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Abstract: The notion of Schematic System has been introduced by Parikh in the early seventies. It is a metamathematical notion describing the concept of deduction system and the operation of substitution of terms and formulas in it. We show a generalization of the Craig Interpolation Theorem for a natural class of schematic systems while we determine sufficient conditions for a schematic system to enjoy Interpolation. (Update)
Context of citations to this paper: More
...applicability of the operators. A detailed description leads to a technical development we will not consider here. The reader can refer to [4] where similar ideas are developed in the logical language of schematic systems. 20 A. Carbone This operation preserves the validity of a...
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BibTeX entry: (Update)
A. Carbone. The Craig Interpolation Theorem for Schematic Systems. To appear in Collegium Logicum -- Annals of the Kurt Godel Society, SpringerVerlag, vol. 2, 1996. http://citeseer.ist.psu.edu/carbone96craig.html More
@misc{ carbone96craig,
author = "A. Carbone",
title = "The Craig Interpolation Theorem for Schematic Systems",
text = "A. Carbone. The Craig Interpolation Theorem for Schematic Systems. To appear
in Collegium Logicum -- Annals of the Kurt Godel Society, SpringerVerlag,
vol. 2, 1996.",
year = "1996",
url = "citeseer.ist.psu.edu/carbone96craig.html" }
Citations (may not include all citations):242 Linear Logic (context) - Girard - 1987
116 Ideas and results in proof theory (context) - Prawitz - 1971
46 Resource Logics: Proof-theoretical Investigations (context) - Roorda - 1991
13 A new form of the Herbrand-Gentzen Theorem (context) - Craig - 1957
11 Annals of Pure and Applied Logic (context) - Buss, of - 1991
9 Studies in Logic (context) - Takeuti - 1987
7 Systematic construction of natural deduction systems for man.. - Baaz, Fermuller et al. - 1993
7 Some results on the length of proofs (context) - Parikh - 1973
6 A unification-theoretic method for investigating the k-prova.. (context) - Farmer - 1991
4 A survey of proof theory II (context) - Kreisel - 1971
2 To appear in Annals of Pure and Applied Logic (context) - Carbone, Cut et al. - 1995
1 Algebra of Proofs (context) - Szab'o - 1977
1 the number of steps in proofs (context) - Kraj'icek - 1989
1 On Logical Flow Graphs (context) - Carbone - 1993
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