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
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/
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. http://links.jstor.org/sici?sici=1079-8986(200006)6:2<225:CLATT>2.0.CO;2-P
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
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
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
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
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
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/
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/
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
Phil 514: Math Logic II MATHEMATICAL logic II Spring 2006 Kevin C. Klement NBG), Quines New Foundations and related systems, Higherorder logic and type theory, and others, http://people.umass.edu/klement/514/
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/49/1/130-a
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
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
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
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
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
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
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/
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
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
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/
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
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
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
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
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
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
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
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
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
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
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
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
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.hu-berlin.de/lics/newsletters/14.html
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
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
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
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/
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
Jørgen 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/
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
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
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
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