Home  Mathematical_Logic  Higherorder Logic And Type Theory 
Page 1 160 of 60 1 
1. Peter B. Andrews Research is in mathematical logic, especially Higherorder logic (type theory) and automated theorem proving. It is directed toward enabling computers to http://gtps.math.cmu.edu/andrews.html  

2. Logic Higher Order Higherorder logic and intuitistic type theory overlaps in many ways. The textbook (Nordstrom, Petersson, Smith, 1990) is a good source for intuitistic http://www.lix.polytechnique.fr/Labo/Dale.Miller/papers/AIencyclopedia/  

3. JSTOR Categorical Logic And Type Theory The following chapters cover the basic semantics of simple type theory, equational logic, and firstorder and Higherorder predicate logic. http://links.jstor.org/sici?sici=10798986(200006)6:2<225:CLATT>2.0.CO;2P 
4. Chad E Brown: Materials Chad E Brown Automated Reasoning in Higherorder logic Set Comprehension and Extensionality in Church s type theory College Publications. http://mathgate.info/cebrown/papers.php  

5. Type Theory And Higher Order Logic?  Object Mix This is maybe OT but I wonder if anyone can interpret this sentence from Wikipedia s article Secondorder logic In mathematical logic, http://objectmix.com/functional/168234typetheoryhigherorderlogic.html 
6. Type Theory, Set Theory And Domain Theory The logic of Nuprl is a constructive type theory, but its types include . This theory can be generalized to Intuitionistic Higherorder logic, say IHOL. http://www.cs.cornell.edu/Info/Projects/NuPrl/Intro/TypeSetDomain/typesetd.html  

7. Higherorder Semantics And Extensionality Peter B. andrews Resolution in type theory, Journal of Symbolic logic, vol. . Gopalan Nadathur and Dale Miller Higherorder logic programming, http://projecteuclid.org/handle/euclid.jsl/1102022211  

8. OCC  Open Calculus Of Constructions To close the gap between these two different paradigms of equational logic and Higherorder type theory we are currently investigating the open calculus of http://formal.cs.uiuc.edu/stehr/occ.html  

9. Linear Type Theories, Semantics And Action Calculi We show that the logic and typetheory DILL arise as a Higherorder instance of our general framework. We then define the Higherorder extension of any http://www.lfcs.inf.ed.ac.uk/reports/97/ECSLFCS97371/  

10. Type Theory And Term Rewriting, Sept 1996 I shall outline the future I forsee for the type theory and term rewriting group at . Inductive types in Higherorder logic and type theory Christine http://www.macs.hw.ac.uk/~fairouz/school1996/  

11. TPHOLs 2001 List Of Presentations Nested General Recursion and Partiality in type theory Ana Bove and Mechanizing in Higherorder logic Proofs of Correctness and Completeness for a Set http://www.dcs.gla.ac.uk/TPHOLs2001/presentations.htm  

12. Phil 514: Math Logic II MATHEMATICAL logic II Spring 2006 Kevin C. Klement NBG), QuineÂs ÂNew FoundationsÂ and related systems, Higherorder logic and type theory, and others, http://people.umass.edu/klement/514/  

13. The Computer Journal  Sign In Page The underlying type theory of Coq is called the Calculus of Inductive Constructions, essentially a typed lambda calculus extended with a Higherorder logic. http://comjnl.oxfordjournals.org/cgi/content/full/49/1/130a  

14. Handbook Of Automated Reasoning  Elsevier Contents Part V. Higherorder logic and logical frameworks. Chapter 15. Classical type theory (Peter B. andrews). 1. Introduction to type theory. http://www.elsevier.biz/wps/find/bookvolume.cws_home/622118/vol2  

15. RAIRO  Theoretical Informatics And Applications (RAIRO: ITA) E. GimÃ©nez, Structural recursive definitions in type theory, in Automata, B. Pientka, Termination and reduction checking for Higherorder logic programs http://www.rairoita.org/articles/ita/ref/2004/04/ita0428NS/ita0428NS.html  

16. Mechanized Reasoning Systems NUPRL is a proof system for an intuitionistic type theory based on Martin TPS is a theorem proving system for first and Higherorder logic with both http://www.calculemus.org/MathUniversalis/3/listsoft.html  

