Converse Ackermann croperty and semiclassical negation

Studia Logica 47 (2):159 - 168 (1988)
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Abstract

A prepositional logic S has the Converse Ackermann Property (CAP) if (AB)C is unprovable in S when C does not contain . In A Routley-Meyer semantics for Converse Ackermann Property (Journal of Philosophical Logic, 16 (1987), pp. 65–76) I showed how to derive positive logical systems with the CAP. There I conjectured that each of these positive systems were compatible with a so-called semiclassical negation. In the present paper I prove that this conjecture was right. Relational Routley-Meyer type semantics are provided for each one of the resulting systems (the positive systems plus the semiclassical negation).

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10.1007/bf00370290

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José M. Méndez
Universidad de Salamanca

Citations of this work

Two versions of minimal intuitionism with the CAP. A note.Gemma Robles & José Méndez - 2010 - Theoria: Revista de Teoría, Historia y Fundamentos de la Ciencia 20 (2):183-190.

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References found in this work

Relevant Logics and Their Rivals.Richard Routley, Val Plumwood, Robert K. Meyer & Ross T. Brady - 1982 - Ridgeview. Edited by Richard Sylvan & Ross Brady.
Entailment: The Logic of Relevance and Neccessity, Vol. I.Alan Ross Anderson & Nuel D. Belnap - 1975 - Princeton, N.J.: Princeton University Press. Edited by Nuel D. Belnap & J. Michael Dunn.
Semantics for relevant logics.Alasdair Urquhart - 1972 - Journal of Symbolic Logic 37 (1):159-169.
On conserving positive logics.Robert K. Meyer - 1973 - Notre Dame Journal of Formal Logic 14 (2):224-236.
Begründung einer strengen Implikation.Wilhelm Ackermann - 1956 - Journal of Symbolic Logic 21 (2):113-128.

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