Computer Science – Logic in Computer Science
Scientific paper
2009-06-09
Computer Science
Logic in Computer Science
49 pages. Accepted for publication in special edition of Annals of Pure and Applied Logic on Computation in Classical Logic. v
Scientific paper
10.1016/j.apal.2010.04.005
A logic-enriched type theory (LTT) is a type theory extended with a primitive mechanism for forming and proving propositions. We construct two LTTs, named LTTO and LTTO*, which we claim correspond closely to the classical predicative systems of second order arithmetic ACAO and ACA. We justify this claim by translating each second-order system into the corresponding LTT, and proving that these translations are conservative. This is part of an ongoing research project to investigate how LTTs may be used to formalise different approaches to the foundations of mathematics. The two LTTs we construct are subsystems of the logic-enriched type theory LTTW, which is intended to formalise the classical predicative foundation presented by Herman Weyl in his monograph Das Kontinuum. The system ACAO has also been claimed to correspond to Weyl's foundation. By casting ACAO and ACA as LTTs, we are able to compare them with LTTW. It is a consequence of the work in this paper that LTTW is strictly stronger than ACAO. The conservativity proof makes use of a novel technique for proving one LTT conservative over another, involving defining an interpretation of the stronger system out of the expressions of the weaker. This technique should be applicable in a wide variety of different cases outside the present work.
Adams Robin
Luo Zhaohui
No associations
LandOfFree
Classical Predicative Logic-Enriched Type Theories does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Classical Predicative Logic-Enriched Type Theories, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Classical Predicative Logic-Enriched Type Theories will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-65132