David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
By a consequence relation on a set L of formulas we understand a relation I Ã¢â¬â c p(L) x L satisfying the conditions called 'Overlap', 'Dilution', and 'Cut for Sets' at p.15 of ; 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  amounts to that familiar from Tarski's work, except that there is no 'finitariness' restriction to the effect that when I I Ã¢â¬â A, for I c L, A c L, we must have I o I Ã¢â¬â 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 Ã¢â¬â the propositional variables (or 'sentence letters') Ã¢â¬â 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 Ã¢â¬â C, there exists B c L with A I Ã¢â¬â B and B I Ã¢â¬â 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 Ã¢â¬â C" (and the like) for "iAi I Ã¢â¬â C", "I, A I Ã¢â¬â C" to mean "I u iAi I Ã¢â¬â C", and "I Ã¢â¬â C" to mean "8 I Ã¢â¬â C". Further, we sometimes abbreviate the claim that A I Ã¢â¬â B and B I Ã¢â¬â C to "A I Ã¢â¬â B I Ã¢â¬â C", and when C is A itself, we always write this simply as "A Ã¢â¬â IIÃ¢â¬â B"..
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
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.
Citations of this work BETA
No citations found.
Similar books and articles
Lloyd Humberstone, The Consequence Relation of Tautological Entailment is Maximally Relevant: Answering a Question of Graham Priest.
Andrew M. Pitts (1992). On an Interpretation of Second Order Quantification in First Order Intuitionistic Propositional Logic. Journal of Symbolic Logic 57 (1):33-52.
Ursula Gropp (1988). Coinductive Formulas and a Many-Sorted Interpolation Theorem. Journal of Symbolic Logic 53 (3):937-960.
Beata Konikowska (1990). A Two-Valued Logic for Reasoning About Different Types of Consequence in Kleene's Three-Valued Logic. Studia Logica 49 (4):541 - 555.
Małgorzata Porębska (1986). Interpolation and Amalgamation Properties in Varieties of Equivalential Algebras. Studia Logica 45 (1):35 - 38.
Lloyd Humberstone (2006). Identical Twins, Deduction Theorems, and Pattern Functions: Exploring the Implicative BCsK Fragment of S. [REVIEW] Journal of Philosophical Logic 35 (5):435 - 487.
Lloyd Humberstone (2007). Identical Twins, Deduction Theorems, and Pattern Functions: Exploring the Implicative BCsK Fragment of S. [REVIEW] Journal of Philosophical Logic 36 (5):435 - 487.
Janusz Czelakowski (1985). Algebraic Aspects of Deduction Theorems. Studia Logica 44 (4):369 - 387.
Katarzyna Slomczyńska (2005). Free Spectra of Linear Equivalential Algebras. Journal of Symbolic Logic 70 (4):1341 - 1358.
I. L. Humberstone (1993). Functional Dependencies, Supervenience, and Consequence Relations. Journal of Logic, Language and Information 2 (4):309-336.
Jan Krajíček (1997). Interpolation Theorems, Lower Bounds for Proof Systems, and Independence Results for Bounded Arithmetic. Journal of Symbolic Logic 62 (2):457-486.
Eva Hoogland & Maarten Marx (2002). Interpolation and Definability in Guarded Fragments. Studia Logica 70 (3):373 - 409.
David Booth (1991). Logical Feedback. Studia Logica 50 (2):225 - 239.
Robin Hirsch, Ian Hodkinson & Roger D. Maddux (2002). Relation Algebra Reducts of Cylindric Algebras and an Application to Proof Theory. Journal of Symbolic Logic 67 (1):197-213.
Sorry, there are not enough data points to plot this chart.
Added to index2010-12-22
Total downloads1 ( #505,694 of 1,679,364 )
Recent downloads (6 months)0
How can I increase my downloads?