How to prove higher order theorems in first order logic

Authors:
Manfred Kerber
Affiliations:
Fachbereich Informatik, Universitat Kaiserslautern, Kaiserslautern, Germany
Venue:
IJCAI'91 Proceedings of the 12th international joint conference on Artificial intelligence - Volume 1
Year:
1991

Citing 2
Cited 2

An introduction to mathematical logic and type theory: to truth through proof

An introduction to mathematical logic and type theory: to truth through proof
The TPS theorem proving system

CADE-10 Proceedings of the tenth international conference on Automated deduction

A Hoare Logic for Call-by-Value Functional Programs

MPC '08 Proceedings of the 9th international conference on Mathematics of Program Construction
Hybrid contract checking via symbolic simplification

PEPM '12 Proceedings of the ACM SIGPLAN 2012 workshop on Partial evaluation and program manipulation

Quantified Score

Hi-index	0.00

Visualization

Abstract

In this paper we are interested in using a first order theorem prover to prove theorems that are formulated in some higher order logic. To this end we present translations of higher order logics into first order logic with flat sorts and equality and give a sufficient criterion for the soundness of these translations. In addition translations are introduced that are sound and complete with respect to L. Henkin's general model semantics. Our higher order logics are based on a restricted type structure in the sense of A. Church, they have typed function symbols and predicate symbols, but no sorts.