Equivalential Interpolation

Abstract
By a consequence relation on a set L of formulas we understand a relation I — c p(L) x L satisfying the conditions called 'Overlap', 'Dilution', and 'Cut for Sets' at p.15 of [25]; we do not repeat the conditions here since we are simply fixing notation and the concept of a consequence relation is well known in any case. (The characterization in [25] amounts to that familiar from Tarski's work, except that there is no 'finitariness' restriction to the effect that when I I — A, for I c L, A c L, we must have I o I — A for some finite I o c I . The presence or absence of this condition makes no difference to anything that follows.) Each language L to be considered will be a sentential language whose formulas are built in the usual way by application of it-ary (primitive) connectives to it simpler formulas, starting with the simplest formulas — the propositional variables (or 'sentence letters') — not constructed with the aid of connectives. We assume, as usual, that there are countably many such variables, and they will be denoted by p, q, r, ... possibly with numerical subscripts. A consequence relation I- on such an L has the Unrestricted Interpolation Property when for any A, C c L with A I — C, there exists B c L with A I — B and B I — C, such that C is constructed only out of such propositional variables as occur both in A and in C. (Such a B is called an interpolant for A and C.) Note that we take the usual notational liberties here, writing "A I — C" (and the like) for "iAi I — C", "I, A I — C" to mean "I u iAi I — C", and "I — C" to mean "8 I — C". Further, we sometimes abbreviate the claim that A I — B and B I — C to "A I — B I — C", and when C is A itself, we always write this simply as "A — II— B"..
Keywords No keywords specified (fix it)
Categories (categorize this paper)
Options
 Save to my reading list
Follow the author(s)
My bibliography
Export citation
Find it on Scholar
Edit this record
Mark as duplicate
Revision history
Request removal from index
Translate to english
Download options
Our Archive


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 26,205
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
Coinductive Formulas and a Many-Sorted Interpolation Theorem.Ursula Gropp - 1988 - Journal of Symbolic Logic 53 (3):937-960.
Algebraic Aspects of Deduction Theorems.Janusz Czelakowski - 1985 - Studia Logica 44 (4):369 - 387.
Functional Dependencies, Supervenience, and Consequence Relations.I. L. Humberstone - 1993 - Journal of Logic, Language and Information 2 (4):309-336.
Logical Feedback.David Booth - 1991 - Studia Logica 50 (2):225 - 239.

Monthly downloads

Sorry, there are not enough data points to plot this chart.

Added to index

2010-12-22

Total downloads

1 ( #866,981 of 2,154,174 )

Recent downloads (6 months)

0

How can I increase my downloads?

My notes
Sign in to use this feature


Discussion
Order:
There  are no threads in this forum
Nothing in this forum yet.

Other forums