17. Citations Of The Clausal Theory Of Types Chapter 3 Higherorder logic. Peter B. andrews. Classical type theory, in Alan Robinson and andrei Voronkov, Eds., Handbook of Automated Reasoning, http://web.aanet.com.au/dwolfram/CTTcites.html  

18. Higherorder Logic  Wikipedia, The Free Encyclopedia Another way in which Higherorder logic differs from firstorder logic is in the constructions allowed in the underlying type theory. http://en.wikipedia.org/wiki/Higherorder_logic  

19. Categorical Logic And Type Theory  Elsevier Dependent predicate logic, categorically. Polymorphic dependent type theory. Strong and very strong sum and equality. Full higher order dependent type http://www.elsevier.com/wps/product/cws_home/601539  

20. Church's Type Theory (Stanford Encyclopedia Of Philosophy) Tarski (1923) noted that in the context of Higherorder logic, one can define .. of elementary type theory is analogous to firstorder logic in certain http://plato.stanford.edu/entries/typetheorychurch/  

21. Paperback Announcement: Categorical Logic And Type Theory Prospectus Introduction to fibred category theory Simple type theory Equational logic First order predicate logic Higher order predicate logic The effective http://pvs.csl.sri.com/mailarchive/pvs/msg00521.html  

22. Workshop On LambdaCalculus, Type Theory, And Natural Language, 2005 This page describes the second workshop on Lambda Calculus, type theory ``Hyperintensional Semantics in A Higherorder logic with Definable Subtypes http://lcttnl.foxearth.org/  

23. Classical Type Theory 58 Gerard Pierre Huet, Constrained resolution a complete method for Higherorder logic., 1972. 59 HUET G. P. 1973a, A Mechanization of type theory, http://portal.acm.org/citation.cfm?id=778524 
24. HOG Pollard, Carl (2005) Hyperintensional semantics in a higher order logic with grammar with a type theory based on Lambek and Scott s higher order http://www.ling.ohiostate.edu/~hana/hog/  

25. The Choice Of A Foundational System Simple type theory (higher order or \omegaorder logic) is a direct descendant of Russell s type theory, as simplified by chwistek, ramseyfm and http://www.rbjones.com/rbjpub/logic/jrh0111.htm  

26. Edinburgh Research Archive : Item 1842/1203 In this thesis we study them in the context of dependent type theory. them are the firstorder Nominal logic, the Higherorder logic FMHOL, the theory http://hdl.handle.net/1842/1203  

27. Combining HOL With Isabelle Some time may be spent investigating alternative logics for formal reasoning, such as set theory. The type system of Higherorder logic catches many errors, http://www.cl.cam.ac.uk/~lp15/Grants/holisa.html  

28. Introduction To HigherOrder Categorical Logic  Cambridge Part II demonstrates that another formulation of Higherorder logic, (intuitionistic) type theories, is closely related to topos theory. http://www.cambridge.org/us/catalogue/catalogue.asp?isbn=0521356539 
29. Logic Matters: Negative Type Theory But while the idea of a negative type theory is a formally natural one Â and Are we entitled to draw from this the conclusion that higher order or http://logicmatters.blogspot.com/2007/08/negativetypetheory.html  

30. FLoC 2006  IJCAR A stable proposal for extending TPTP3 to include Higherorder logic is presented. logic  in our case a sequent calculus for classical type theory http://www.easychair.org/FLoC06/IJCARday229.html  

31. Herman Geuvers  Research Page The Calculus of Constructions and Higher Order logic, in The CurryHoward isomorphism, ed. The connection between type theory and logic, notably via the http://www.cs.ru.nl/~herman/research.html  

32. Summer School And Workshop On Proof Theory, Computation And Complexity Semantics and Cutelimination for Church s (Intuitionistic) theory of Types, with Applications to Higherorder logic Programming http://www.ki.inf.tudresden.de/~guglielm/WPT2/  

33. An Intensional Type Theory: Motivation And CutElimination  Lambda The Ultimate An Intensional type theory Motivation and CutElimination, Paul C. Gilmore. By the theory TT is meant the higher order predicate logic with the following http://lambdatheultimate.org/node/2137  

34. Publications Coercive subtyping in type theory. Proc. of CSL 96, the 1996 Annual Conference of conservativity of calculus of constructions over Higherorder logic. http://www.dur.ac.uk/CARG/publications.html  

