Journal of Symbolic Logic 63 (3):869-890 (1998)

Abstract
Illative combinatory logic consists of the theory of combinators or lambda calculus extended by extra constants (and corresponding axioms and rules) intended to capture inference. In a preceding paper, [2], we considered 4 systems of illative combinatory logic that are sound for first order intuitionistic propositional and predicate logic. The interpretation from ordinary logic into the illative systems can be done in two ways: following the propositions-as-types paradigm, in which derivations become combinators, or in a more direct way, in which derivations are not translated. Both translations are closely related in a canonical way. In the cited paper we proved completeness of the two direct translations. In the present paper we prove that also the two indirect translations are complete. These proofs are direct whereas in another version, [3], we proved completeness by showing that the two corresponding illative systems are conservative over the two systems for the direct translations. Moreover we shall prove that one of the systems is also complete for predicate calculus with higher type functions
Keywords No keywords specified (fix it)
Categories (categorize this paper)
DOI 10.2307/2586717
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

PhilArchive copy


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 71,259
Through your library

References found in this work BETA

Typed Lambda Calculi. S. Abramsky Et AL.H. P. Barendregt - 1992 - In S. Abramsky, D. Gabbay & T. Maibaurn (eds.), Handbook of Logic in Computer Science. Oxford University Press. pp. 117--309.

Add more references

Citations of this work BETA

Typed Lambda Calculus.Henk P. Barendregt, Wil Dekkers & Richard Statman - 1977 - In Jon Barwise & H. Jerome Keisler (eds.), Handbook of Mathematical Logic. North-Holland Pub. Co.. pp. 1091--1132.

Add more citations

Similar books and articles

Analytics

Added to PP index
2009-01-28

Total views
44 ( #259,100 of 2,518,487 )

Recent downloads (6 months)
1 ( #408,186 of 2,518,487 )

How can I increase my downloads?

Downloads

My notes