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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 Higher-order predicate logic.

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/168234-type-theory-higher-order-logic.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. Higher-order 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 Higher-order instance of our general framework. We then define the Higher-order extension of any
http://www.lfcs.inf.ed.ac.uk/reports/97/ECS-LFCS-97-371/

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), Quines New Foundations and related systems, Higherorder logic and type theory, and others,
http://people.umass.edu/klement/514/

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/49/1/130-a

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. Giménez, Structural recursive definitions in type theory, in Automata, B. Pientka, Termination and reduction checking for Higherorder logic programs
http://www.rairo-ita.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 Higher-order 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. Higher-order Logic - Wikipedia, The Free Encyclopedia
Another way in which Higherorder logic differs from first-order logic is in the constructions allowed in the underlying type theory.
http://en.wikipedia.org/wiki/Higher-order_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 first-order logic in certain
http://plato.stanford.edu/entries/type-theory-church/

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/mail-archive/pvs/msg00521.html

22. Workshop On Lambda-Calculus, 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.ohio-state.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, ramsey-fm 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 Higher-order logic FM-HOL, 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 Higher-Order 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  and Are we entitled to draw from this the conclusion that higher order or
http://logicmatters.blogspot.com/2007/08/negative-type-theory.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/FLoC-06/IJCAR-day229.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 Higher-order logic Programming
http://www.ki.inf.tu-dresden.de/~guglielm/WPT2/

33. An Intensional Type Theory: Motivation And Cut-Elimination | 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://lambda-the-ultimate.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 Theorem-Proving 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 Higher-order logic.
http://www.cs.rhul.ac.uk/~zhaohui/type.html

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

Proof theory of type systems, logic and type systems, typed lambda calculi as models of (higher order) computation, semantics of type systems,

40. Team-Parsifal:
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 Martin-Löf type theory is a conservative
http://www.tcs.informatik.uni-muenchen.de/~mhofmann/homepage/publications.html

43. Computer Science Logic - Mathematical Logic And Formal Languages Journals, Books
Computer Science logic Foundations of Computing. Higher-order logic, nonmonotonic reasoning, as well as logics and type systems for biology.
http://www.springer.com/3-540-45458-6?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://www-maths.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

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 lambda-HOL (a type theory for Higher Order logic) Extensions to lambda-HOL the Lambda Cube
http://www.math.uu.nl/people/jvoosten/mc2006-2007/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.uni-trier.de/~ley/db/indices/a-tree/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 245-283
http://www.sigmod.org/dblp/db/indices/a-tree/p/Pfenning:Frank.html