Constantine |title=Residuated Structures in Algebra and Logic |publisher=American Mathematical Society |isbn=978-1-4704-6985-6 |url=https://books.google.com/books?id=CkPsEAAAQBAJ&pg=PA36 |language=en |date=2023 }} * {{cite web |last1=Moschovakis |first1=Joan |title=Intuitionistic Logic |url=https://plato.stanford.edu/entries/logic-intuitionistic/ |website=The Stanford Encyclopedia of Philosophy |publisher=Metaphysics Research Lab, Stanford University |access-date=23 March 2025 |date=2024 }} * {{cite book |last1=Nederpelt |first1=Rob |last2=Geuvers |first2=Herman |title=Type Theory and Formal Proof: An Introduction |publisher=Cambridge University Press |isbn=978-1-316-06108-4 |url=https://books.google.com/books?id=orsrBQAAQBAJ&pg=PA159 |language=en |date=2014 }} * {{cite book |last1=O'Regan |first1=Gerard |title=Concise Guide to Formal Methods: Theory, Fundamentals and Industry Applications |publisher=Springer |isbn=978-3-319-64021-1 |edition=1st 2017 |chapter=5. A Short History of Logic |date=2017 |pages=89–104}} * {{cite web |last1=Pelletier |first1=Francis Jeffry |last2=Hazen |first2=Allen |title=Natural Deduction Systems in Logic |url=https://plato.stanford.edu/entries/natural-deduction/ |website=The Stanford Encyclopedia of Philosophy |publisher=Metaphysics Research Lab, Stanford University |access-date=26 March 2025 |date=2024 }} * {{cite book |last1=Polkinghorne |first1=John |title=Meaning in Mathematics |publisher=Oxford University Press |isbn=978-0-19-960505-7 |url=https://books.google.com/books?id=AJV0P1pPBNoC&pg=PA65 |language=en |date=2011 }} * {{cite book |last1=Pollard |first1=Stephen |title=Philosophical Introduction to Set Theory |publisher=Courier Dover Publications |isbn=978-0-486-80582-5 |url=https://books.google.com/books?id=6cY-CgAAQBAJ&pg=PA98 |language=en |date=2015 }} * {{cite book |last1=Porta |first1=Marcela |last2=Maillet |first2=Katherine |last3=Mas |first3=Marta |last4=Martinez |first4=Carmen |editor1-last=Ao |editor1-first=Sio-Iong |editor2-last=Amouzegar |editor2-first=Mahyar |editor3-last=Rieger |editor3-first=Burghard B. |title=Intelligent Automation and Systems Engineering |publisher=Springer Science & Business Media |isbn=978-1-4614-0373-9 |chapter-url=https://books.google.com/books?id=NDMID6mWcZcC&pg=PA237 |language=en |chapter=Towards a Strategy to Fight the Computer Science Declining Phenomenon |date=2011 |pages=231–242}} * {{cite web |last1=Priest |first1=Graham |last2=Tanaka |first2=Koji |last3=Weber |first3=Zach |title=Paraconsistent Logic |url=https://plato.stanford.edu/entries/logic-paraconsistent/ |website=The Stanford Encyclopedia of Philosophy |publisher=Metaphysics Research Lab, Stanford University |access-date=24 March 2025 |date=2025 }} * {{cite web |last1=Rathjen |first1=Michael |last2=Sieg |first2=Wilfried |title=Proof Theory |url=https://plato.stanford.edu/entries/proof-theory/ |website=The Stanford Encyclopedia of Philosophy |publisher=Metaphysics Research Lab, Stanford University |access-date=26 March 2025 |date=2024 }} * {{cite book |last1=Reynolds |first1=John C. |title=Theories of Programming Languages |publisher=Cambridge University Press |isbn=978-1-139-93625-5 |url=https://books.google.com/books?id=X_ToAwAAQBAJ&pg=PA12 |language=en |date=1998 }} * {{cite book |last1=Schechter |first1=Joshua |editor-last1=Pashler |editor-first1=Harold |title=Encyclopedia of the Mind |publisher=Sage |isbn=978-1-4129-5057-2 |language=en |chapter=Deductive Reasoning |date=2013 |pages=226–230 }} * {{cite book |last1=Schlesinger |first1=I. M. |last2=Keren-Portnoy |first2=Tamar |last3=Parush |first3=Tamar |title=The Structure of Arguments |date=1 January 2001 |publisher=John Benjamins Publishing |isbn=978-90-272-2359-3 |language=en }} * {{cite book |last1=Shanker |first1=Stuart |editor1-last=Shanker |editor1-first=Stuart |title=Philosophy of Science, Logic and Mathematics in the Twentieth Century |publisher=Psychology Press |isbn=978-0-415-30881-6 |chapter-url=https://books.google.com/books?id=jIzT7AT3ILIC&pg=PA442 |language=en |chapter=Glossary |date=2003 }} * {{cite web |last1=Shapiro |first1=Stewart |last2=Kouri Kissel |first2=Teresa |title=Classical Logic |url=https://plato.stanford.edu/entries/logic-classical/ |website=The Stanford Encyclopedia of Philosophy |publisher=Metaphysics Research Lab, Stanford University |date=2024 }} * {{cite book |last1=Sider |first1=Theodore |title=Logic for Philosophy |publisher=Oxford University Press |isbn=978-0-19-957559-6 |language=en |date=2010 }} * {{cite web |last1=Smith |first1=Robin |title=Aristotle's Logic |url=https://plato.stanford.edu/entries/aristotle-logic/ |website=The Stanford Encyclopedia of Philosophy |publisher=Metaphysics Research Lab, Stanford University |access-date=24 March 2025 |date=2022 }} * {{cite book |last1=Smullyan |first1=Raymond M. |title=A Beginner's Guide to Mathematical Logic |publisher=Dover Publications |isbn=978-0-486-49237-7 |url=https://books.google.com/books?id=n6S-AwAAQBAJ&pg=PA102 |language=en |date=2014 }} * {{cite book |last1=Sørensen |first1=Morten Heine |last2=Urzyczyn |first2=Pawel |title=Lectures on the Curry-Howard Isomorphism |publisher=Elsevier |isbn=978-0-08-047892-0 |url=https://books.google.com/books?id=_mtnm-9KtbEC&pg=PA161 |language=en |date=2006 }} * {{cite book |last1=Tourlakis |first1=George |title=Mathematical Logic |publisher=John Wiley & Sons |isbn=978-1-118-03069-1 |url=https://books.google.com/books?id=8jAwgCTgnycC&pg=PA40 |language=en |date=2011 }} * {{cite book |last1=Tully |first1=Robert |editor-last1=Honderich |editor-first1=Ted |title=The Oxford Companion to Philosophy |date=2005 |publisher=Oxford University Press |chapter=Logic, Informal |isbn=978-0-19-926479-7 |pages=532–533}} * {{cite web |last1=Väänänen |first1=Jouko |title=Second-order and Higher-order Logic |url=https://plato.stanford.edu/entries/logic-higher-order/ |website=The Stanford Encyclopedia of Philosophy |publisher=Metaphysics Research Lab, Stanford University |access-date=23 March 2025 |date=2024 }} * {{cite book |last1=Walton |first1=Douglas |editor-last1=Craig |editor-first1=Edward |title=Routledge Encyclopedia of Philosophy |date=1996 |publisher=Routledge |chapter=Formal and Informal Logic |isbn=978-0-415-07310-3 |url=https://www.rep.routledge.com/articles/thematic/formal-and-informal-logic/v-1 |doi=10.4324/9780415249126-X014-1 }} * {{cite web |last1=Weber |first1=Zach |title=Paraconsistent Logic |url=https://iep.utm.edu/para-log/ |website=Internet Encyclopedia of Philosophy |access-date=23 March 2025}} * {{cite book |last1=Williamson |first1=Jon |last2=Russo |first2=Federica |title=Key Terms in Logic |publisher=Continuum |isbn=978-1-84706-114-0 |url=https://books.google.com/books?id=SmYu9-1HGtYC&pg=PA45 |language=en |date=2010 }} * {{cite web |last1=Zalta |first1=Edward N. |title=Gottlob Frege |url=https://plato.stanford.edu/entries/frege/ |website=The Stanford Encyclopedia of Philosophy |publisher=Metaphysics Research Lab, Stanford University |access-date=31 March 2025 |date=2024 }} {{refend}} {{Mathematical logic}} {{DEFAULTSORT:Rule Of Inference}} [[Category:Rules of inference| ]]
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