35. IngentaConnect TPS: A TheoremProving System For Classical Type Theory Keywords Higherorder logic; type theory; mating; connection; expansion proof; Document type Regular paper. Affiliations 1 Mathematics Department, http://www.ingentaconnect.com/content/klu/jars/1996/00000016/00000003/00081315  

36. AARNEWS  June 2003 The last three chapters of the book provide an introduction to type theory (Higherorder logic). The author shows how various mathematical concepts can be http://www.mcs.anl.gov/AAR/issuejune03/index.html  

37. Publications By Z. Luo Weyl s predicative classical mathematics as a logicenriched type theory. adequacy conservativity of calculus of constructions over Higherorder logic. http://www.cs.rhul.ac.uk/~zhaohui/type.html  

38. FOM: Questions On Higherorder Logic FOM Questions on Higherorder logic 3) Is the set of validities for 3rdorderlogic or for type theory stronger under Turing reducibility than the http://cs.nyu.edu/pipermail/fom/2000September/004275.html  

39. LICS Newsletter 14 Proof theory of type systems, logic and type systems, typed lambda calculi as models of (higher order) computation, semantics of type systems, http://www2.informatik.huberlin.de/lics/newsletters/14.html  

40. TeamParsifal: A proof theory for generic judgments, in ACM Trans. on Computational logic, October 2005 . The type system of a Higherorder logic programming language, http://ralyx.inria.fr/2006/Raweb/parsifal/bibliography.html  

41. Powell's Books  Cambridge Tracts In Theoretical Computer Science #42: Basic Sim type theory is one of the most important tools in the design of higherlevel Computational Learning theory An Introduction Higher Order logic and http://www.powells.com/biblio?isbn=9780521054225 
42. Publications Implementing a Program logic of Objects in a Higherorder logic Theorem Prover . It is shown that extensional MartinLÃ¶f type theory is a conservative http://www.tcs.informatik.unimuenchen.de/~mhofmann/homepage/publications.html  

43. Computer Science Logic  Mathematical Logic And Formal Languages Journals, Books Computer Science logic Foundations of Computing. Higherorder logic, nonmonotonic reasoning, as well as logics and type systems for biology. http://www.springer.com/3540454586?referer=www.springeronline.com 
44. J Roger Hindley : Research These two systems were invented in the 1920s by mathematicians for use in Higherorder logic, and came to be applied in programming theory from the 1970s http://wwwmaths.swan.ac.uk/staff/jrh/JRHresearch.html  

45. Type Theory Simply typed lambda calculus; Church s higher order logic; Isabelle; Lambda calculus with A permodel of dependent type theory (Pierre Hyvernat) http://www.cs.chalmers.se/~peterd/kurser/tt03/  

46. Practical Foundations Of Mathematics In higher order logic, predicates (or, by comprehension, subsets) are first The type of propositions Even though set theory can be presented in a first http://www.cs.man.ac.uk/~pt/Practical_Foundations/html/s28.html  

47. JÃ¸rgen Villadsen Supralogic Using Transfinite type theory with type Variables for A Paraconsistent Higher Order logic. Springer Lecture Notes in Computer Science http://www2.imm.dtu.dk/~jv/  

48. Course Information Dependent type theory II lambdaP Higher Order logic lambdaHOL (a type theory for Higher Order logic) Extensions to lambdaHOL the Lambda Cube http://www.math.uu.nl/people/jvoosten/mc20062007/logic/courses.html  

49. DBLP: Thierry Coquand 30, Thierry Coquand Program Construction in Intuitionistic type theory (Abstract). Thomas Ehrhard An Equational Presentation of Higher Order logic. http://www.informatik.unitrier.de/~ley/db/indices/atree/c/Coquand:Thierry.html  

50. DBLP: Frank Pfenning 26 Gopalan Nadathur, Frank Pfenning The type System of a Higherorder logic Programming Language. types in logic Programming 1992 245283 http://www.sigmod.org/dblp/db/indices/atree/p/Pfenning:Frank.html  

51. New Foundations Home Page There is a theorem prover Watson whose higher order logic is an untyped Richard Kaye has worked on the theory KF which is a subtheory of both NF and http://math.boisestate.edu/~holmes/holmes/nf.html  

Page 1 160 of 60 1 