The existence of matrices strongly adequate for e, R and their fragments

Studia Logica 38 (1):75 - 85 (1979)
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Abstract

A logic is a pair (P,Q) where P is a set of formulas of a fixed propositional language and Q is a set of rules. A formula is deducible from X in the logic (P, Q) if it is deducible from XP via Q. A matrix is strongly adequate to (P, Q) if for any , X, is deducible from X iff for every valuation in , is designated whenever all the formulas in X are. It is proved in the present paper that if Q = {modus ponens, adjunction } and P {E, R, E +, R +, E I, R I } then there exists a matrix strongly adequate to (P, Q).

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10.1007/bf00493673

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original Tokarz, Marek (1978) "The existence of matrices strongly adequate for E, R and their fragments". Bulletin of the Section of Logic 7(3):121-125

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Citations of this work

Fragments of R-Mingle.W. J. Blok & J. G. Raftery - 2004 - Studia Logica 78 (1-2):59-106.
On matrices characteristic of relevant logics.Wies law Dziobiak - 1981 - Bulletin of the Section of Logic 10 (3):113-114.

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References found in this work

The pure calculus of entailment.Alan Ross Anderson & Nuel D. Belnap - 1962 - Journal of Symbolic Logic 27 (1):19-52.
Completeness of relevant quantification theories.Robert K. Meyer, J. Michael Dunn & Hugues Leblanc - 1974 - Notre Dame Journal of Formal Logic 15 (1):97-121.

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