The american plan completed: Alternative classical-style semantics, without stars, for relevant and paraconsistent logics

Studia Logica 43 (1-2):131 - 158 (1984)
Abstract
American-plan semantics with 4 values 1, 0, { {1, 0}} {{}}, interpretable as True, False, Both and Neither, are furnished for a range of logics, including relevant affixing systems. The evaluation rules for extensional connectives take a classical form: in particular, those for negation assume the form 1 (A, a) iff 0 (A, a) and 0 (A, a) iff 1 (A, a), so eliminating the star function *, on which much criticism of relevant logic semantics has focussed. The cost of these classical features is a further relation (or operation), required in evaluating falsity assignments of implication formulae.Two styles of 4 valued relational semantics are developed; firstly a semantics using notions of double truth and double validity for basic relevant systemB and some extensions of it; and secondly, since the first semantics makes heavy weather of validating negation principles such as Contraposition, a reduced semantics using more complex implicational rules for relevant systemC and various of its extensions. To deal satisfactorily with elite systemsR,E andT, however, further complication is inevitable; and a relation of mateship (suggested by the Australian plan) is introduced to permit cross-over from 1 to 0 values and vice versa.
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DOI 10.1007/BF00935746
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References found in this work BETA
A Useful Four-Valued Logic.N. D. Belnap - 1977 - In J. M. Dunn & G. Epstein (eds.), Modern Uses of Multiple-Valued Logic. D. Reidel.
The Semantics of Entailment—II.Richard Routley & Robert K. Meyer - 1972 - Journal of Philosophical Logic 1 (1):53 - 73.
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Citations of this work BETA
“Four-Valued” Semantics for the Relevant Logic R.Edwin D. Mares - 2004 - Journal of Philosophical Logic 33 (3):327-341.
On Permutation in Simplified Semantics.Greg Restall & Tony Roy - 2009 - Journal of Philosophical Logic 38 (3):333 - 341.
Richard (Routley) Sylvan: Writings on Logic and Metaphysics.Dominic Hyde - 2001 - History and Philosophy of Logic 22 (4):181-205.

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