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Intuitionistic logic
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==References== {{refbegin}} *{{cite conference |last1=Alechina |first1=Natasha |last2=Mendler |first2=Michael |last3=De Paiva |first3=Valeria |author3-link=Valeria de Paiva |last4=Ritter |first4=Eike |date=January 2003 |title=Categorical and Kripke Semantics for Constructive S4 Modal Logic |url=http://www.cs.nott.ac.uk/~nza/papers/Alechina++:01a.pdf |series=[[Lecture Notes in Computer Science]] |conference=Proceedings of the 15th International Workshop on Computer Science Logic |doi=10.1007/3-540-44802-0_21 }} *{{cite journal |last=Aoyama |first=Hiroshi |year=2004 |title= LK, LJ, Dual Intuitionistic Logic, and Quantum Logic |journal=[[Notre Dame Journal of Formal Logic]] |volume=45 |issue= 4 |pages= 193–213 |doi=10.1305/ndjfl/1099238445 |doi-access=free }} *{{cite web |url=http://www.cs.le.ac.uk/people/nb118/Publications/ESSLLI'05.pdf |title=Intuitionistic Logic |last1= Bezhanishvili |first1= Nick |last2= De Jongh |first2= Dick |at=[[University of Amsterdam]] (Institute for Logic, Language and Computation) }} *{{Cite journal |last1= Brunner |first1= A.B.M. |author1-link= |last2= Carnielli |first2= Walter |author2-link= Walter Carnielli |doi= 10.1016/j.jal.2004.07.016 |title= Anti-intuitionism and paraconsistency |journal= Journal of Applied Logic |volume= 3 |issue= 1 |date= March 2005 |pages= 161–184 |doi-access= free }} *{{cite web |last=Burgess |first=John |date=January 2014 |title=Intuitions of Three Kinds in Gödel's Views on the Continuum |url=https://www.princeton.edu/~jburgess/Goedel.pdf |doi=10.1017/CBO9780511756306.002 |doi-broken-date=1 November 2024 <!-- This line generates a script warning. --> }} *{{cite book |last1= Chagrov |first1= Alexander |last2= Zakharyaschev |first2= Michael |year=1997 |title=Modal Logic |volume=35 |series=Oxford Logic Guides |publisher=[[Oxford University Press]] |pages=XV, 605 |isbn=0-19-853779-4 }} *{{cite journal |last1 = Constable |first1 = R. |last2 = Bickford |first2 = M. |year = 2014 |title = Intuitionistic completeness of first-order logic |journal = Annals of Pure and Applied Logic |volume = 165 |pages = 164–198 |doi = 10.1016/j.apal.2013.07.009 |arxiv=1110.1614 |s2cid = 849930 }} *{{Cite book |last = Van Dalen |first = Dirk |author-link = Dirk van Dalen |chapter= Intuitionistic Logic |year = 2001 |title = The Blackwell Guide to Philosophical Logic |pages = 224–257 |editor-last= Goble |editor-first= Lou |publisher = [[Wiley-Blackwell|Blackwell Publishing]] |location = New York |isbn = 9780631206934 |doi = 10.1002/9781405164801.ch11 }} *{{cite book |last=Van Heijenoort |first=Jean |title=From Frege to Gödel: A Source Book in Mathematical Logic, 1879–1931 |publisher=[[Harvard University Press]] |year=2002 |orig-year=1967 |edition=reprinted with corrections |isbn=9780674324497 |oclc=749638436 }} *{{Cite book |last= Heyting |first= Arend |author-link= Arend Heyting |year= 1930 |language= de |title= Die formalen Regeln der intuitionistischen Logik I, II, III |series= Sitzungsberichte der preussischen Akademie der Wissenschaften |pages= 42–56, 57–71, 158–169 |quote= In three parts }} *{{cite book |last=Japaridze |first=Giorgi |author-link=Giorgi Japaridze |date=January 2009 |chapter=In the Beginning was Game Semantics? |chapter-url=https://link.springer.com/chapter/10.1007%2F978-1-4020-9374-6_11 |title=Games: Unifying Logic, Language and Philosophy |volume=15 |url=https://www.springer.com/book/9781402093739 |editor1-last=Majer |editor1-first=O. |editor2-last=Pietarinen |editor2-first=A.-V. |editor3-last=Tulenheimo |editor3-first=T. |publisher=[[Springer Publishing|Springer]] |pages=249–350 |doi=10.1007/978-1-4020-9374-6_11 |arxiv=cs/0507045 |isbn=978-1-4020-9373-9 }} *{{Cite book |last= Kripke |first= Saul A. |author-link= Saul Kripke |date= 1965 |chapter= Semantical analysis of intuitionistic logic I |series= Studies in Logic and the Foundations of Mathematics |title= Formal Systems and Recursive Functions. Proceedings of the Eighth Logic Colloquium Oxford, July 1963 |chapter-url= https://www.princeton.edu/~hhalvors/restricted/kripke_intuitionism.pdf |pages= 92–130 |doi= 10.1016/S0049-237X(08)71685-9 |publisher= [[Elsevier|North-Holland Publishing Company]] |location= Amsterdam |editor1-last= Crossley |editor1-first= J.N. |editor2-last= Dummett |editor2-first= M.A.E. |volume=40 |isbn= 9780444534057 }} *{{Citation |last=Lévy |first=Michel |date=29 April 2011 |title=Logique modale propositionnelle S4 et logique intuitioniste propositionnelle |url=http://teachinglogic.liglab.fr/INT1/S4Lint.pdf |language=fr }} *{{cite book |last1=Rasiowa |first1=Helena |last2=Sikorski |first2=Roman |year=1963 |title=The Mathematics of Metamathematics |publisher=Państwowe Wydawn. Naukowe |location=Warsaw |series=Monografie matematyczne |pages=519 }} *{{cite journal |last=Shehtman |first=Valentin |date=1990 |title=Modal counterparts of Medvedev logic of finite problems are not finitely axiomatizable |url=https://link.springer.com/article/10.1007/BF00370370 |doi=10.1007/BF00370370 |journal=[[Studia Logica]] |volume=49 |issue=3 |pages=365–385 }} *{{Cite book |last1= Sørensen |first1= Morten H. |last2= Urzyczyn |first2= Paweł |date= 2006 |title= Lectures on the Curry-Howard Isomorphism |chapter= chapter 2: Intuitionistic Logic |series= Studies in Logic and the Foundations of Mathematics |edition= 1 |isbn= 978-0-444-52077-7 |publisher= [[Elsevier]] |location= Amsterdam |volume=149 }} *{{cite book |last=Takeuti |first=Gaisi |author-link=Gaisi Takeuti |title=Proof theory |edition=Second |publisher=Dover Publications |location=Mineola, New York |year=2013 |orig-year=1975 |url=https://books.google.com/books?id=Idl6K-W69NYC |isbn=978-0-486-49073-1 }} *{{cite journal |last=Tarski |first=Alfred |date=1938 |title=Der Aussagenkalkül und die Topologie |url=http://matwbn.icm.edu.pl/tresc.php?wyd=1&tom=31 |doi=10.1007/BF00370370 |journal=[[Fundamenta Mathematicae]] |volume=31 |pages=103–134 }} * {{cite web |last1=Troelstra |first1=A.S. |last2=Van Ulsen |first2= P. |title=The discovery of E.W. Beth's semantics for intuitionistic logic |url=https://festschriften.illc.uva.nl/j50/contribs/troelstra/troelstra.pdf |publisher=Institute for Logic, Language and Computation (ILLC) |at=Universiteit van Amsterdam }} {{refend}}
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