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 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 http://projecteuclid.org/euclid.jsl/1183745571
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: 71,410
External links

Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library

References found in this work BETA

No references found.

Add more references

Citations of this work BETA

No citations found.

Add more citations

Similar books and articles

Conjunction Without Conditions in Illative Combinatory Logic.M. Bunder - 1984 - Bulletin of the Section of Logic 13 (4):207-213.
The Church-Rosser Property in Symmetric Combinatory Logic.Katalin Bimbó - 2005 - Journal of Symbolic Logic 70 (2):536 - 556.
The Semantic Completeness of a Global Intuitionistic Logic.Hiroshi Aoyama - 1998 - Mathematical Logic Quarterly 44 (2):167-175.
Illative Combinatory Logic Without Equality as a Primitive Predicate.M. W. Bunder - 1982 - Notre Dame Journal of Formal Logic 23 (1):62-70.
Some Results on Combinators in the System TRC.Thomas Jech - 1999 - Journal of Symbolic Logic 64 (4):1811-1819.
Reverse Mathematics and Completeness Theorems for Intuitionistic Logic.Takeshi Yamazaki - 2001 - Notre Dame Journal of Formal Logic 42 (3):143-148.

Analytics

Added to PP index
2017-02-21

Total views
3 ( #1,362,995 of 2,519,866 )

Recent downloads (6 months)
1 ( #406,012 of 2,519,866 )

How can I increase my downloads?

Downloads

My notes